Fundamentals of Physics 7th Edition_ Tes

Fundamentals of Physics 7th Edition_ Tes
Chapter 1:
MEASUREMENT
1. The SI standard of time is based on:
A. the daily rotation of the earth
B. the frequency of light emitted by Kr86
C. the yearly revolution of the earth about the sun
D. a precision pendulum clock
E. none of these
Ans: E
2. A nanosecond is:
A. 109 s
B. 10−9 s
C. 10−10 s
D. 10−10 s
E. 10−12
Ans: B
3. The SI standard of length is based on:
A. the distance from the north pole to the equator along a meridian passing through Paris
B. wavelength of light emitted by Hg198
C. wavelength of light emitted by Kr86
D. a precision meter stick in Paris
E. the speed of light
Ans: E
4. In 1866, the U. S. Congress defined the U. S. yard as exactly 3600/3937 international meter.
This was done primarily because:
A. length can be measured more accurately in meters than in yards
B. the meter is more stable than the yard
C. this definition relates the common U. S. length units to a more widely used system
D. there are more wavelengths in a yard than in a meter
E. the members of this Congress were exceptionally intelligent
Ans: C
5. Which of the following is closest to a yard in length?
A. 0.01 m
B. 0.1 m
C. 1 m
D. 100 m
E. 1000 m
Ans: C
Chapter 1:
MEASUREMENT
1
6. There is no SI base unit for area because:
A. an area has no thickness; hence no physical standard can be built
B. we live in a three (not a two) dimensional world
C. it is impossible to express square feet in terms of meters
D. area can be expressed in terms of square meters
E. area is not an important physical quantity
Ans: D
7. The SI base unit for mass is:
A. gram
B. pound
C. kilogram
D. ounce
E. kilopound
Ans: C
8. A gram is:
A. 10−6 kg
B. 10−3 kg
C. 1 kg
D. 103 kg
E. 106 kg
Ans: B
9. Which of the following weighs about a pound?
A. 0.05 kg
B. 0.5 kg
C. 5 kg
D. 50 kg
E. 500 kg
Ans: D
10. (5.0 × 104 ) × (3.0 × 106 ) =
A. 1.5 × 109
B. 1.5 × 1010
C. 1.5 × 1011
D. 1.5 × 1012
E. 1.5 × 1013
Ans: C
11. (5.0 × 104 ) × (3.0 × 10−6 ) =
A. 1.5 × 10−3
B. 1.5 × 10−1
C. 1.5 × 101
D. 1.5 × 103
E. 1.5 × 105
Ans: B
2
Chapter 1:
MEASUREMENT
12. 5.0 × 105 + 3.0 × 106 =
A. 8.0 × 105
B. 8.0 × 106
C. 5.3 × 105
D. 3.5 × 105
E. 3.5 × 106
Ans: E
13. (7.0 × 106 )/(2.0 × 10−6 ) =
A. 3.5 × 10−12
B. 3.5 × 10−6
C. 3.5
D. 3.5 × 106
E. 3.5 × 1012
Ans: E
14. The number of significant figures in 0.00150 is:
A. 2
B. 3
C. 4
D. 5
E. 6
Ans: B
15. The number of significant figures in 15.0 is:
A. 1
B. 2
C. 3
D. 4
E. 5
Ans: C
16. 3.2 × 2.7 =
A. 9
B. 8
C. 8.6
D. 8.64
E. 8.640
Ans: C
Chapter 1:
MEASUREMENT
3
17. 1.513 + 27.3 =
A. 29
B. 28.8
C. 28.9
D. 28.81
E. 28.813
( )Ans: B
18. 1 mi is equivalent to 1609 m so 55 mph is:
A. 15 m/s
B. 25 m/s
C. 66 m/s
D. 88 m/s
E. 1500 m/s
Ans: B
19. A sphere with a radius of 1.7 cm has a volume of:
A. 2.1 × 10−5 m3
B. 9.1 × 10−4 m3
C. 3.6 × 10−3 m3
D. 0.11 m3
E. 21 m3
Ans: A
20. A sphere with a radius of 1.7 cm has a surface area of:
A. 2.1 × 10−5 m2
B. 9.1 × 10−4 m2
C. 3.6 × 10−3 m2
D. 0.11 m2
E. 36 m2
Ans: C
21. A right circular cylinder with a radius of 2.3 cm and a height of 1.4 m has a volume of:
A. 0.20 m3
B. 0.14 m3
C. 9.3 × 10−3 m3
D. 2.3 × 10−3 m3
E. 7.4 × 10−4 m3
Ans: D
22. A right circular cylinder with a radius of 2.3 cm and a height of 1.4 cm has a total surface area
of:
A. 1.7 × 10−3 m2
B. 3.2 × 10−3 m2
C. 2.0 × 10−3 m3
D. 5.3 × 10−3 m2
E. 7.4 × 10−3 m2
Ans: D
4
Chapter 1:
MEASUREMENT
23. A cubic box with an edge of exactly 1 cm has a volume of:
A. 10−9 m3
B. 10−6 m3
C. 10−3 m3
D. 103 m3
E. 106 m3
Ans: B
24. A square with an edge of exactly 1 cm has an area of:
A. 10−6 m2
B. 10−4 m2
C. 102 m2
D. 104 m2
E. 106 m2
Ans: B
25. 1 m is equivalent to 3.281 ft. A cube with an edge of 1.5 ft has a volume of:
A. 1.2 × 102 m3
B. 9.6 × 10−2 m3
C. 10.5 m3
D. 9.5 × 10−2 m3
E. 0.21 m3
Ans: B
26. During a short interval of time the speed v in m/s of an automobile is given by v = at2 + bt3 ,
where the time t is in seconds. The units of a and b are respectively:
A. m · s2 ; m · s4
B. s3 /m; s4 /m
C. m/s2 ; m/s3
3
4
D. m/s ; m/s
4
5
E. m/s ; m/s
Ans: D
27. Suppose A = BC, where A has the dimension L/M and C has the dimension L/T. Then B
has the dimension:
A. T/M
B. L2 /TM
C. TM/L2
D. L2 T/M
E. M/L2 T
Ans: A
Chapter 1:
MEASUREMENT
5
28. Suppose A = B n C m , where A has dimensions LT, B has dimensions L 2 T−1 , and C has
dimensions LT2 . Then the exponents n and m have the values:
A. 2/3; 1/3
B. 2; 3
C. 4/5; −1/5
D. 1/5; 3/5
E. 1/2; 1/2
Ans: D
6
Chapter 1:
MEASUREMENT
Chapter 2:
MOTION ALONG A STRAIGHT LINE
1. A particle moves along the x axis from xi to xf . Of the following values of the initial and final
coordinates, which results in the displacement with the largest magnitude?
A. xi = 4 m, xf = 6 m
B. xi = −4 m, xf = −8 m
C. xi = −4 m, xf = 2 m
D. xi = 4 m, xf = −2 m
E. xi = −4 m, xf = 4 m
ans: E
2. A particle moves along the x axis from xi to xf . Of the following values of the initial and final
coordinates, which results in a negative displacement?
A. xi = 4 m, xf = 6 m
B. xi = −4 m, xf = −8 m
C. xi = −4 m, xf = 2 m
D. xi = −4 m, xf = −2 m
E. xi = −4 m, xf = 4 m
ans: B
3. The average speed of a moving object during a given interval of time is always:
A. the magnitude of its average velocity over the interval
B. the distance covered during the time interval divided by the time interval
C. one-half its speed at the end of the interval
D. its acceleration multiplied by the time interval
E. one-half its acceleration multiplied by the time interval.
ans: B
4. Two automobiles are 150 kilometers apart and traveling toward each other. One automobile
is moving at 60 km/h and the other is moving at 40 km/h mph. In how many hours will they
meet?
A. 2.5
B. 2.0
C. 1.75
D. 1.5
E. 1.25
ans: D
5. A car travels 40 kilometers at an average speed of 80 km/h and then travels 40 kilometers at
an average speed of 40 km/h. The average speed of the car for this 80-km trip is:
A. 40 km/h
B. 45 km/h
C. 48 km/h
D. 53 km/h
E. 80 km/h
ans: D
Chapter 2:
MOTION ALONG A STRAIGHT LINE
7
6. A car starts from Hither, goes 50 km in a straight line to Yon, immediately turns around,
and returns to Hither. The time for this round trip is 2 hours. The magnitude of the average
velocity of the car for this round trip is:
A. 0
B. 50 km/hr
C. 100 km/hr
D. 200 km/hr
E. cannot be calculated without knowing the acceleration
ans: A
7. A car starts from Hither, goes 50 km in a straight line to Yon, immediately turns around, and
returns to Hither. The time for this round trip is 2 hours. The average speed of the car for
this round trip is:
A. 0
B. 50 km/h
C. 100 km/h
D. 200 km/h
E. cannot be calculated without knowing the acceleration
ans: B
8. The coordinate of a particle in meters is given by x(t) = 16t − 3.0t3 , where the time t is in
seconds. The particle is momentarily at rest at t =
A. 0.75 s
B. 1.3 s
C. 5.3 s
D. 7.3 s
E. 9.3 s
ans: B
9. A drag racing car starts from rest at t = 0 and moves along a straight line with velocity given
by v = bt2 , where b is a constant. The expression for the distance traveled by this car from its
position at t = 0 is:
A. bt3
B. bt3 /3
C. 4bt2
D. 3bt2
E. bt3/2
ans: B
10. A ball rolls up a slope. At the end of three seconds its velocity is 20 cm/s; at the end of eight
seconds its velocity is 0. What is the average acceleration from the third to the eighth second?
A. 2.5 cm/s2
2
B. 4.0 cm/s
2
C. 5.0 cm/s
2
D. 6.0 cm/s
2
E. 6.67 cm/s
ans: B
8
Chapter 2:
MOTION ALONG A STRAIGHT LINE
11. The coordinate of an object is given as a function of time by x = 7t − 3t2 , where x is in meters
and t is in seconds. Its average velocity over the interval from t = 0 to t = 4 s is:
A. 5 m/s
B. −5 m/s
C. 11 m/s
D. −11 m/s
E. −14.5 m/s
ans: B
12. The velocity of an object is given as a function of time by v = 4t − 3t2 , where v is in m/s and
t is in seconds. Its average velocity over the interval from t = 0 to t = 2 s:
A. is 0
B. is −2 m/s
C. is 2 m/s
D. is −4 m/s
E. cannot be calculated unless the initial position is given
ans: A
13. The coordinate of an object is given as a function of time by x = 4t2 − 3t3 , where x is in meters
and t is in seconds. Its average acceleration over the interval from t = 0 to t = 2 s is:
2
A. −4 m/s
2
B. 4 m/s
2
C. −10 m/s
2
D. 10 m/s
2
E. −13 m/s
ans: C
14. Each of four particles move along an x axis. Their coordinates (in meters) as functions of time
(in seconds) are given by
particle 1: x(t) = 3.5 − 2.7t3
particle 2: x(t) = 3.5 + 2.7t3
particle 3: x(t) = 3.5 + 2.7t2
particle 4: x(t) = 3.5 − 3.4t − 2.7t2
Which of these particles have constant acceleration?
A. All four
B. Only 1 and 2
C. Only 2 and 3
D. Only 3 and 4
E. None of them
ans: D
Chapter 2:
MOTION ALONG A STRAIGHT LINE
9
15. Each of four particles move along an x axis. Their coordinates (in meters) as functions of time
(in seconds) are given by
particle 1: x(t) = 3.5 − 2.7t3
particle 2: x(t) = 3.5 + 2.7t3
particle 3: x(t) = 3.5 + 2.7t2
particle 4: x(t) = 3.5 − 3.4t − 2.7t2
Which of these particles is speeding up for t > 0?
A. All four
B. Only 1
C. Only 2 and 3
D. Only 2, 3, and 4
E. None of them
ans: A
16. An object starts from rest at the origin and moves along the x axis with a constant acceleration
of 4 m/s2 . Its average velocity as it goes from x = 2 m to x = 8 m is:
A. 1 m/s
B. 2 m/s
C. 3 m/s
D. 5 m/s
E. 6 m/s
ans: E
17. Of
A.
B.
C.
D.
E.
the following situations, which one is impossible?
A body having velocity east and acceleration east
A body having velocity east and acceleration west
A body having zero velocity and non-zero acceleration
A body having constant acceleration and variable velocity
A body having constant velocity and variable acceleration
ans: E
18. Throughout a time interval, while the speed of a particle increases as it moves along the x axis,
its velocity and acceleration might be:
A. positive and negative, respectively
B. negative and positive, respectively
C. negative and negative, respectively
D. negative and zero, respectively
E. positive and zero, respectively
ans: C
19. A particle moves on the x axis. When its acceleration is positive and increasing:
A. its velocity must be positive
B. its velocity must be negative
C. it must be slowing down
D. it must be speeding up
E. none of the above must be true
ans: E
10
Chapter 2:
MOTION ALONG A STRAIGHT LINE
20. The position y of a particle moving along the y axis depends on the time t according to the
equation y = at − bt2 . The dimensions of the quantities a and b are respectively:
A. L2 /T, L3 /T2
B. L/T2 , L2 /T
C. L/T, L/T2
D. L3 /T, T2 /L
E. none of these
ans: C
21. A particle moves along the x axis according to the equation x = 6t2 , where x is in meters and
t is in seconds. Therefore:
A. the acceleration of the particle is 6 m/s2
B. t cannot be negative
C. the particle follows a parabolic path
D. each second the velocity of the particle changes by 9.8 m/s
E. none of the above
ans: E
22. Over a short interval near time t = 0 the coordinate of an automobile in meters is given by
x(t) = 27t − 4.0t3 , where t is in seconds. At the end of 1.0 s the acceleration of the auto is:
A. 27 m/s2
B. 4.0 m/s2
C. −4.0 m/s2
D. −12 m/s2
E. −24 m/s2
ans: E
23. Over a short interval, starting at time t = 0, the coordinate of an automobile in meters is given
by x(t) = 27t − 4.0t3 , where t is in seconds. The magnitudes of the initial (at t = 0) velocity
and acceleration of the auto respectively are:
A. 0; 12 m/s2
B. 0; 24 m/s2
C. 27 m/s; 0
D. 27 m/s; 12 m/s2
E. 27 m/s; 24 m/s2
ans: C
24. At time t = 0 a car has a velocity of 16 m/s. It slows down with an acceleration given by
−0.50t, in m/s2 for t in seconds. It stops at t =
A. 64 s
B. 32 s
C. 16 s
D. 8.0 s
E. 4.0 s
ans: D
Chapter 2:
MOTION ALONG A STRAIGHT LINE
11
25. At time t = 0 a car has a velocity of 16 m/s. It slows down with an acceleration given by
−0.50t, in m/s2 for t in seconds. At the end of 4.0 s it has traveled:
A. 0
B. 12 m
C. 14 m
D. 25 m
E. 59 m
ans: E
26. At time t = 0 a car has a velocity of 16 m/s. It slows down with an acceleration given by
−0.50t, in m/s2 for t in seconds. By the time it stops it has traveled:
A. 15 m
B. 31 m
C. 62 m
D. 85 m
E. 100 m
ans: D
27. Starting at time t = 0, an object moves along a straight line with velocity in m/s given by
v(t) = 98 − 2t2 , where t is in seconds. When it momentarily stops its acceleration is:
A. 0
B. −4.0 m/s2
C. −9.8 m/s2
D. −28 m/s2
E. 49 m/s2
ans: D
28. Starting at time t = 0, an object moves along a straight line. Its coordinate in meters is given
by x(t) = 75t − 1.0t3 , where t is in seconds. When it momentarily stops its acceleration is:
A. 0
B. −73 m/s2
C. −30 m/s2
D. −9.8 m/s2
E. 9.2 × 103 m/s2
ans: C
29. A car, initially at rest, travels 20 m in 4 s along a straight line with constant acceleration. The
acceleration of the car is:
A. 0.4 m/s2
2
B. 1.3 m/s
2
C. 2.5 m/s
D. 4.9 m/s2
E. 9.8 m/s2
ans: C
12
Chapter 2:
MOTION ALONG A STRAIGHT LINE
30. A racing car traveling with constant acceleration increases its speed from 10 m/s to 50 m/s over
a distance of 60 m. How long does this take?
A. 2.0 s
B. 4.0 s
C. 5.0 s
D. 8.0 s
E. The time cannot be calculated since the speed is not constant
ans: B
31. A car starts from rest and goes down a slope with a constant acceleration of 5 m/s2 . After
5 s the car reaches the bottom of the hill. Its speed at the bottom of the hill, in meters per
second, is:
A. 1
B. 12.5
C. 25
D. 50
E. 160
ans: C
32. A car moving with an initial velocity of 25 m/s north has a constant acceleration of 3 m/s2
south. After 6 seconds its velocity will be:
A. 7 m/s north
B. 7 m/s south
C. 43 m/s north
D. 20 m/s north
E. 20 m/s south
ans: A
33. An object with an initial velocity of 12 m/s west experiences a constant acceleration of 4 m/s2
west for 3 seconds. During this time the object travels a distance of:
A. 12 m
B. 24 m
C. 36 m
D. 54 m
E. 144 m
ans: D
34. How far does a car travel in 6 s if its initial velocity is 2 m/s and its acceleration is 2 m/s2 in
the forward direction?
A. 12 m
B. 14 m
C. 24 m
D. 36 m
E. 48 m
ans: E
Chapter 2:
MOTION ALONG A STRAIGHT LINE
13
35. At a stop light, a truck traveling at 15 m/s passes a car as it starts from rest. The truck travels
at constant velocity and the car accelerates at 3 m/s2 . How much time does the car take to
catch up to the truck?
A. 5 s
B. 10 s
C. 15 s
D. 20 s
E. 25 s
ans: B
36. A ball is in free fall. Its acceleration is:
A. downward during both ascent and descent
B. downward during ascent and upward during descent
C. upward during ascent and downward during descent
D. upward during both ascent and descent
E. downward at all times except at the very top, when it is zero
ans: A
37. A ball is in free fall. Upward is taken to be the positive direction. The displacement of the ball
during a short time interval is:
A. positive during both ascent and descent
B. negative during both ascent and descent
C. negative during ascent and positive during descent
D. positive during ascent and negative during descent
E. none of the above
ans: D
38. A baseball is thrown vertically into the air. The acceleration of the ball at its highest point is:
A. zero
B. g, down
C. g, up
D. 2g, down
E. 2g, up
ans: B
39. Which one of the following statements is correct for an object released from rest?
A. The average velocity during the first second of time is 4.9 m/s
B. During each second the object falls 9.8 m
C. The acceleration changes by 9.8 m/s2 every second
D. The object falls 9.8 m during the first second of time
E. The acceleration of the object is proportional to its weight
ans: A
14
Chapter 2:
MOTION ALONG A STRAIGHT LINE
40. A freely falling body has a constant acceleration of 9.8 m/s2 . This means that:
A. the body falls 9.8 m during each second
B. the body falls 9.8 m during the first second only
C. the speed of the body increases by 9.8 m/s during each second
D. the acceleration of the body increases by 9.8 m/s2 during each second
E. the acceleration of the body decreases by 9.8 m/s2 during each second
ans: C
41. An
A.
B.
C.
D.
E.
object is shot vertically upward. While it is rising:
its velocity and acceleration are both upward
its velocity is upward and its acceleration is downward
its velocity and acceleration are both downward
its velocity is downward and its acceleration is upward
its velocity and acceleration are both decreasing
ans: B
42. An object is thrown straight up from ground level with a speed of 50 m/s. If g = 10 m/s2 its
distance above ground level 1.0 s later is:
A. 40 m
B. 45 m
C. 50 m
D. 55 m
E. 60 m
ans: B
43. An object is thrown straight up from ground level with a speed of 50 m/s. If g = 10 m/s2 its
distance above ground level 6.0 s later is:
A. 0.00 m
B. 270 m
C. 330 m
D. 480 m
E. none of these
ans: E
44. At a location where g = 9.80 m/s2 , an object is thrown vertically down with an initial speed
of 1.00 m/s. After 5.00 s the object will have traveled:
A. 125 m
B. 127.5 m
C. 245 m
D. 250 m
E. 255 m
ans: B
Chapter 2:
MOTION ALONG A STRAIGHT LINE
15
45. An object is thrown vertically upward at 35 m/s. Taking g = 10 m/s2 , the velocity of the
object 5 s later is:
A. 7.0 m/s up
B. 15 m/s down
C. 15 m/s up
D. 85 m/s down
E. 85 m/s up
ans: B
46. A feather, initially at rest, is released in a vacuum 12 m above the surface of the earth. Which
of the following statements is correct?
A. The maximum velocity of the feather is 9.8 m/s
B. The acceleration of the feather decreases until terminal velocity is reached
C. The acceleration of the feather remains constant during the fall
D. The acceleration of the feather increases during the fall
E. The acceleration of the feather is zero
ans: C
47. An
A.
B.
C.
D.
E.
object is released from rest. How far does it fall during the second second of its fall?
4.9 m
9.8 m
15 m
20 m
25 m
ans: C
48. A heavy ball falls freely, starting from rest. Between the third and fourth second of time it
travels a distance of:
A. 4.9 m
B. 9.8 m
C. 29.4 m
D. 34.3 m
E. 39.8 m
ans: D
49. As a rocket is accelerating vertically upward at 9.8 m/s2 near Earth’s surface, it releases a
projectile. Immediately after release the acceleration (in m/s2 ) of the projectile is:
A. 9.8 down
B. 0
C. 9.8 up
D. 19.6 up
E. none of the above
ans: A
16
Chapter 2:
MOTION ALONG A STRAIGHT LINE
50. A stone is released from a balloon that is descending at a constant speed of 10 m/s. Neglecting
air resistance, after 20 s the speed of the stone is:
A. 2160 m/s
B. 1760 m/s
C. 206 m/s
D. 196 m/s
E. 186 m/s
ans: C
51. An object dropped from the window of a tall building hits the ground in 12.0 s. If its acceleration
is 9.80 m/s2 , the height of the window above the ground is:
A. 29.4 m
B. 58.8 m
C. 118 m
D. 353 m
E. 706 m
ans: E
52. Neglecting the effect of air resistance a stone dropped off a 175-m high building lands on the
ground in:
A. 3 s
B. 4 s
C. 6 s
D. 18 s
E. 36 s
ans: C
53. A stone is thrown vertically upward with an initial speed of 19.5 m/s. It will rise to a maximum
height of:
A. 4.9 m
B. 9.8 m
C. 19.4 m
D. 38.8 m
E. none of these
ans: C
54. A baseball is hit straight up and is caught by the catcher 2.0 s later. The maximum height of
the ball during this interval is:
A. 4.9 m
B. 7.4 m
C. 9.8 m
D. 12.6 m
E. 19.6 m
ans: A
Chapter 2:
MOTION ALONG A STRAIGHT LINE
17
55. An object is thrown straight down with an initial speed of 4 m/s from a window which is 8 m
above the ground. The time it takes the object to reach the ground is:
A. 0.80 s
B. 0.93 s
C. 1.3 s
D. 1.7 s
E. 2.0 s
ans: B
56. A stone is released from rest from the edge of a building roof 190 m above the ground. Neglecting air resistance, the speed of the stone, just before striking the ground, is:
A. 43 m/s
B. 61 m/s
C. 120 m/s
D. 190 m/s
E. 1400 m/s
ans: B
57. An object is thrown vertically upward with a certain initial velocity in a world where the
that to which
acceleration due to gravity is 19.6 m/s2 . The height to which it rises is
the object would rise if thrown upward with the same initial velocity on the Earth. Neglect
friction.
A. √
half
2 times
B.
C. twice
D. four times
E. cannot be calculated from the given data
ans: A
58. A projectile is shot vertically upward with a given initial velocity. It reaches a maximum height
of 100 m. If, on a second shot, the initial velocity is doubled then the projectile will reach a
maximum height of:
A. 70.7 m
B. 141.4 m
C. 200 m
D. 241 m
E. 400 m
ans: E
59. One object is thrown vertically upward with an initial velocity of 100 m/s and another object
with an initial velocity of 10 m/s. The maximum height reached by the first object will be
that of the other.
A. 10 times
B. 100 times
C. 1000 times
D. 10, 000 times
E. none of these
ans: B
18
Chapter 2:
MOTION ALONG A STRAIGHT LINE
60. The area under a velocity-time graph represents:
A. acceleration
B. change in acceleration
C. speed
D. change in velocity
E. displacement
ans: E
61. Displacement can be obtained from:
A. the slope of an acceleration-time graph
B. the slope of a velocity-time graph
C. the area under an acceleration-time graph
D. the area under a velocity-time graph
E. the slope of an acceleration-time graph
ans: D
62. An object has a constant acceleration of 3 m/s2 . The coordinate versus time graph for this
object has a slope:
A. that increases with time
B. that is constant
C. that decreases with time
D. of 3 m/s
E. of 3 m/s2
ans: A
63. The coordinate-time graph of an object is a straight line with a positive slope. The object has:
A. constant displacement
B. steadily increasing acceleration
C. steadily decreasing acceleration
D. constant velocity
E. steadily increasing velocity
ans: D
Chapter 2:
MOTION ALONG A STRAIGHT LINE
19
64. Which of the following five coordinate versus time graphs represents the motion of an object
moving with a constant nonzero speed?
x
..
..
.
...
...
.
.
..
....
.
.
.
.
.
.........
x
t
.....
.....
.....
.....
.....
.....
.....
...
A
x
...........................................
t
t
B
x
............
.....
.
.
.
...
...
.
.
..
..
.
.
C
x
...
..
..
..
..
..
.
t
D
t
E
ans: B
65. Which of the following five acceleration versus time graphs is correct for an object moving in
a straight line at a constant velocity of 20 m/s?
a
a
...........................................
t
...
....
.
.
...
.....
.
.
.
.
....
.....
.
.
..
A
a
t
B
a
...
....
.
.
.
...
.....
.
.
.
.
...
.....
.
.
.
.
...
C
a
t
...........................................
D
ans: E
20
Chapter 2:
..
..
.
..
...
.
.
..
....
.
.
.
.
.
..........
MOTION ALONG A STRAIGHT LINE
E
t
t
66. Which of the following five coordinate versus time graphs represents the motion of an object
whose speed is increasing?
x
..
..
.
...
...
.
.
..
....
.
.
.
.
.
.........
x
t
.....
.....
.....
.....
.....
.....
.....
...
A
x
t
...
...
...
...
....
....
......
.........
....
B
x
.......
.......
.
.
.
.
....
...
.
.
..
..
.
..
t
C
x
...
.....
.
.
.
...
.....
.
.
.
.
....
.....
.
.
...
t
t
D
E
ans: A
67. A car accelerates from rest on a straight road. A short time later, the car decelerates to a stop
and then returns to its original position in a similar manner, by speeding up and then slowing
to a stop. Which of the following five coordinate versus time graphs best describes the motion?
x
...
... .....
.
.
... ....
...
...
.
... ......
... ....
....
x
t
....
...... .....
.
.
.
.
.
...
......
...
......
.
A
x .......
.. ...
... ....
...
.
... ..
... ..
... ...
...
t
B
x ........
....
....
...
...
...
....
.....
......
C
x
t
D
t
.....
... .....
.
............... ..............
t
E
ans: E
Chapter 2:
MOTION ALONG A STRAIGHT LINE
21
68. The acceleration of an object, starting from rest, is shown in the graph below. Other than at
t = 0, when is the velocity of the object equal to zero?
a(m/s2 )
5
....................................
...
...
...
...
.
.
.
.
...
..
.
.
.
.
.
.
.
.
.
.
.
.
.
...
.
..
...
.
.
.
... 4
....
...
..
.
...5
1
2
3 .....
.
...
...
... ....
... ...
... ...
....
−5
A.
B.
C.
D.
E.
t(s)
During the interval from 1.0 s to 3.0 s
At t = 3.5 s
At t = 4.0 s
At t = 5.0 s
At no other time less than or equal to 5 s
ans: E
69. An elevator is moving upward with constant acceleration. The dashed curve shows the position
y of the ceiling of the elevator as a function of the time t. At the instant indicated by the dot,
a bolt breaks loose and drops from the ceiling. Which curve best represents the position of the
bolt as a function of time?
y
..... A
......
.
.
.
.
.
..
. ...
... ..................................
........
. ........
...
.
..
.
..
......
...
...
.B
...
.
.
.
.
.
.
.
.
.
..
.
.
.
.
.
.......................
. .......
.
.
.
.
.... .
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
...........
... ........
....
.
........
C
...
.....
.
.
.
.
......
.
..........
...
......
.
.
.
.
.
.
.
............... D
.....
.. E
...
.. ...
....... .....
.
...
.......
.
...
.
ans: B
22
Chapter 2:
MOTION ALONG A STRAIGHT LINE
t
70. The diagram shows a velocity-time graph for a car moving in a straight line. At point Q the
car must be:
v
P
............................................
.
.
.
.
.
.
.
.......
.....
......
.....
.
.
.....
.
.
.
.
.....
.
..
.
....
.
.
.
....
..
...
..
Q ..
A.
B.
C.
D.
E.
t
moving with zero acceleration
traveling downhill
traveling below ground-level
reducing speed
traveling in the reverse direction to that at point P
ans: E
71. The diagram shows a velocity-time graph for a car moving in a straight line. At point P the
car must be:
v
.....................................
..............
.
.
.
.
.
.
.
.
.
P ........
........
.
.
.
.
.
.....
......
.
.
.
.
.
...
.....
.....
A.
B.
C.
D.
E.
t
moving with zero acceleration
climbing the hill
accelerating
stationary
moving at about 45◦ with respect to the x axis
ans: C
Chapter 2:
MOTION ALONG A STRAIGHT LINE
23
72. The graph represents the straight line motion of a car. How far does the car travel between
t = 2 s and t = 5 s?
v(m/s)
12
...................................................
.....
..
.....
.
.
.....
.
.
.....
.
.....
..
6
.
.....
.
.....
..
.
.....
.
.....
.
..
..
2
5
9
A.
B.
C.
D.
E.
t(s)
4m
12 m
24 m
36 m
60 m
ans: D
73. The diagram represents the straight line motion of a car. Which of the following statements is
true?
v(m/s)
12
....................................................
.....
..
.....
.
.
.....
.
.....
.
.....
6 ...
.....
.
.....
.
..
.....
.
.....
.
.
.
2
5
9
A.
B.
C.
D.
E.
24
The
The
The
The
The
ans:
car
car
car
car
car
B
accelerates, stops, and reverses
accelerates at 6 m/s2 for the first 2 s
is moving for a total time of 12 s
decelerates at 12 m/s2 for the last 4 s
returns to its starting point when t = 9 s
Chapter 2:
MOTION ALONG A STRAIGHT LINE
t(s)
74. Consider the following five graphs (note the axes carefully). Which of these represents motion
at constant speed?
x
...
.....
.
.
.
.
...
.....
.
.
.
.
.....
....
.
.
.
..
v
t
...
....
.
.
.
...
.....
.
.
.
.
....
.....
.
.
..
I
a
t
...
.....
.
.
.
.
...
...
.
.
.
.
.....
....
.
.
.
..
II
v
III
a
...........................................
...........................................
t
t
IV
A.
B.
C.
D.
E.
t
V
IV only
IV and V only
I, II, and III only
I and II only
I and IV only
ans: E
75. An object is dropped from rest. Which of the following five graphs correctly represents its
motion? The positive direction is taken to be downward.
v
v
...........................................
t
...
.....
.
.
.
.
....
.....
.
.
.
..
....
.
.
..
A
v
t
..
..
.
.
...
...
.
.
..
.....
.
.
.
.
.
.........
B
v
............
.....
.
.
.
.
...
...
.
...
.. .
y
t
D
t
C
..........
... ......
...
...
.
...
..
...
...
...
...
.
.
t
E
ans: B
Chapter 2:
MOTION ALONG A STRAIGHT LINE
25
76. A stone is dropped from a cliff. The graph (carefully note the axes) which best represents its
motion while it falls is:
x
.
.....
.
.
.
.
....
.....
.
.
.
....
.....
.
.
...
v
t
.
..
.
..
...
.
.
..
....
.
.
.
.
.
............
A
v
t
..
.....
.
.
.
.
....
.....
.
.
...
.....
.
.
.
.
....
B
a
.
..
.
..
...
.
.
..
....
.
.
.
.
............
t
C
a
t
.
....
.
.
.
...
.....
.
.
.
.
....
....
.
.
.
.
....
D
t
E
ans: C
77. An object is thrown vertically into the air. Which of the following five graphs represents the
velocity (v) of the object as a function of the time (t)? The positive direction is taken to be
upward.
v
..
....
.
.
.
.
...
.....
.
.
.
.
...
.....
.
.
.
.
....
v
v
...........................................
t
t
A
B
v
..
..
.
.
...
...
.
.
..
.....
.
.
.
.
.
.
.........
v
t
..
..........
.....
.
.
.
.
...
...
.
...
...
D
ans: C
26
Chapter 2:
.....
.....
.....
.....
.....
.....
.....
....
C
MOTION ALONG A STRAIGHT LINE
E
t
t
Chapter 3:
VECTORS
1. We say that the displacement of a particle is a vector quantity. Our best justification for this
assertion is:
A. displacement can be specified by a magnitude and a direction
B. operating with displacements according to the rules for manipulating vectors leads to results in agreement with experiments
C. a displacement is obviously not a scalar
D. displacement can be specified by three numbers
E. displacement is associated with motion
ans: B
2. The vectors a, b, and c are related by c = b − a. Which diagram below illustrates this
relationship?
.....
...............
.............
c................................. .
......
.
.
.
.
...
.
...
... b
......
..
......
.
..
.. .......
.. ...
.........
...........................................................................
..
a
..........................
.. .
...............
c................................ .
......
.
.
.
.
.
...
...
... b
......
..
......
.
..
......
.. ..
......
....................................................................
..
a
A
B
...........
............................
........
.............. ....
b ......... . ..........
c
b .......... .. ..........
c
...
.
...
...
...
...
.
...
. ....
..
.
.............
...................................................................
..
...
.
...
...
...
...
...
...
.
..
.
.. ...
..................................................................
..
a
a
C
D
E. None of these
ans: D
3. A vector of magnitude 3 CANNOT be added to a vector of magnitude 4 so that the magnitude
of the resultant is:
A. zero
B. 1
C. 3
D. 5
E. 7
ans: A
4. A vector of magnitude 20 is added to a vector of magnitude 25. The magnitude of this sum
might be:
A. zero
B. 3
C. 12
D. 47
E. 50
ans: C
Chapter 3:
VECTORS
27
5. A vector S of magnitude 6 and another vector T have a sum of magnitude 12. The vector T :
A. must have a magnitude of at least 6 but no more than 18
B. may have a magnitude of 20
C. cannot have a magnitude greater than 12
D. must be perpendicular to S
E. must be perpendicular to the vector sum
ans: A
6. The vector −A is:
A. greater than A in magnitude
B. less than A in magnitude
C. in the same direction as A
D. in the direction opposite to A
E. perpendicular to A
ans: D
7. The vector V3 in the diagram is equal to:
.......
...................
.. .........
......
..
......
..
......
......
..
......V3
V2 ..
.......
..
.. ...
... .....
..
......
...
....
......
θ .....
..
......
...
..
..
.
........................................................................................................
V1
A.
B.
C.
D.
E.
V1 − V2
V1 + V2
V2 − V1
V1 cos θ
V1 /(cos θ)
ans: C
8. If |A + B|2 = A2 + B 2 , then:
A.
B.
C.
D.
E.
28
A and B must be parallel and in the same direction
A and B must be parallel and in opposite directions
either A or B must be zero
the angle between A and B must be 60◦
none of the above is true
ans: E
Chapter 3:
VECTORS
9. If |A + B| = A + B and neither A nor B vanish, then:
A.
B.
C.
D.
E.
A and B are parallel and in the same direction
A and B are parallel and in opposite directions
the angle between A and B is 45◦
the angle between A and B is 60◦
A is perpendicular to B
ans: A
10. If |A − B| = A + B and neither A nor B vanish, then:
A.
B.
C.
D.
E.
A and B are parallel and in the same direction
A and B are parallel and in opposite directions
the angle between A and B is 45◦
the angle between A and B is 60◦
A is perpendicular to B
ans: B
11. Four vectors (A, B, C, D) all have the same magnitude. The angle θ between adjacent vectors
is 45◦ as shown. The correct vector equation is:
.
........ B
.....
......
.
.
A ..
.
.
..
....
.. 45◦ ........
........................
.. ............. 45◦
............................................................................C
..... ..... ◦
....... 45
.....
.....
.....
.....
...........
D
A.
B.
C.
D.
E.
A−B−C
√+ D = 0
B + D − 2C = 0
A+B =B+D
A+B+C
√+ D = 0
(A + C)/ 2 = −B
ans: B
12. Vectors A and B lie in the xy plane. We can deduce that A = B if:
A. A2x + A2y = Bx2 + By2
B. Ax + Ay = Bx + By
C. Ax = Bx and Ay = By
D. Ay /Ax = By /Bx
E. Ax = Ay and Bx = By
ans: C
Chapter 3:
VECTORS
29
13. A vector has a magnitude of 12. When its tail is at the origin it lies between the positive x
axis and the negative y axis and makes an angle of 30◦ with the x axis. Its y component is:
√
A. 6/ √3
B. −6 3
C. 6
D. −6
E. 12
ans: D
14. If the x component of a vector A, in the xy plane, is half as large as the magnitude of the
vector, the tangent of the angle between the vector and the x axis is:
√
3
A.
B. √
1/2
3/2
C.
D. 3/2
E. 3
ans: D
15. If A = (6 m) î − (8 m) ĵ then 4A has magnitude:
A. 10 m
B. 20 m
C. 30 m
D. 40 m
E. 50 m
ans: D
16. A vector has a component of 10 m in the +x direction, a component of 10 m in the +y direction,
and a component of 5 m in the +z direction. The magnitude of this vector is:
A. zero
B. 15 m
C. 20 m
D. 25 m
E. 225 m
ans: B
17. Let
A.
B.
C.
D.
E.
30
V = (2.00 m) î + (6.00 m) ĵ − (3.00 m) k̂. The magnitude of V is:
5.00 m
5.57 m
7.00 m
7.42 m
8.54 m
ans: C
Chapter 3:
VECTORS
18. A vector in the xy plane has a magnitude of 25 m and an x component of 12 m. The angle it
makes with the positive x axis is:
A. 26◦
B. 29◦
C. 61◦
D. 64◦
E. 241◦
ans: C
19. The angle between A = (25 m) î + (45 m) ĵ and the positive x axis is:
A. 29◦
B. 61◦
C. 151◦
D. 209◦
E. 241◦
ans: B
20. The angle between A = (−25 m) î + (45 m) ĵ and the positive x axis is:
A. 29◦
B. 61◦
C. 119◦
D. 151◦
E. 209◦
ans: C
21. Let A = (2 m) î +(6 m) ĵ−(3 m) k̂ and B = (4 m) î +(2 m) ĵ+(1 m) k̂. The vector sum S = A+ B
is:
A. (6 m) î + (8 m) ĵ − (2 m) k̂
B. (−2 m) î + (4 m) ĵ − (4 m) k̂
C. (2 m) î − (4 m) ĵ + (4 m) k̂
D. (8 m) î + (12 m) ĵ − (3 m) k̂
E. none of these
ans: A
22. Let A = (2 m) î + (6 m) ĵ − (3 m) k̂ and B = (4 m) î + (2 m ĵ + (1 m) k̂. The vector difference
D = A − B is:
A. (6 m) î + (8 m) ĵ − (2 m) k̂
B. (−2 m) î + (4 m) ĵ − (4 m) k̂
C. (2 m) î − (4 m) ĵ + (4 m) k̂
D. (8 m) î + (12 m) ĵ − (3 m) k̂
E. none of these
ans: B
Chapter 3:
VECTORS
31
23. If A = (2 m) î − (3 m) ĵ and B = (1 m) î − (2 m) ĵ, then A − 2B =
A. (1 m) ĵ
B. (−1 m) ĵ
C. (4 m) î − (7 m) ĵ
D. (4 m) î + (1 m) ĵ
E. (−4 m) î + (7 m) ĵ
ans: A
24. In the diagram, A has magnitude 12 m and B has magnitude 8 m. The x component of A + B
is about:
y
A.
B.
C.
D.
E.
.............. .......
.
.
.
.
A .... ............... 60◦
....
..
...
.....
.
.
.
...
.
..
.
...
.
.
.
.
.
...
.
..
.
.
... .
.
.
.
.
.
........ B
..
..
.
...
.
.
◦
...
.
.
.
45
.
. ..
..... ....
x
5.5 m
7.6 m
12 m
14 m
15 m
ans: C
25. A certain vector in the xy plane has an x component of 4 m and a y component of 10 m. It is
then rotated in the xy plane so its x component is doubled. Its new y component is about:
A. 20 m
B. 7.2 m
C. 5.0 m
D. 4.5 m
E. 2.2 m
ans: B
26. Vectors A and B each have magnitude L. When drawn with their tails at the same point, the
angle between them is 30◦ . The value of A · B is:
A. zero
B. √
L2
C.
3L2 /2
D. 2L2
E. none of these
ans: C
32
Chapter 3:
VECTORS
27. Let A = (2 m) î + (6 m) ĵ − (3 m) k̂ and B = (4 m) î + (2 m) ĵ + (1 m) k̂. Then A · B =
A.
B.
C.
D.
E.
(8 m) î + (12 m) ĵ − (3 m) k̂
(12 m) î − (14 m) ĵ − (20 m) k̂
23 m2
17 m2
none of these
ans: D
28. Two vectors have magnitudes of 10 m and 15 m. The angle between them when they are drawn
with their tails at the same point is 65◦ . The component of the longer vector along the line of
the shorter is:
A. 0
B. 4.2 m
C. 6.3 m
D. 9.1 m
E. 14 m
ans: C
29. Let S = (1 m) î + (2 m) ĵ + (2 m) k̂ and T = (3 m) î + (4 m) k̂. The angle between these two
vectors is given by:
A. cos−1 (14/15)
B. cos−1 (11/225)
C. cos−1 (104/225)
D. cos−1 (11/15)
E. cannot be found since S and T do not lie in the same plane
ans: D
30. Two vectors lie with their tails at the same point. When the angle between them is increased
by 20◦ their scalar product has the same magnitude but changes from positive to negative.
The original angle between them was:
A. 0
B. 60◦
C. 70◦
D. 80◦
E. 90◦
ans: D
31. If the magnitude of the sum of two vectors is less than the magnitude of either vector, then:
A. the scalar product of the vectors must be negative
B. the scalar product of the vectors must be positive
C. the vectors must be parallel and in opposite directions
D. the vectors must be parallel and in the same direction
E. none of the above
ans: A
Chapter 3:
VECTORS
33
32. If the magnitude of the sum of two vectors is greater than the magnitude of either vector, then:
A. the scalar product of the vectors must be negative
B. the scalar product of the vectors must be positive
C. the vectors must be parallel and in opposite directions
D. the vectors must be parallel and in the same direction
E. none of the above
ans: E
33. Vectors A and B each have magnitude L. When drawn with their tails at the same point, the
angle between them is 60◦ . The magnitude of the vector product A × B is:
A. L2 /2
B. √
L2
C.
3L2 /2
D. 2L2
E. none of these
ans: C
34. Two vectors lie with their tails at the same point. When the angle between them is increased
by 20◦ the magnitude of their vector product doubles. The original angle between them was
about:
A. 0
B. 18◦
C. 25◦
D. 45◦
E. 90◦
ans: B
35. Two vectors have magnitudes of 10 m and 15 m. The angle between them when they are drawn
with their tails at the same point is 65◦ . The component of the longer vector along the line
perpendicular to the shorter vector, in the plane of the vectors, is:
A. 0
B. 4.2 m
C. 6.3 m
D. 9.1 m
E. 14 m
ans: E
36. The two vectors (3 m) î − (2 m) ĵ and (2 m) î + (3 m) ĵ − (2 m) k̂ define a plane. It is the plane of
the triangle with both tails at one vertex and each head at one of the other vertices. Which of
the following vectors is perpendicular to the plane?
A. (4 m) î + (6 m) ĵ + (13 m) k̂
B. (−4 m) î + (6 m) ĵ + (13 m) k̂
C. (4 m) î − (6 m) ĵ + (13 m) k̂
D. (4 m) î + (6 m ĵ − (13 m) k̂
E. (4 m) î + (6 m) ĵ
ans: A
34
Chapter 3:
VECTORS
37. Let R = S × T and θ = 90◦ , where θ is the angle between S and T when they are drawn with
their tails at the same point. Which of the following is NOT true?
A. |R| = |S||T | sin θ
B. −R = T × S
C. R · S = 0
D. R · T = 0
E. S · T = 0
ans: E
38. The value of î · ( ĵ × k̂) is:
A. zero
B. +1
C. −1
D. √
3
3
E.
ans: B
39. The value of k̂ · ( k̂ × î) is:
A. zero
B. +1
C. −1
D. √
3
3
E.
ans: A
Chapter 3:
VECTORS
35
Chapter 4:
MOTION IN TWO AND THREE DIMENSIONS
1. Velocity is defined as:
A. rate of change of position with time
B. position divided by time
C. rate of change of acceleration with time
D. a speeding up or slowing down
E. change of position
ans: A
2. Acceleration is defined as:
A. rate of change of position with time
B. speed divided by time
C. rate of change of velocity with time
D. a speeding up or slowing down
E. change of velocity
ans: C
3. Which of the following is a scalar quantity?
A. Speed
B. Velocity
C. Displacement
D. Acceleration
E. None of these
ans: A
4. Which of the following is a vector quantity?
A. Mass
B. Density
C. Speed
D. Temperature
E. None of these
ans: E
5. Which of the following is NOT an example of accelerated motion?
A. Vertical component of projectile motion
B. Circular motion at constant speed
C. A swinging pendulum
D. Earth’s motion about sun
E. Horizontal component of projectile motion
ans: E
36
Chapter 4:
MOTION IN TWO AND THREE DIMENSIONS
6. A particle goes from x = −2 m, y = 3 m, z = 1 m to x = 3 m, y = −1 m, z = 4 m. Its
displacement is:
A. (1 m) î + (2 m) ĵ + (5 m) k̂
B. (5 m) î − (4 m) ĵ + (3 m) k̂
C. −(5 m) î + (4 m) ĵ − (3 m) k̂
D. −(1 m) î − (2 m) ĵ − (5 m) k̂
E. −(5 m) î − (2 m) ĵ + (3 m) k̂
ans: B
7. A jet plane in straight horizontal flight passes over your head. When it is directly above you,
the sound seems to come from a point behind the plane in a direction 30◦ from the vertical.
The speed of the plane is:
A. the same as the speed of sound
B. half the speed of sound
C. three-fifths the speed of sound
D. 0.866 times the speed of sound
E. twice the speed of sound
ans: B
8. A plane traveling north at 200 m/s turns and then travels south at 200 m/s. The change in its
velocity is:
A. zero
B. 200 m/s north
C. 200 m/s south
D. 400 m/s north
E. 400 m/s south
ans: E
9. Two bodies are falling with negligible air resistance, side by side, above a horizontal plane. If
one of the bodies is given an additional horizontal acceleration during its descent, it:
A. strikes the plane at the same time as the other body
B. strikes the plane earlier than the other body
C. has the vertical component of its velocity altered
D. has the vertical component of its acceleration altered
E. follows a straight line path along the resultant acceleration vector
ans: A
10. The velocity of a projectile equals its initial velocity added to:
A. a constant horizontal velocity
B. a constant vertical velocity
C. a constantly increasing horizontal velocity
D. a constantly increasing downward velocity
E. a constant velocity directed at the target
ans: D
Chapter 4:
MOTION IN TWO AND THREE DIMENSIONS
37
11. A stone thrown from the top of a tall building follows a path that is:
A. circular
B. made of two straight line segments
C. hyperbolic
D. parabolic
E. a straight line
ans: D
12. Identical guns fire identical bullets horizontally at the same speed from the same height above
level planes, one on the Earth and one on the Moon. Which of the following three statements
is/are true?
I. The horizontal distance traveled by the bullet is greater for the Moon.
II. The flight time is less for the bullet on the Earth.
III. The velocity of the bullets at impact are the same.
A. III only
B. I and II only
C. I and III only
D. II and III only
E. I, II, III
ans: B
13. A stone is thrown horizontally and follows the path XYZ shown. The direction of the acceleration of the stone at point Y is:
•........................................................
.........
........
........
X
.......
.......
•....................
...
Y ......................
.....
.....
.....
.....
.....
....
....
...
....
....
....
....
....
....
....
.
horizontal
Z •
A. ↓
B. →
C.
D.
E.
ans: A
38
Chapter 4:
MOTION IN TWO AND THREE DIMENSIONS
14. A bullet shot horizontally from a gun:
A. strikes the ground much later than one dropped vertically from the same point at the same
instant
B. never strikes the ground
C. strikes the ground at approximately the same time as one dropped vertically from the same
point at the same instant
D. travels in a straight line
E. strikes the ground much sooner than one dropped from the same point at the same instant
ans: C
15. A bomber flying in level flight with constant velocity releases a bomb before it is over the
target. Neglecting air resistance, which one of the following is NOT true?
A. The bomber is over the target when the bomb strikes
B. The acceleration of the bomb is constant
C. The horizontal velocity of the plane equals the vertical velocity of the bomb when it hits
the target
D. The bomb travels in a curved path
E. The time of flight of the bomb is independent of the horizontal speed of the plane
ans: C
16. The airplane shown is in level flight at an altitude of 0.50 km and a speed of 150 km/h. At
what distance d should it release a heavy bomb to hit the target X? Take g = 10 m/s2 .
.......
... .......
... ....................................................
...
.
.............................................
...................................................
..............
↑
|
|
|
0.5 km
|
|
|
↓
... ... ... ... ...
150 km/h
...................................................
X
•
←−−−−−−−− d −−−−−−−−→
... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
A.
B.
C.
D.
E.
150 m
295 m
420 m
2550 m
15, 000 m
ans: C
Chapter 4:
MOTION IN TWO AND THREE DIMENSIONS
39
17. An object is shot from the back of a railroad flatcar moving at 40 km/h on a straight horizontal
road. The launcher is aimed upward, perpendicular to the bed of the flatcar. The object falls:
A. in front of the flatcar
B. behind the flatcar
C. on the flatcar
D. either behind or in front of the flatcar, depending on the initial speed of the object
E. to the side of the flatcar
ans: C
18. A ball is thrown horizontally from the top of a 20-m high hill. It strikes the ground at an angle
of 45◦ . With what speed was it thrown?
...
.............................................................................................
...
..
↑
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.....
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|
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20 m
...............................................................................................................................................
. ....
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| ..................................................................................................................................................................................................................
◦ ...........
......................................................................
....
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.
.
45
.........
.
.
↓ ...................................................................................................................
...
A.
B.
C.
D.
E.
14 m/s
20 m/s
28 m/s
32 m/s
40 m/s
ans: B
19. A stone is thrown outward from the top of a 59.4-m high cliff with an upward velocity component of 19.5 m/s. How long is stone in the air?
A. 4.00 s
B. 5.00 s
C. 6.00 s
D. 7.00 s
E. 8.00 s
ans: C
20. A large cannon is fired from ground level over level ground at an angle of 30◦ above the
horizontal. The muzzle speed is 980 m/s. Neglecting air resistance, the projectile will travel
what horizontal distance before striking the ground?
A. 4.3 km
B. 8.5 km
C. 43 km
D. 85 km
E. 170 km
ans: D
40
Chapter 4:
MOTION IN TWO AND THREE DIMENSIONS
21. A boy on the edge of a vertical cliff 20 m high throws a stone horizontally outward with a speed
of 20 m/s. It strikes the ground at what horizontal distance from the foot of the cliff? Use
2
g = 10 m/s .
A. 10 m
B. 40 m
C. 50√
m
D. 50 5 m
E. none of these
ans: B
22. Which of the curves on the graph below best represents the vertical component vy of the
velocity versus the time t for a projectile fired at an angle of 45◦ above the horizontal?
............... F
vy
........................
.
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.
A ....................................................................... B
....................................
.......
..................
......
.
.
.
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.
.
.
.. C t
.
.
.......
O.
.......
.......
.......
.
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.
.................. E
D
A.
B.
C.
D.
E.
OC
DE
AB
AE
AF
ans: D
Chapter 4:
MOTION IN TWO AND THREE DIMENSIONS
41
23. A cannon fires a projectile as shown. The dashed line shows the trajectory in the absence of
gravity; points MNOP correspond to the position of the projectile at one second intervals. If
2
g = 10 m/s , the lengths X,Y,Z are:
.
....
..
...
..
...
..
....
.
....
.
....
..
...
.
....
Y
..
...
.
........................................
.........
...
.
.
.
.
.
.
.
.......
.......
.....
.....
.....
.. ....
....
...........
.
...
.
.
....
... ......
.
.
...
... .....
.
.
....
...... .....
.
.
...
.
.. ........
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...
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.
....
...
..
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...
......
..
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......
......
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..
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..
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...
...
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..
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......
...
.... ....... ...........
...................... ....... ..........
..........
..
M
•
•
A.
B.
C.
D.
E.
•X
•
N
O
Z
•
P
5 m, 10 m, 15 m
5 m, 20 m, 45 m
10 m, 40 m, 90 m
10 m, 20 m, 30 m
0.2 m, 0.8 m, 1.8 m
ans: B
24. A dart is thrown horizontally toward X at 20 m/s as shown. It hits Y 0.1 s later. The distance
XY is:
.........
.
.... ...............
........
...
.......
...
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...
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...
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...
...
...
...
....
...
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.....
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...
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.................................. ....................................
.
...
.
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.
......................... .....
.
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.
....
.
.
.
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.
...............
..............
.
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.
..
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.
. .......
...........
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..........
....
........
.........
.
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........
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..
........
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...
.......
...
.......
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.....
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...
.......
...
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... .........
....
......
...
....
......
.......
...
.
...
........
...
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...
........ .............
....... .. .......
........ ...... ....
........ ....... ...
........ .......
.......... .....................
..
•••••••••••
•••• ••••••
•
••
•
•• ••••••••••••• ••••
•
• • • ••
•••• ••• • ••• •••
••• •••• •• ••
••• ••• •• ••
••• •••••• ••
•••
••••• •••••••
••••••••
•
A.
B.
C.
D.
E.
42
2m
1m
0.5 m
0.1 m
0.05 m
ans: E
Chapter 4:
MOTION IN TWO AND THREE DIMENSIONS
X
Y
25. A projectile is fired from ground level over level ground with an initial velocity that has a
2
vertical component of 20 m/s and a horizontal component of 30 m/s. Using g = 10 m/s , the
distance from launching to landing points is:
A. 40 m
B. 60 m
C. 80 m
D. 120 m
E. 180 m
ans: D
26. An object, tied to a string, moves in a circle at constant speed on a horizontal surface as shown.
The direction of the displacement of this object, as it travels from W to X is:
•
W
......................................
........
......
.....
......
....
.....
....
....
.
.
...
...
.
...
..
.
...
..
....
...
...
..
...
..
...
.
...
...
...
..
.
...
.
.
.
...
..
...
..
...
...
....
...
...
.....
...........
.....
.
.
......
.
.
.
.
...
........
....
.......................................
...
.
.
.
.
.
......
.......
.....
• Z
.....
.....
...
Y ••••••••.••••.•••••••
•
X •
A. ←
B. ↓
C. ↑
D.
E.
ans: E
27. A toy racing car moves with constant speed around the circle shown below. When it is at point
A its coordinates are x = 0, y = 3 m and its velocity is (6 m/s) î. When it is at point B its
velocity and acceleration are:
y
•A
......................................
........
......
......
......
.....
....
....
...
.
.
...
..
.
.
...
...
...
.
.
.
..
.
...
.....
..
..
..
...
.
...
...
...
..
.
...
.
.
.
...
.
...
...
...
...
....
...
.....
.....
.
.
......
.
.
.
...
........
......................................
B•
A.
B.
C.
D.
E.
x
2
−(6 m/s) ĵ and (12 m/s ) î, respectively
2
(6 m/s) î and −(12 m/s ) î, respectively
2
(6 m/s) ĵ and (12 m/s ) î, respectively
2
(6 m/s) î and (2 m/s ) ĵ, respectively
(6 m/s) ĵ and 0, respectively
ans: C
Chapter 4:
MOTION IN TWO AND THREE DIMENSIONS
43
28. An airplane makes a gradual 90◦ turn while flying at a constant speed of 200 m/s. The process
takes 20.0 seconds to complete. For this turn the magnitude of the average acceleration of the
plane is:
A. zero
2
B. 40 m/s
2
C. 20 m/s
2
D. 14 m/s
2
E. 10 m/s
ans: D
29. An airplane is flying north at 500 km/h. It makes a gradual 180◦ turn at constant speed,
changing its direction of travel from north through east to south. The process takes 40 s. The
average acceleration of the plane for this turn (in km/h·s) is:
A. 12.5 km/h · s, north
B. 12.5 km/h · s, east
C. 12.5 km/h · s, south
D. 25 km/h · s, north
E. 25 km/h · s, south
ans: E
30. An object is moving on a circular path of radius π meters at a constant speed of 4.0 m/s. The
time required for one revolution is:
A. 2/π2 s
B. π 2 /2 s
C. π/2 s
D. π 2 /4
E. 2/π s
ans: B
31. A particle moves at constant speed in a circular path. The instantaneous velocity and instantaneous acceleration vectors are:
A. both tangent to the circular path
B. both perpendicular to the circular path
C. perpendicular to each other
D. opposite to each other
E. none of the above
ans: C
32. A stone is tied to a string and whirled at constant speed in a horizontal circle. The speed
is then doubled without changing the length of the string. Afterward the magnitude of the
acceleration of the stone is:
A. the same
B. twice as great
C. four times as great
D. half as great
E. one-fourth as great
ans: C
44
Chapter 4:
MOTION IN TWO AND THREE DIMENSIONS
33. Two objects are traveling around different circular orbits with constant speed. They both have
the same acceleration but object A is traveling twice as fast as object B. The orbit radius for
the orbit radius for object B.
object A is
A. one-fourth
B. one-half
C. the same as
D. twice
E. four times
ans: E
34. A stone is tied to a 0.50-m string and whirled at a constant speed of 4.0 m/s in a vertical circle.
Its acceleration at the top of the circle is:
2
A. 9.8 m/s , up
B. 9.8 m/s2 , down
2
C. 8.0 m/s , down
2
D. 32 m/s , up
2
E. 32 m/s , down
ans: E
35. A stone is tied to a 0.50-m string and whirled at a constant speed of 4.0 m/s in a vertical circle.
Its acceleration at the bottom of the circle is:
2
A. 9.8 m/s , up
B. 9.8 m/s2 , down
C. 8.0 m/s2 , up
2
D. 32 m/s , up
2
E. 32 m/s , down
ans: D
36. A car rounds a 20-m radius curve at 10 m/s. The magnitude of its acceleration is:
A. 0
2
B. 0.20 m/s
2
C. 5.0 m/s
D. 40 m/s2
2
E. 400 m/s
ans: C
37. For a biological sample in a 1.0-m radius centrifuge to have a centripetal acceleration of 25g
its speed must be:
A. 11 m/s
B. 16 m/s
C. 50 m/s
D. 122 m/s
E. 245 m/s
ans: B
Chapter 4:
MOTION IN TWO AND THREE DIMENSIONS
45
38. A girl jogs around a horizontal circle with a constant speed. She travels one fourth of a
revolution, a distance of 25 m along the circumference of the circle, in 5.0 s. The magnitude of
her acceleration is:
2
A. 0.31 m/s
B. 1.3 m/s2
C. 1.6 m/s2
2
D. 3.9 m/s
2
E. 6.3 m/s
ans: C
39. A stone is tied to the end of a string and is swung with constant speed around a horizontal
circle with a radius of 1.5 m. If it makes two complete revolutions each second, the magnitude
of its acceleration is:
2
A. 0.24 m/s
2
B. 2.4 m/s
C. 24 m/s2
2
D. 240 m/s
2
E. 2400 m/s
ans: D
40. A Ferris wheel with a radius of 8.0 m makes 1 revolution every 10 s. When a passenger is at
the top, essentially a diameter above the ground, he releases a ball. How far from the point on
the ground directly under the release point does the ball land?
A. 0
B. 1.0 m
C. 8.0 m
D. 9.1 m
E. 16 m
ans: D
41. A boat is able to move through still water at 20 m/s. It makes a round trip to a town 3.0 km
upstream. If the river flows at 5 m/s, the time required for this round trip is:
A. 120 s
B. 150 s
C. 200 s
D. 300 s
E. 320 s
ans: E
46
Chapter 4:
MOTION IN TWO AND THREE DIMENSIONS
42. A boat is traveling upstream at 14 km/h with respect to a river that is flowing at 6 km/h (with
respect to the ground). A man runs directly across the boat, from one side to the other, at
6 km/h (with respect to the boat). The speed of the man with respect to the ground is:
A. 10 km/h
B. 14 km/h
C. 18.5 km/h
D. 21 km/h
E. 26 km/h
ans: A
43. A ferry boat is sailing at 12 km/h 30◦ W of N with respect to a river that is flowing at 6.0 km/h
E. As observed from the shore, the ferry boat is sailing:
A. 30◦ E of N
B. due N
C. 30◦ W of N
D. 45◦ E of N
E. none of these
ans: B
44. A boy wishes to row across a river in the shortest possible time. He can row at 2 m/s in still
water and the river is flowing at 1 m/s. At what angle θ should he point the bow (front) of his
boat?
....
..
..
∼∼∼∼ .... .....
∼∼∼∼
..
∼∼∼∼ ... .....
θ
A.
B.
C.
D.
E.
...
... ...
... .
...
.................
...
..
.
...
....
.
...
...
......
...
....
....
.... .......
....
..... .
...
....
...
..
..............................................
.....
1 m/s
∼∼∼∼
∼∼∼∼
30◦
45◦
60◦
63◦
90◦
ans: E
Chapter 4:
MOTION IN TWO AND THREE DIMENSIONS
47
45. A girl wishes to swim across a river to a point directly opposite as shown. She can swim at
2 m/s in still water and the river is flowing at 1 m/s. At what angle θ with respect to the line
joining the starting and finishing points should she swim?
.........................................................
1 m/s
∼∼∼∼
∼∼∼∼
A.
B.
C.
D.
E.
finish
•
θ
•
start
..
...
..
∼∼∼∼
∼∼∼∼
∼∼∼∼
∼∼∼∼
.
.....................
....
.........
.
.......
....
......
..... ..
....
..
....
.
....
.
....
..
....
.
.
.
..
.
....
30◦
45◦
60◦
63◦
90◦
ans: A
46. A motor boat can travel at 10 km/h in still water. A river flows at 5 km/h west. A boater
wishes to cross from the south bank to a point directly opposite on the north bank. At what
angle must the boat be headed?
A. 27◦ E of N
B. 30◦ E of N
C. 45◦ E of N
D. 60◦ E of N
E. depends on the width of the river
ans: B
47. Two projectiles are in flight at the same time. The acceleration of one relative to the other:
2
A. is always 9.8 m/s
B. can be as large as 19.8 m/s2
C. can be horizontal
D. is zero
E. none of these
ans: D
48
Chapter 4:
MOTION IN TWO AND THREE DIMENSIONS
Chapter 5:
FORCE AND MOTION – I
1. An
A.
B.
C.
D.
E.
example of an inertial reference frame is:
any reference frame that is not accelerating
a frame attached to a particle on which there are no forces
any reference frame that is at rest
a reference frame attached to the center of the universe
a reference frame attached to Earth
ans: B
2. An
A.
B.
C.
D.
E.
object moving at constant velocity in an inertial frame must:
have a net force on it
eventually stop due to gravity
not have any force of gravity on it
have zero net force on it
have no frictional force on it
ans: D
3. In SI units a force is numerically equal to the
A. velocity of the standard kilogram
B. speed of the standard kilogram
C. velocity of any object
D. acceleration of the standard kilogram
E. acceleration of any object
ans: D
, when the force is applied to it.
4. Which of the following quantities is NOT a vector?
A. Mass
B. Displacement
C. Weight
D. Acceleration
E. Force
ans: A
5. A newton is the force:
A. of gravity on a 1 kg body
B. of gravity on a 1 g body
2
C. that gives a 1 g body an acceleration of 1 cm/s
2
D. that gives a 1 kg body an acceleration of 1 m/s
2
E. that gives a 1 kg body an acceleration of 9.8 m/s
ans: D
Chapter 5:
FORCE AND MOTION – I
49
6. The unit of force called the newton is:
2
A. 9.8 kg · m/s
2
B. 1 kg · m/s
C. defined by means of Newton’s third law
D. 1 kg of mass
E. 1 kg of force
ans: B
7. A force of 1 N is:
A. 1 kg/s
B. 1 kg · m/s
C. 1 kg · m/s2
D. 1 kg · m2 /s
2
E. 1 kg · m2 /s
ans: C
8. The standard 1-kg mass is attached to a compressed spring and the spring is released. If the
mass initially has an acceleration of 5.6 m/s2 , the force of the spring has a magnitude of:
A. 2.8 N
B. 5.6 N
C. 11.2 N
D. 0
E. an undetermined amount
ans: B
9. Acceleration is always in the direction:
A. of the displacement
B. of the initial velocity
C. of the final velocity
D. of the net force
E. opposite to the frictional force
ans: D
10. The term “mass” refers to the same physical concept as:
A. weight
B. inertia
C. force
D. acceleration
C. volume
ans: B
50
Chapter 5:
FORCE AND MOTION – I
11. The inertia of a body tends to cause the body to:
A. speed up
B. slow down
C. resist any change in its motion
D. fall toward Earth
E. decelerate due to friction
ans: C
12. A heavy ball is suspended as shown. A quick jerk on the lower string will break that string but
a slow pull on the lower string will break the upper string. The first result occurs because:
. . . . . . . . . . . . . . . . . . . . .
.. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. ..
... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
..................
.. ...........
........
•••••••••
•••••••••••••••••••••••••••••••••••••••••••
•••••••••
..................
.. ...........
........
A.
B.
C.
D.
E.
upper string
lower string
the force is too small to move the ball
action and reaction is operating
the ball has inertia
air friction holds the ball back
the ball has too much energy
ans: C
2
13. When a certain force is applied to the standard kilogram its acceleration is 5.0 m/s . When
the same force is applied to another object its acceleration is one-fifth as much. The mass of
the object is:
A. 0.2 kg
B. 0.5 kg
C. 1.0 kg
D. 5.0 kg
E. 10 kg
ans: D
14. Mass differs from weight in that:
A. all objects have weight but some lack mass
B. weight is a force and mass is not
C. the mass of an object is always more than its weight
D. mass can be expressed only in the metric system
E. there is no difference
ans: B
Chapter 5:
FORCE AND MOTION – I
51
15. The mass of a body:
A. is slightly different at different places on Earth
B. is a vector
C. is independent of the free-fall acceleration
D. is the same for all bodies of the same volume
E. can be measured most accurately on a spring scale
ans: C
16. The mass and weight of a body:
A. differ by a factor of 9.8
B. are identical
C. are the same physical quantities expressed in different units
D. are both a direct measure of the inertia of the body
E. have the same ratio as that of any other body placed at that location
ans: E
17. An object placed on an equal-arm balance requires 12 kg to balance it. When placed on a
spring scale, the scale reads 12 kg. Everything (balance, scale, set of weights and object) is
now transported to the Moon where the free-fall acceleration is one-sixth that on Earth. The
new readings of the balance and spring scale (respectively) are:
A. 12 kg, 12 kg
B. 2 kg, 2 kg
C. 12 kg, 2 kg
D. 2 kg, 12 kg
E. 12 kg, 72 kg
ans: C
18. Two objects, one having three times the mass of the other, are dropped from the same height
in a vacuum. At the end of their fall, their velocities are equal because:
A. anything falling in vacuum has constant velocity
B. all objects reach the same terminal velocity
C. the acceleration of the larger object is three times greater than that of the smaller object
D. the force of gravity is the same for both objects
E. none of the above
ans: E
19. A feather and a lead ball are dropped from rest in vacuum on the Moon. The acceleration of
the feather is:
A. more than that of the lead ball
B. the same as that of the lead ball
C. less than that of the lead ball
2
D. 9.8 m/s
E. zero since it floats in a vacuum
ans: B
52
Chapter 5:
FORCE AND MOTION – I
20. The block shown moves with constant velocity on a horizontal surface. Two of the forces on
it are shown. A frictional force exerted by the surface is the only other horizontal force on the
block. The frictional force is:
3N
5N
..
.............................................................
..
.
................................................
..
... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
A.
B.
C.
D.
E.
0
2 N, leftward
2 N, rightward
slightly more than 2 N, leftward
slightly less than 2 N, leftward
ans: B
21. Two forces, one with a magnitude of 3 N and the other with a magnitude of 5 N, are applied
to an object. For which orientations of the forces shown in the diagrams is the magnitude of
the acceleration of the object the least?
3N
......
......
.. .......
....
..
..
5N
..
..............................................
..
..
............................................................
..
3N
..
..................
..
.... .
.
.
.
.
...
5N
..
............................................................
..
A
...........................................................
..
B
C
3N
3N
..
........................................
..
..........
..........
.. ....
....
....
.
5N
..
............................................................
..
..
............................................................
..
D
3N
5 .N
..
5N
E
ans: A
22. A crate rests on a horizontal surface and a woman pulls on it with a 10-N force. Rank the
situations shown below according to the magnitude of the normal force exerted by the surface
on the crate, least to greatest.
...
........
.........
....
...
..
10 N
..
.................
.. ..
....
.
.
.
...
10 N
..
.......................................
..
... ... ... ... ... ... ... ... ... ... ... ... ... ...
... ... ... ... ... ... ... ... ... ... ... ... ... ...
1
A.
B.
C.
D.
E.
... ... ... ... ... ... ... ... ... ... ... ... ... ...
... ... ... ... ... ... ... ... ... ... ... ... ... ...
2
10 N
... ... ... ... ... ... ... ... ... ... ... ... ... ...
... ... ... ... ... ... ... ... ... ... ... ... ... ...
3
1, 2, 3
2, 1, 3
2, 3, 1
1, 3, 2
3, 2, 1
ans: E
Chapter 5:
FORCE AND MOTION – I
53
23. A heavy wooden block is dragged by a force F along a rough steel plate, as shown in the
diagrams for two cases. The magnitude of the applied force F is the same for both cases. The
normal force in (ii), as compared with the normal force in (i) is:
F
..
...
.....................................
..
F
.. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. ..
.. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . . . . . . . . .
.. .. .. .. .. .. .. ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
.............
........
....... ..... ................
.......
..........
.
.......
......
.
.
.
.
.
.
.
.
...
..........
..
... ................... ..
.......
.......
. ...... .
.......
................ .
.
.
.
.
.
.........
.
.
...... ..
...
....... .. .
...
......... .. .
...
......... .. .
...
........ .. .
... ...................... .
... ............. .
.. .
........... ..
........ .. .
.............. .
.
.
.
.
.
.
.......... .
.
.
....
...
(i)
A.
B.
C.
D.
E.
(ii)
the same
greater
less
less for some angles of the incline and greater for others
less or greater, depending on the magnitude of the applied force F .
ans: C
24. Equal forces F act on isolated bodies A and B. The mass of B is three times that of A. The
magnitude of the acceleration of A is:
A. three times that of B
B. 1/3 that of B
C. the same as B
D. nine times that of B
E. 1/9 that of B
ans: A
25. A car travels east at constant velocity. The net force on the car is:
A. east
B. west
C. up
D. down
E. zero
ans: E
26. A constant force of 8.0 N is exerted for 4.0 s on a 16-kg object initially at rest. The change in
speed of this object will be:
A. 0.5 m/s
B. 2 m/s
C. 4 m/s
D. 8 m/s
E. 32 m/s
ans: B
54
Chapter 5:
FORCE AND MOTION – I
27. A 6-kg object is moving south. A net force of 12 N north on it results in the object having an
acceleration of:
2
A. 2 m/s , north
2
B. 2 m/s , south
C. 6 m/s2 , north
2
D. 18 m/s , north
2
E. 18 m/s , south
ans: A
28. A 9000-N automobile is pushed along a level road by four students who apply a total forward
force of 500 N. Neglecting friction, the acceleration of the automobile is:
2
A. 0.055 m/s
2
B. 0.54 m/s
2
C. 1.8 m/s
2
D. 9.8 m/s
2
E. 18 m/s
ans: B
29. An object rests on a horizontal frictionless surface. A horizontal force of magnitude F is
applied. This force produces an acceleration:
A. only if F is larger than the weight of the object
B. only while the object suddenly changes from rest to motion
C. always
D. only if the inertia of the object decreases
E. only if F is increasing
ans: C
30. A 25-kg crate is pushed across a frictionless horizontal floor with a force of 20 N, directed 20◦
below the horizontal. The acceleration of the crate is:
2
A. 0.27 m/s
2
B. 0.75 m/s
C. 0.80 m/s2
2
D. 170 m/s
2
E. 470 m/s
ans: B
31. A ball with a weight of 1.5 N is thrown at an angle of 30◦ above the horizontal with an initial
speed of 12 m/s. At its highest point, the net force on the ball is:
A. 9.8 N, 30◦ below horizontal
B. zero
C. 9.8 N, up
D. 9.8 N, down
E. 1.5 N, down
ans: E
Chapter 5:
FORCE AND MOTION – I
55
32. Two forces are applied to a 5.0-kg crate; one is 6.0 N to the north and the other is 8.0 N to the
west. The magnitude of the acceleration of the crate is:
2
A. 0.50 m/s
2
B. 2.0 m/s
C. 2.8 m/s2
2
D. 10 m/s
2
E. 50 m/s
ans: B
33. A 400-N steel ball is suspended by a light rope from the ceiling. The tension in the rope is:
A. 400 N
B. 800 N
C. zero
D. 200 N
E. 560 N
ans: A
34. A heavy steel ball B is suspended by a cord from a block of wood W. The entire system is
dropped through the air. Neglecting air resistance, the tension in the cord is:
A. zero
B. the difference in the masses of B and W
C. the difference in the weights of B and W
D. the weight of B
E. none of these
ans: A
35. A circus performer of weight W is walking along a “high wire” as shown. The tension in the
wire:
........
.......
. ..
.....................
..
..................................................
..........
.... ..
...
.... ..
....... ..................... ...
.
.
.
.
. ....
.... .
... .... ... ....
............ .....
.... .........................
.
.. .
...................
..............
...
..
..................................................................................................................
...
...
...
....
...
...
...
.
.
...
...
....
...
...
.
...
.
...
....
...
.
.
...
....
...
...
...
...
...
...
...
...
...
...
...
.
.
.
....... ....... ...... ....... ....... ....... ....... ....... ....... ....... ....... ....... ....... ....... ....... ....... ....... ....... ....... ....... ....... ....... ....... ....... ....... ....... ....... ....... ........ ....... .......
... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
....
..
A.
B.
C.
D.
E.
56
is approximately W
is approximately W/2
is much less than W
is much more than W
depends on whether he stands on one foot or two feet
ans: D
Chapter 5:
FORCE AND MOTION – I
.....
2
36. A 1000-kg elevator is rising and its speed is increasing at 3 m/s . The tension force of the cable
on the elevator is:
A. 6800 N
B. 1000 N
C. 3000 N
D. 9800 N
E. 12800 N
ans: E
∗37. A 5-kg block is suspended by a rope from the ceiling of an elevator as the elevator accelerates
2
downward at 3.0 m/s . The tension force of the rope on the block is:
A. 15 N, up
B. 34 N, up
C. 34 N, down
D. 64 N, up
E. 64 N, down
ans: B
38. A crane operator lowers a 16, 000-N steel ball with a downward acceleration of 3 m/s2 . The
tension force of the cable is:
A. 4900 N
B. 11, 000 N
C. 16, 000 N
D. 21, 000 N
E. 48, 000 N
ans: B
39. A 1-N pendulum bob is held at an angle θ from the vertical by a 2-N horizontal force F as
shown. The tension in the string supporting the pendulum bob (in newtons) is:
. . . . . . . . . . . . . . . . . . . . .
... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
.. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. ..
...
...
..
................
.
θ ....
..
..
.
••..•••••••
•••••••••••••••••••••••.•••.•••.•.••.••..••..•••.•.•......................................................................... F
•••••••••••••
A.
B.
C.
D.
E.
cos θ
2/ cos θ
√
5
1
none of these
ans: C
Chapter 5:
FORCE AND MOTION – I
57
2
40. A car moves horizontally with a constant acceleration of 3 m/s . A ball is suspended by a
string from the ceiling of the car. The ball does not swing, being at rest with respect to the
car. What angle does the string make with the vertical?
A. 17◦
B. 35◦
C. 52◦
D. 73◦
E. Cannot be found without knowing the length of the string
ans: A
2
41. A man weighing 700 Nb is in an elevator that is accelerating upward at 4 m/s . The force
exerted on him by the elevator floor is:
A. 71 N
B. 290 N
C. 410 N
D. 700 N
E. 990 N
ans: E
42. You stand on a spring scale on the floor of an elevator. Of the following, the scale shows the
highest reading when the elevator:
A. moves upward with increasing speed
B. moves upward with decreasing speed
C. remains stationary
D. moves downward with increasing speed
E. moves downward at constant speed
ans: A
43. You stand on a spring scale on the floor of an elevator. Of the following, the scale shows the
highest reading when the elevator:
A. moves downward with increasing speed
B. moves downward with decreasing speed
C. remains stationary
D. moves upward with decreasing speed
E. moves upward at constant speed
ans: B
44. When a 25-kg crate is pushed across a frictionless horizontal floor with a force of 200 N, directed
20◦ below the horizontal, the magnitude of the normal force of the floor on the crate is:
A. 25 N
B. 68 N
C. 180 N
D. 250 N
E. 310 N
ans: E
58
Chapter 5:
FORCE AND MOTION – I
45. A block slides down a frictionless plane that makes an angle of 30◦ with the horizontal. The
acceleration of the block is:
2
A. 980 cm/s
2
B. 566 cm/s
C. 849 cm/s2
D. zero
2
E. 490 cm/s
ans: E
46. A 25-N crate slides down a frictionless incline that is 25◦ above the horizontal. The magnitude
of the normal force of the incline on the crate is:
A. 11 N
B. 23 N
C. 25 N
D. 100 N
E. 220 N
ans: B
47. A 25-N crate is held at rest on a frictionless incline by a force that is parallel to the incline. If
the incline is 25◦ above the horizontal the magnitude of the applied force is:
A. 4.1 N
B. 4.6 N
C. 8.9 N
D. 11 N
E. 23 N
ans: D
48. A 25-N crate is held at rest on a frictionless incline by a force that is parallel to the incline. If
the incline is 25◦ above the horizontal the magnitude of the normal force of the incline on the
crate is:
A. 4.1 N
B. 4.6 N
C. 8.9 N
D. 11 N
E. 23 N
ans: E
49. A 32-N force, parallel to the incline, is required to push a certain crate at constant velocity up
a frictionless incline that is 30◦ above the horizontal. The mass of the crate is:
A. 3.3 kg
B. 3.8 kg
C. 5.7 kg
D. 6.5 kg
E. 160 kg
ans: D
Chapter 5:
FORCE AND MOTION – I
59
50. A sled is on an icy (frictionless) slope that is 30◦ above the horizontal. When a 40-N force,
parallel to the incline and directed up the incline, is applied to the sled, the acceleration of the
2
sled is 2.0 m/s , down the incline. The mass of the sled is:
A. 3.8 kg
B. 4.1 kg
C. 5.8 kg
D. 6.2 kg
E. 10 kg
ans: E
51. When a 40-N force, parallel to the incline and directed up the incline, is applied to a crate on
2
a frictionless incline that is 30◦ above the horizontal, the acceleration of the crate is 2.0 m/s ,
up the incline. The mass of the crate is:
A. 3.8 kg
B. 4.1 kg
C. 5.8 kg
D. 6.2 kg
E. 10 kg
ans: C
52. The “reaction” force does not cancel the “action” force because:
A. the action force is greater than the reaction force
B. they are on different bodies
C. they are in the same direction
D. the reaction force exists only after the action force is removed
E. the reaction force is greater than the action force
ans: B
53. A book rests on a table, exerting a downward force on the table. The reaction to this force is:
A. the force of Earth on the book
B. the force of the table on the book
C. the force of Earth on the table
D. the force of the book on Earth
E. the inertia of the book
ans: B
54. A lead block is suspended from your hand by a string. The reaction to the force of gravity on
the block is the force exerted by:
A. the string on the block
B. the block on the string
C. the string on the hand
D. the hand on the string
E. the block on Earth
ans: E
60
Chapter 5:
FORCE AND MOTION – I
2
55. A 5-kg concrete block is lowered with a downward acceleration of 2.8 m/s by means of a rope.
The force of the block on the rope is:
A. 14 N, up
B. 14 N, down
C. 35 N, up
D. 35 N, down
E. 49 N, up
ans: D
56. A 90-kg man stands in an elevator that is moving up at a constant speed of 5.0 m/s. The force
exerted by him on the floor is about:
A. zero
B. 90 N
C. 880 N
D. 450 N
E. 49 N
ans: C
57. A 90-kg man stands in an elevator that has a downward acceleration of 1.4 m/s2 . The force
exerted by him on the floor is about:
A. zero
B. 90 N
C. 760 N
D. 880 N
E. 1010 N
ans: C
58. A 5-kg concrete block is lowered with a downward acceleration of 2.8 m/s2 by means of a rope.
The force of the block on Earth is:
A. 14 N, up
B. 14 N, down
C. 35 N, up
D. 35 N, down
E. 49 N, up
ans: E
Chapter 5:
FORCE AND MOTION – I
61
59. Two blocks are connected by a string and pulley as shown. Assuming that the string and pulley
are massless, the magnitude of the acceleration of each block is:
.. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. ..
.. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. ..
... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
............
........ .............
....
...
...
...
....
..
...
..
...
..
...
..
...
...
.
.
....
........
.....
...................
•
•
90 g
110 g
A.
B.
C.
D.
E.
2
0.049 m/s
2
0.020 m/s
0.0098 m/s2
2
0.54 m/s
2
0.98 m/s
ans: E
60. A 70-N block and a 35-N block are connected by a string as shown. If the pulley is massless
and the surface is frictionless, the magnitude of the acceleration of the 35-N block is:
.....................
......
....
....
...
...
...
....
.
..
...
...
...
.
.
.....
.
.
.
.
.
.
.
..................
... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
... ... ... ... ... ... ... ... ... ... ... ... ... ... ... .......
..
.
.. ....
..
......
..
........
.
.......
..
.......
..
.. .....
..
......
..
........
.
.......
..
...
70 N
.
...•
.. ....
pulley
35 N
A.
B.
C.
D.
E.
62
2
1.6 m/s
2
3.3 m/s
2
4.9 m/s
6.7 m/s2
2
9.8 m/s
ans: B
Chapter 5:
FORCE AND MOTION – I
61. A 13-N weight and a 12-N weight are connected by a massless string over a massless, frictionless
pulley. The 13-N weight has a downward acceleration with magnitude equal to that of a freely
falling body times:
A. 1
B. 1/12
C. 1/13
D. 1/25
E. 13/25
ans: D
62. A massless rope passes over a massless pulley suspended from the ceiling. A 4-kg block is
attached to one end and a 5-kg block is attached to the other end. The acceleration of the 5-kg
block is:
A. g/4
B. 5g/9
C. 4g/9
D. g/5
E. g/9
ans: E
63. Two blocks, weighing 250 N and 350 N, respectively, are connected by a string that passes over
a massless pulley as shown. The tension in the string is:
. . . . . . . . . . . . . . . . . . . . .
... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
............
........ .............
.....
...
...
...
...
..
...
..
...
.
...
..
..
...
.
.
....
..
.
.
......
.
.
........................
•
•
250 N
350 N
A.
B.
C.
D.
E.
210 N
290 N
410 N
500 N
4900 N
ans: B
Chapter 5:
FORCE AND MOTION – I
63
64. Three books (X, Y, and Z) rest on a table. The weight of each book is indicated. The net force
acting on book Y is:
X
4N
5N
Z
10 N
.. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. ..
Y
. . . . . . . . . . .
... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... .. .. .. .. .. .. .. .. .. .. ..
... ... ... ... ... ... .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. ..
A.
B.
C.
D.
E.
4 N down
5 N up
9 N down
zero
none of these
ans: D
65. Three books (X, Y, and Z) rest on a table. The weight of each book is indicated. The force of
book Z on book Y is:
X
4N
5N
Z
10 N
.. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. ..
Y
.. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. ..
... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
A.
B.
C.
D.
E.
0
5N
9N
14 N
19 N
ans: C
66. Three blocks (A,B,C), each having mass M , are connected by strings as shown. Block C is
pulled to the right by a force F that causes the entire system to accelerate. Neglecting friction,
the net force acting on block B is:
A
B
C
..
...........................................
..
F
... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
.. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. ..
A.
B.
C.
D.
E.
64
zero
F /3
F /2
2F /3
F
ans: B
Chapter 5:
FORCE AND MOTION – I
67. Two blocks with masses m and M are pushed along a horizontal frictionless surface by a
horizontal applied force F as shown. The magnitude of the force of either of these blocks on
the other is:
F
..
...........................................
..
M
m
... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
.. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. ..
A.
B.
C.
D.
E.
mF/(m + M )
mF/M
mF/(M − m)
M F/(M + m)
M F/m
ans: A
68. Two blocks (A and B) are in contact on a horizontal frictionless surface. A 36-N constant force
is applied to A as shown. The magnitude of the force of A on B is:
36 N
..
...........................................
..
A
B
mA = 4.0 kg
mB = 20 kg
... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
.. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. ..
A.
B.
C.
D.
E.
1.5 N
6.0 N
29 N
30 N
36 N
ans: D
69. A short 10-g string is used to pull a 50-g toy across a frictionless horizontal surface. If a
3.0 × 10−2 -N force is applied horizontally to the free end, the force of the string on the toy, at
the other end, is:
A. 0.15 N
B. 6.0 × 10−3 N
C. 2.5 × 10−2 N
D. 3.0 × 10−2 N
E. 3.5 × 10−2 N
ans: C
Chapter 5:
FORCE AND MOTION – I
65
Chapter 6:
FORCE AND MOTION – II
1. A brick slides on a horizontal surface. Which of the following will increase the magnitude of
the frictional force on it?
A. Putting a second brick on top
B. Decreasing the surface area of contact
C. Increasing the surface area of contact
D. Decreasing the mass of the brick
E. None of the above
ans: A
2. The coefficient of kinetic friction:
A. is in the direction of the frictional force
B. is in the direction of the normal force
C. is the ratio of force to area
D. can have units of newtons
E. is none of the above
ans: E
3. When the brakes of an automobile are applied, the road exerts the greatest retarding force:
A. while the wheels are sliding
B. just before the wheels start to slide
C. when the automobile is going fastest
D. when the acceleration is least
E. at the instant when the speed begins to change
ans: B
4. A forward horizontal force of 12 N is used to pull a 240-N crate at constant velocity across a
horizontal floor. The coefficient of friction is:
A. 0.5
B. 0.05
C. 2
D. 0.2
E. 20
ans: B
5. The speed of a 4.0-N hockey puck, sliding across a level ice surface, decreases at the rate of
2
0.61 m/s . The coefficient of kinetic friction between the puck and ice is:
A. 0.062
B. 0.41
C. 0.62
D. 1.2
E. 9.8
ans: A
66
Chapter 6:
FORCE AND MOTION – II
6. A crate rests on a horizontal surface and a woman pulls on it with a 10-N force. No matter
what the orientation of the force, the crate does not move. Rank the situations shown below
according to the magnitude of the frictional force of the surface on the crate, least to greatest.
..
........
..........
...
....
..
10 N
..
..................
.. .
... .
....
...
10 N
..
........................................
..
... ... ... ... ... ... ... ... ... ... ... ... ... ...
... ... ... ... ... ... ... ... ... ... ... ... ... ...
1
A.
B.
C.
D.
E.
... ... ... ... ... ... ... ... ... ... ... ... ... ...
... ... ... ... ... ... ... ... ... ... ... ... ... ...
2
10 N
... ... ... ... ... ... ... ... ... ... ... ... ... ...
... ... ... ... ... ... ... ... ... ... ... ... ... ...
3
1, 2, 3
2, 1, 3
2, 3, 1
1, 3, 2
3, 2, 1
ans: E
7. A crate with a weight of 50 N rests on a horizontal surface. A person pulls horizontally on it
with a force of 10 N and it does not move. To start it moving, a second person pulls vertically
upward on the crate. If the coefficient of static friction is 0.4, what is the smallest vertical force
for which the crate moves?
...
.......
.........
..
...
...
.
10 N
..
...................................................
..
... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
A.
B.
C.
D.
E.
4N
10 N
14 N
25 N
35 N
ans: D
8. A 40-N crate rests on a rough horizontal floor. A 12-N horizontal force is then applied to it. If
the coefficients of friction are µs = 0.5 and µk = 0.4, the magnitude of the frictional force on
the crate is:
A. 8 N
B. 12 N
C. 16 N
D. 20 N
E. 40 N
ans: B
Chapter 6:
FORCE AND MOTION – II
67
9. A 24-N horizontal force is applied to a 40-N block initially at rest on a rough horizontal surface.
If the coefficients of friction are µs = 0.5 and µk = 0.4, the magnitude of the frictional force on
the block is:
A. 8 N
B. 12 N
C. 16 N
D. 20 N
E. 400 N
ans: C
10. A horizontal shove of at least 200 N is required to start moving a 800-N crate initially at rest
on a horizontal floor. The coefficient of static friction is:
A. 0.25
B. 0.125
C. 0.50
D. 4.00
E. none of these
ans: A
11. A force F (larger than the largest possible force of static friction) is applied to the left to an
object moving to the right on a horizontal surface. Then:
A. the object must be moving at constant speed
B. F and the friction force act in opposite directions
C. the object must be slowing down
D. the object must be speeding up
E. the object must come to rest and remain at rest
ans: C
12. A bureau rests on a rough horizontal surface (µs = 0.50, µk = 0.40). A constant horizontal
force, just sufficient to start the bureau in motion, is then applied. The acceleration of the
bureau is:
A. 0
2
B. 0.98 m/s
2
C. 3.3 m/s
2
D. 4.5 m/s
E. 8.9 m/s2
ans: B
13. A car is traveling at 15 m/s on a horizontal road. The brakes are applied and the car skids to
a stop in 4.0 s. The coefficient of kinetic friction between the tires and road is:
A. 0.38
B. 0.69
C. 0.76
D. 0.92
E. 1.11
ans: A
68
Chapter 6:
FORCE AND MOTION – II
14. A boy pulls a wooden box along a rough horizontal floor at constant speed by means of a force
P as shown. In the diagram f is the magnitude of the force of friction, N is the magnitude of
the normal force, and Fg is the magnitude of the force of gravity. Which of the following must
be true?
...
.......
........
....
...
...
....
.
f
N
..
..........................................................
..
..
..................................................
..
Fg : force of gravity
f : frictional force
N : normal force
P
.. .. .. .. .. .. .. .. .. .. .. .. .. .. .... .. .. .. .. .. .. .. .. .. .. .. .. .. ..
... ... ... ... ... .... .... .... .... .... .... .... .... .... ....... .... .... .... .... .... .... .... .... .... .... .... .... .... ....
... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...... ... ... ... ... ... ... ... ... ... ... ... ... ...
...
...
.........
.........
g
.
F
A.
B.
C.
D.
E.
P = f and N
P = f and N
P > f and N
P > f and N
none of these
ans: A
= Fg
> Fg
< Fg
= Fg
15. A boy pulls a wooden box along a rough horizontal floor at constant speed by means of a force
P as shown. In the diagram f is the magnitude of the force of friction, N is the magnitude of
the normal force, and Fg is the magnitude of the force of gravity. Which of the following must
be true?
.......
..........
...
....
..
.
f
N
...............
..........
...... .
......
.
.
.
.
.
.
.
......
......
.......
Fg : force of gravity
f : frictional force
N : normal force
P
θ
.
.......................................................................
..
... ... ... ... ... ... ... ... ... ... ... ... ... ... ..... ... ... ... ... ... ... ... ... ... ... .. .. .. ..
... ... ... ... ... ... ... ... ... ... ... ... ... ... ...... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ....... ... ... ... ... ... ... ... ... ... ... ... ... ...
...
....
...
..
....... ..
........
g
..
F
A.
B.
C.
D.
E.
P = f and N
P = f and N
P > f and N
P > f and N
none of these
ans: C
= Fg
> Fg
< Fg
= Fg
Chapter 6:
FORCE AND MOTION – II
69
16. A 400-N block is dragged along a horizontal surface by an applied force F as shown. The coefficient of kinetic friction is µk = 0.4 and the block moves at constant velocity. The magnitude
of F is:
..................
........
......
.....
.
.
.
.
....
......
......
......
.....
.
.
.
.
.
....
.....
......
.....
.....
F
(3/5)F
(4/5)F
... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... .. .. .. ..
... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
A.
B.
C.
D.
E.
100 N
150 N
200 N
290 N
400 Nb
ans: B
17. A block of mass m is pulled at constant velocity along a rough horizontal floor by an applied
force T as shown. The magnitude of the frictional force is:
..................
... ..
...... .
......
.
.
.
.
....
.
.
.
.
....
......
......
......
.....
.
.
.
.
.
.
.. .
...... ....
.....
...
.....
T
θ
.. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. ..
... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... .... .... ....
... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
A.
B.
C.
D.
E.
70
T cos θ
T sin θ
zero
mg
mg cos θ
ans: A
Chapter 6:
FORCE AND MOTION – II
18. A block of mass m is pulled along a rough horizontal floor by an applied force T as shown.
The vertical component of the force exerted on the block by the floor is:
....................
... .
...... .
.....
.
.
.
.
...
.
.
.
.
.
.....
.....
......
......
......
.
.
.
.
.. .
...... .....
......
...
......
T
θ
. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
.. .. .. .. .. .. .. .. .. .. .. .. .. .. .. ... ... ... ... ... ... ... ... ... ... ... ... ... ...
... ... ... ... ... ... ... ... ... ... ... ... ... ... ... .. .. .. .. .. .. .. .. ... ... ... ... ... ...
... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... .. .. .. .. .. ..
A.
B.
C.
D.
E.
mg
mg − T cos θ
mg + T cos θ
mg − T sin θ
mg + T sin θ
ans: D
19. A 12-kg crate rests on a horizontal surface and a boy pulls on it with a force that is 30◦ below
the horizontal. If the coefficient of static friction is 0.40, the minimum magnitude force he
needs to start the crate moving is:
A. 44 N
B. 47 N
C. 54 N
D. 56 N
E. 71 N
ans: E
20. A crate resting on a rough horizontal floor is to be moved horizontally. The coefficient of static
friction is 0.40. To start the crate moving with the weakest possible applied force, in what
direction should the force be applied?
A. Horizontal
B. 24◦ below the horizontal
C. 22◦ above the horizontal
D. 24◦ above the horizontal
E. 66◦ below the horizontal
ans: C
21. A 50-N force is applied to a crate on a horizontal rough floor, causing it to move horizontally.
If the coefficient of kinetic friction is 0.50, in what direction should the force be applied to
obtain the greatest acceleration?
A. Horizontal
B. 60◦ above the horizontal
C. 30◦ above the horizontal
D. 27◦ above the horizontal
E. 30◦ below the horizontal
ans: D
Chapter 6:
FORCE AND MOTION – II
71
22. A professor holds an eraser against a vertical chalkboard by pushing horizontally on it. He
pushes with a force that is much greater than is required to hold the eraser. The force of
friction exerted by the board on the eraser increases if he:
A. pushes with slightly greater force
B. pushes with slightly less force
C. stops pushing
D. pushes so his force is slightly downward but has the same magnitude
E. pushes so his force is slightly upward but has the same magnitude
ans: D
23. A horizontal force of 12 N pushes a 0.5-kg book against a vertical wall. The book is initially at
rest. If the coefficients of friction are µs = 0.6 and µk = 0.8 which of the following is true?
A. The magnitude of the frictional force is 4.9 N
B. The magnitude of the frictional force is 7.2 N
C. The normal force is 4.9 N
D. The book will start moving and accelerate
E. If started moving downward, the book will decelerate
ans: A
24. A horizontal force of 5.0 N pushes a 0.50-kg book against a vertical wall. The book is initially
at rest. If the coefficients of friction are µs = 0.6 and µk = 0.80, the magnitude of the frictional
force is:
A. 0
B. 4.9 N
C. 3.0 N
D. 5.0 N
E. 4.0 N
ans: E
25. A horizontal force of 12 N pushes a 0.50-kg book against a vertical wall. The book is initially
at rest. If µs = 0.6 and µk = 0.80, the acceleration of the book in m/s2 is:
A. 0
2
B. 9.4 m/s
2
C. 9.8 m/s
2
D. 14.4 m/s
E. 19.2 m/s2
ans: A
26. A horizontal force of 5.0 N pushes a 0.50-kg block against a vertical wall. The block is initially
at rest. If µs = 0.60 and µk = 0.80, the acceleration of the block in m/s2 is:
A. 0
B. 1.8
C. 6.0
D. 8.0
E. 9.8
ans: B
72
Chapter 6:
FORCE AND MOTION – II
27. A heavy wooden block is dragged by a force F along a rough steel plate, as shown below for
two possible situations. The magnitude of F is the same for the two situations. The magnitude
of the frictional force in (ii), as compared with that in (i) is:
F
..
......................................
..
.......
...................
....... .....
.
.......
............... ...
.......
.
....
.
.......
.
.
.
.
...
..........
....
.
.
.
.
.
.
... ...........................
....
.
.
.
.
.
.
.
.
.
.
.
.................... .
.....
.
.
.
.
.
.
.
.
.
.
.
...
...... . . .
...
........ .. .. ..
...
................ ..
...
......... .... .
...
..................... .
.
.
.
.
.
...
.
.
.
... .........................
... . . .
........ .. ..
.................
................... ..
.
.
.
.
.
.
..... .. . .
............. .
.........
... .
F
.. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. ..
... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... .... .... ....
... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
(ii)
(i)
A.
B.
C.
D.
E.
the same
greater
less
less for some angles and greater for others
can be less or greater, depending on the magnitude of the applied force.
ans: C
28. A block is first placed on its long side and then on its short side on the same inclined plane, as
shown. The block slides down the plane on its short side but remains at rest on its long side.
A possible explanation is:
.........
....... .....
...
.......
.
......
...
.
.
.......
.
.
.
.
..
...
....... ..
.......
... ........................
......
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
..
........ .. ..
.........
............ ..
...
.............. ..
...
........... ... .
...
...................... .
.
.
.
.
.
.
.
...
.. .
...
......... .. .. .
... ........................... .
................. .
...........................
.
.
.
.
.
.
..
....... . ..
...
......... .. .. .
.............. .
....... ..
...
m
m
v
θ
θ
(ii)
A.
B.
C.
D.
E.
.....
....... .....
.......
...
.......
...
.........
...
...
...
...
...
....
...
...
...........
...
.......... ..
...
...
.................. ..
...
.
.
.
.
.
.
.
...
...
...... . .. ..
...
...
........... .. ..
... ........................ ...
...... ....
.................. ..
.. ......
...
.................
......... ..
.
.
.
.
.
.
.
.
.
.
.
.
.
.
...
.
.. .
... ........................... .
.. ......... .. .. .
.................. .
...........................
.
.
.
.
.
.
...
....... . ..
..
......... .. .. .
.............. .
....... ..
...
(ii)
the short side is smoother
the frictional force is less because the contact area is less
the center of gravity is higher in the second case
the normal force is less in the second case
the force of gravity is more nearly down the plane in the second case
ans: A
29. A box rests on a rough board 10 meters long. When one end of the board is slowly raised to a
height of 6 meters above the other end, the box begins to slide. The coefficient of static friction
is:
A. 0.8
B. 0.25
C. 0.4
D. 0.6
E. 0.75
ans: E
Chapter 6:
FORCE AND MOTION – II
73
30. A block is placed on a rough wooden plane. It is found that when the plane is tilted 30◦ to
the horizontal, the block will slide down at constant speed. The coefficient of kinetic friction
of the block with the plane is:
A. 0.500
B. 0.577
C. 1.73
D. 0.866
E. 4.90
ans: B
31. A crate is sliding down an incline that is 35◦ above the horizontal. If the coefficient of kinetic
friction is 0.40, the acceleration of the crate is:
A. 0
2
B. 2.4 m/s
C. 5.8 m/s2
2
D. 8.8 m/s
2
E. 10.3 m/s
ans: B
32. A 5.0-kg crate is resting on a horizontal plank. The coefficient of static friction is 0.50 and the
coefficient of kinetic friction is 0.40. After one end of the plank is raised so the plank makes
an angle of 25◦ with the horizontal, the force of friction is:
A. 0
B. 18 N
C. 21 N
D. 22 N
E. 44 N
ans: C
33. A 5.0-kg crate is resting on a horizontal plank. The coefficient of static friction is 0.50 and the
coefficient of kinetic friction is 0.40. After one end of the plank is raised so the plank makes
an angle of 30◦ with the horizontal, the force of friction is:
A. 0
B. 18 N
C. 21 N
D. 22 N
E. 44 N
ans: B
74
Chapter 6:
FORCE AND MOTION – II
34. A 5.0-kg crate is on an incline that makes an angle of 30◦ with the horizontal. If the coefficient
of static friction is 0.50, the minimum force that can be applied parallel to the plane to hold
the crate at rest is:
A. 0
B. 3.3 N
C. 30 N
D. 46 N
E. 55 N
ans: B
35. A 5.0-kg crate is on an incline that makes an angle of 30◦ with the horizontal. If the coefficient
of static friction is 0.5, the maximum force that can be applied parallel to the plane without
moving the crate is:
A. 0
B. 3.3 N
C. 30 N
D. 46 N
E. 55 N
ans: D
36. Block A, with mass mA , is initially at rest on a horizontal floor. Block B, with mass mB , is
initially at rest on the horizontal top surface of A. The coefficient of static friction between the
two blocks is µs . Block A is pulled with a horizontal force. It begins to slide out from under
B if the force is greater than:
A. mA g
B. mB g
C. µs mA g
D. µs mB g
E. µs (mA + mB )g
ans: E
37. The system shown remains at rest. Each block weighs 20 N. The force of friction on the upper
block is:
......................
.......
...
.........
...
....... ....
.
.
.
.
.
...
.
.
.
.
.
.
.
..
...
.
.......
....... ....
...
..
......
...
.......
.
.
.
.
.
.
.
.
.
.
.
.
....
...
..
....
....
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.................
..........
.......
.....
.
.
.
.
.
.
.
.
.
.
.
.
.
...
..
... . ..
.......
...
......... .. ..
.......
... .................... ...
.......
...... .. .
.......
................ ..
.
.
.
.
.........
.
.
.
...
......... . .
........ ... ..
...
.......... ... ..
...
......... ... ..
...
............... ...
.
.
.
...
.
.
.
.
...
....... . .
... ..................... ..
............... ... .
....
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.
.
.
.
.
.
..
......... ... .
.......... ... .
....... ... ..
....... ..
.....
.......
W
a
W = 20 N
a = 3m
b = 4m
W
b
A.
B.
C.
D.
E.
4N
8N
12 N
16 N
20 N
ans: B
Chapter 6:
FORCE AND MOTION – II
75
38. Block A, with a mass of 50 kg, rests on a horizontal table top. The coefficient of static friction
is 0.40. A horizontal string is attached to A and passes over a massless, frictionless pulley as
shown. The smallest mass mB of block B, attached to the dangling end, that will start A
moving when it is attached to the other end of the string is:
..................
....
.......
...
....
..
...
..
.....
...
...
..
...
.
.
....
.
.
.
........ .........
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ..
... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
... ... ... ... ... ... ... ... ... ... ... ... ... ... ... .......
..
.......
..
........
..
.. ....
..
........
..
.......
..
.......
..
........
..
.. ....
..
........
..
...
A
•.
.....
.....
pulley
B
A.
B.
C.
D.
E.
20 kg
30 kg
40 kg
50 kg
70 kg
ans: A
39. Block A, with a mass of 10 kg, rests on a 35◦ incline. The coefficient of static friction is 0.40.
An attached string is parallel to the incline and passes over a massless, frictionless pulley at
the top. The largest mass mB of block B, attached to the dangling end, for which A begins to
slide down the incline is:
..........................
.......
...
..........
...
....... ..
.
...........
....... ....
.
.
.
.
.
.
.
.
.
.
.
.
...
...
...
....
....
.
.
.
.
.
..
.
.
.
.
.
.
.
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.
...
....
..
....
....
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
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.
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.
...................
... .......
....
.......
.
.
.
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.
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.
...
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....
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... .................... ...
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.......
.............. ...
.
.
.
.
.........
.
.
.
...
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...
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.......... .. ..
...
......... .. ...
...
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.
...
.
.
.
.
.
...
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...
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... ...................... ...
.. .
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.
.
.
.
.
.
....
....... .. ... .
......... .. .
...... ... ..
....... ..
......
.......
A
A.
B.
C.
D.
E.
76
2.5 kg
3.5 kg
5.9 kg
9.0 kg
10.5 kg
ans: A
Chapter 6:
FORCE AND MOTION – II
B
40. Block A, with a mass of 10 kg, rests on a 35◦ incline. The coefficient of static friction is 0.40.
An attached string is parallel to the incline and passes over a massless, frictionless pulley at
the top. The largest mass mB , attached to the dangling end, for which A remains at rest is:
........
........ ...........
........
...
.........
...
...... ...
....
.
.
.
.
.
.
.
.
.
.
.
.
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.
...
..
....... .....
.......
...
...
.......
......
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
... ......
....
.. ......... .........
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
........
.......
... .
.......
...
......... ..
.......
...
......... ... ..
.......
... ....................... ..
.......
.......
............. .
.
.
.
.
.
.
.
.
.
.
.
.
......
........ ... ..
...
.......... .. .
...
......... .. .
...
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...
................ ..
.
.
.
.
.
.
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..
...
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...
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...
... ........................ ...
...... ... .
.
.
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.
.
........ .. ...
........... .. .
........ .. ..
....... ... ..
....... ..
.....
.......
A
A.
B.
C.
D.
E.
B
2.5 kg
3.5 kg
5.9 kg
9.0 kg
10.5 kg
ans: D
41. Block A, with a mass of 10 kg, rests on a 30◦ incline. The coefficient of kinetic friction is 0.20.
The attached string is parallel to the incline and passes over a massless, frictionless pulley at
the top. Block B, with a mass of 8.0 kg, is attached to the dangling end of the string. The
acceleration of B is:
........
....... ..........
........
...
.........
...
....... ...
.
.....
.
.
.
.
.
.
.
.
.
.
..
...
.......
....... .....
...
...
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.
.......
.
.
.
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.
.
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.
... ......
. ......... ........
.
.....
.
.
.
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.
.
.
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.
.
.
.
.
.
.
.
.
........
........
...
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...
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.......
... ...................... ...
.......
...... ... .
......
.
.
.
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.
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.
.
.
.
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.
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.
.......
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...
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...
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......... ... ..
...
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...
.
.
.
.
.
.
.
...
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...
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...
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... ................ ... ..
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.
.
.
.
.
.
.
....... .. .. .
.......... ... .
.......... .. .
....... .. ..
...... ..
......
.......
A
A.
B.
C.
D.
E.
B
0.69 m/s2 , up the plane
2
0.69 m/s , down the plane
2
2.6 m/s , up the plane
2
2.6 m/s , down the plane
0
ans: B
Chapter 6:
FORCE AND MOTION – II
77
42. Block A, with a mass of 10 kg, rests on a 30◦ incline. The coefficient of kinetic friction is 0.20.
The attached string is parallel to the incline and passes over a massless, frictionless pulley at
the top. Block B, with a mass of 3.0 kg, is attached to the dangling end of the string. The
acceleration of B is:
....................
.......
...
.........
...
....... ..
...
....... ...
........
.
.
.
.
.
.
.
.
.
.
.
.
..
...
...
....
.....
.
.
.
.
.
..
.
.
.
.
.
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.
.
...
...
..
....
....
.
.
.
.
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.
.
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.
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.
.
.
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.
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.
... ........
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....
.
.
.
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.
.
.
.
.
.
.
....
... .
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...
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.
.
.
.
.
.
.
.
.
.
...
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...
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...
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...
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...
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.
.
.
.
.
...
.
...
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......... ... ...
...
... ...................... ...
.................. .
.
.
.
.
.
..... .. .
........... .. .
......... .. ..
....... .. ..
...... ..
....
.......
A
A.
B.
C.
D.
E.
B
0.20 m/s2 , up
2
0.20 m/s , down
2
2.8 m/s , up
2
2.8 m/s , down
0
ans: A
43. A 1000-kg airplane moves in straight flight at constant speed. The force of air friction is 1800 N.
The net force on the plane is:
A. zero
B. 11800 N
C. 1800 N
D. 9800 N
E. none of these
ans: A
44. Why do raindrops fall with constant speed during the later stages of their descent?
A. The gravitational force is the same for all drops
B. Air resistance just balances the force of gravity
C. The drops all fall from the same height
D. The force of gravity is negligible for objects as small as raindrops
E. Gravity cannot increase the speed of a falling object to more than 9.8 m/s
ans: B
45. A ball is thrown downward from the edge of a cliff with an initial speed that is three times the
terminal speed. Initially its acceleration is
A. upward and greater than g
B. upward and less than g
C. downward and greater than g
D. downward and less than g
E. downward and equal to g
ans: A
78
Chapter 6:
FORCE AND MOTION – II
46. A ball is thrown upward into the air with a speed that is greater than terminal speed. On the
way up it slows down and, after its speed equals the terminal speed but before it gets to the
top of its trajectory:
A. its speed is constant
B. it continues to slow down
C. it speeds up
D. its motion becomes jerky
E. none of the above
ans: B
47. A ball is thrown upward into the air with a speed that is greater than terminal speed. It lands
at the place where it was thrown. During its flight the force of air resistance is the greatest:
A. just after it is thrown
B. halfway up
C. at the top of its trajectory
D. halfway down
E. just before it lands.
ans: A
48. Uniform circular motion is the direct consequence of:
A. Newton’s third law
B. a force that is always tangent to the path
C. an acceleration tangent to the path
D. a force of constant magnitude that is always directed away from the same fixed point
E. a force of constant magnitude that is always directed toward the same fixed point
ans: E
49. An
A.
B.
C.
D.
E.
object moving in a circle at constant speed:
must have only one force acting on it
is not accelerating
is held to its path by centrifugal force
has an acceleration of constant magnitude
has an acceleration that is tangent to the circle
ans: D
50. An object of mass m and another object of mass 2m are each forced to move along a circle of
radius 1.0 m at a constant speed of 1.0 m/s. The magnitudes of their accelerations are:
A. equal
√
B. in the ratio of 2 : 1
C. in the ratio of 2 : 1
D. in the ratio of 4 : 1
E. zero
ans: A
Chapter 6:
FORCE AND MOTION – II
79
51. The magnitude of the force required to cause a 0.04-kg object to move at 0.6 m/s in a circle of
radius 1.0 m is:
A. 2.4 × 10−2 N
B. 1.4 × 10−2 N
C. 1.4π × 10−2 N
D. 2.4π2 × 10−2 N
E. 3.13 N
ans: B
52. A 0.2-kg stone is attached to a string and swung in a circle of radius 0.6 m on a horizontal
and frictionless surface. If the stone makes 150 revolutions per minute, the tension force of the
string on the stone is:
A. 0.03 N
B. 0.2 N
C. 0.9 N
D. 1.96 N
E. 30 N
ans: E
53. Which of the following five graphs is correct for a particle moving in a circle of radius r at a
constant speed of 10 m/s?
a
a
...........................................
r
..
.....
.
.
.
.
....
....
.
.
.
.
....
.....
.
.
...
A
a
r
..
...
.
..
...
.
.
..
.....
.
.
.
.
.
..........
B
a
..........
......
.
.
.
...
...
.
.
...
..
.
.
C
a
r
D
r
...
...
...
....
....
....
......
.............
r
E
ans: E
54. An object moves around a circle. If the radius is doubled keeping the speed the same then the
magnitude of the centripetal force must be:
A. twice as great
B. half as great
C. four times as great
D. one-fourth as great
E. the same
ans: B
80
Chapter 6:
FORCE AND MOTION – II
55. An object moves in a circle. If the mass is tripled, the speed halved, and the radius unchanged,
then the magnitude of the centripetal force must be multiplied by a factor of:
A. 3/2
B. 3/4
C. 9/4
D. 6
E. 12
ans: B
56. If a
A.
B.
C.
D.
E.
satellite moves above Earth’s atmosphere in a circular orbit with constant speed, then:
its acceleration and velocity are always in the same direction
the net force on it is zero
its velocity is constant
it will fall back to Earth when its fuel is used up
its acceleration is toward the Earth
ans: E
57. A 800-N passenger in a car presses against the car door with a 200 N force when the car makes
a left turn at 13 m/s. The (faulty) door will pop open under a force of 800 N. Of the following,
the least speed for which the passenger is thrown out of the car is:
A. 14 m/s
B. 19 m/s
C. 20 m/s
D. 26 m/s
E. 54 m/s
ans: D
58. If a certain car, going with speed v1 , rounds a level curve with a radius R1 , it is just on the
verge of skidding. If its speed is now doubled, the radius of the tightest curve on the same road
that it can round without skidding is:
A. 2R1
B. 4R1
C. R1 /2
D. R1 /4
E. R1
ans: B
59. An automobile moves on a level horizontal road in a circle of radius 30 m. The coefficient of
friction between tires and road is 0.50. The maximum speed with which this car can round
this curve is:
A. 3.0 m/s
B. 4.9 m/s
C. 9.8 m/s
D. 12 m/s
E. 13 m/s
ans: D
Chapter 6:
FORCE AND MOTION – II
81
60. The driver of a 1000-kg car tries to turn through a circle of radius 100 m on an unbanked curve
at a speed of 10 m/s. The actual frictional force between the tires and slippery road has a
magnitude of 900 N. The car:
A. slides into the inside of the curve
B. makes the turn
C. slows down due to the frictional force
D. makes the turn only if it goes faster
E. slides off to the outside of the curve
ans: E
61. A car rounds a 75-m radius curve at a constant speed of 18 m/s. A ball is suspended by a
string from the ceiling the car and moves with the car. The angle between the string and the
vertical is:
A. 0
B. 1.4◦
C. 24◦
D. 90◦
E. cannot be found without knowing the mass of the ball
ans: C
62. A giant wheel, having a diameter of 40 m, is fitted with a cage and platform on which a man of
mass m stands. The wheel is rotated in a vertical plane at such a speed that the force exerted
by the man on the platform is equal to his weight when the cage is at X, as shown. The net
force on the man at point X is:
X
•
......................................
..........
................ ...........
.......
.. ............ ......
......
.............
....
.
.
..........
...
... ...........
.
..
... ..
.
...
..
.
.
...
.
.
.
..
..
.........
........
...
....
...
..........
.
.
...
..... ..
...
.
...
...
...
...
..
...
...
...
.
.
....
.
.....
....
......
.....
.....
.......
...........
.......
.................................
wheel
A.
B.
C.
D.
E.
82
zero
mg, down
mg, up
2mg, down
2mg, up
ans: D
Chapter 6:
FORCE AND MOTION – II
man in
cage
......
..... ...
........
63. A giant wheel, 40 m in diameter, is fitted with a cage and platform on which a man can stand.
The wheel rotates at such a speed that when the cage is at X (as shown) the force exerted by
the man on the platform is equal to his weight. The speed of the man is:
X
•
.....
.................. ........................
........
................. ........
......
.. ............. ......
.....
.............
...
.
...........
.
.
..
... ...........
.
.
.
...
...
.
...
...
....
.
..
.
.........
..
.......
..
.
....
...
........
..
....... ...
...
.
.
...
..
...
..
...
...
...
...
....
..
.
.
.....
.....
......
......
.......
..........
.......
...................................
man in
cage
......
..... .....
.......
wheel
A.
B.
C.
D.
E.
14 m/s
20 m/s
28 m/s
80 m/s
120 m/s
ans: B
64. A person riding a Ferris wheel is strapped into her seat by a seat belt. The wheel is spun so
that the centripetal acceleration is g. Select the correct combination of forces that act on her
when she is at the top. In the table Fg = force of gravity, down; Fb = seat belt force, down;
and Fs = seat force, up.
A.
B.
C.
D.
E.
Fg
0
mg
0
mg
mg
ans: B
Fb
mg
0
0
mg
0
Fs
0
0
mg
0
mg
65. One end of a 1.0-m long string is fixed, the other end is attached to a 2.0-kg stone. The stone
swings in a vertical circle, passing the bottom point at 4.0 m/s. The tension force of the string
at this point is about:
A. 0
B. 12 N
C. 20 N
D. 32 N
E. 52 N
ans: E
Chapter 6:
FORCE AND MOTION – II
83
66. One end of a 1.0-m string is fixed, the other end is attached to a 2.0-kg stone. The stone
swings in a vertical circle, passing the top point at 4.0 m/s. The tension force of the string (in
newtons) at this point is about:
A. 0
B. 12
C. 20
D. 32
E. 52
ans: B
67. A coin is placed on a horizontal phonograph turntable. Let N be the magnitude of the normal
force exerted by the turntable on the coin, f be the magnitude of the frictional force exerted
by the turntable on the coin, and fs, max be the maximum possible force of static friction. The
speed of the turntable is increased in small steps. If the coin does not slide, then
A. N increases, f increases, and fs, max stays the same
B. N increases, f increases, and fs, max increases
C. f increases and both N and fs, max stay the same
D. N , f , and fs, max all stay the same
E. N , f , and fs, max all increase
ans: C
68. The iron ball shown is being swung in a vertical circle at the end of a 0.7-m long string. How
slowly can the ball go through its top position without having the string go slack?
............
........
....
....
....... ........ ......
.
...
.
.
.
.
..
...
....
.
.
.
...
...
..
....
...
..
...
.
..
..
...
..
..
.
....
...
..
.
.......
......
....... .......
•••.••
..•..••.•••
.
.
.
.
...
•...
A.
B.
C.
D.
E.
1.3 m/s
2.6 m/s
3.9 m/s
6.9 m/s
9.8 m/s
ans: B
69. A block is suspended by a rope from the ceiling of a car. When the car rounds a 45-m radius
horizontal curve at 22 m/s (about 50 mph), what angle does the rope make with the vertical?
A. 0
B. 25◦
C. 48◦
D. 65◦
E. 90◦
ans: C
84
Chapter 6:
FORCE AND MOTION – II
70. Circular freeway entrance and exit ramps are commonly banked to handle a car moving at
13 m/s. To design a similar ramp for 26 m/s one should:
A. increase radius by factor of 2
B. decrease radius by factor of 2
C. increase radius by factor of 4
D. decrease radius by factor of √
4
E. increase radius by factor of 2
ans: C
71. At what angle should the roadway on a curve with a 50 m radius be banked to allow cars to
negotiate the curve at 12 m/s even if the roadway is icy (and the frictional force is zero)?
A. 0
B. 16◦
C. 18◦
D. 35◦
E. 73◦
ans: B
Chapter 6:
FORCE AND MOTION – II
85
Chapter 7:
KINETIC ENERGY AND WORK
1. Which of the following is NOT a correct unit for work?
A. erg
B. ft·lb
C. watt
D. newton·meter
E. joule
ans: C
2. Which of the following groups does NOT contain a scalar quantity?
A. velocity, force, power
B. displacement, acceleration, force
C. acceleration, speed, work
D. energy, work, distance
E. pressure, weight, time
ans: B
3. A boy holds a 40-N weight at arm’s length for 10 s. His arm is 1.5 m above the ground. The
work done by the force of the boy on the weight while he is holding it is:
A. 0
B. 6.1 J
C. 40 J
D. 60 J
E. 90 J
ans: A
4. A crate moves 10 m to the right on a horizontal surface as a woman pulls on it with a 10-N force.
Rank the situations shown below according to the work done by her force, least to greatest.
10 N
10 N
..
........................................
..
... ... ... ... ... ... ... ... ... ... ... ... ... ...
... ... ... ... ... ... ... ... ... ... ... ... ... ...
1
A.
B.
C.
D.
E.
86
...
...
...
..
... ... ... ... ... ... ... ... ... ... ... ....... ... ...
... ... ... ... ... ... ... ... ... ... ... ... ... ...
...
...
...
...
..
...........
.......
.
2
1, 2, 3
2, 1, 3
2, 3, 1
1, 3, 2
3, 2, 1
ans: E
Chapter 7:
KINETIC ENERGY AND WORK
...
........
.. .....
....
..
..
10 N
... ... ... ... ... ... ... ... ... ... ... ... ... ...
... ... ... ... ... ... ... ... ... ... ... ... ... ...
3
5. An object moves in a circle at constant speed. The work done by the centripetal force is zero
because:
A. the displacement for each revolution is zero
B. the average force for each revolution is zero
C. there is no friction
D. the magnitude of the acceleration is zero
E. the centripetal force is perpendicular to the velocity
ans: E
6. An object of mass 1 g is whirled in a horizontal circle of radius 0.5 m at a constant speed of
2 m/s. The work done on the object during one revolution is:
A. 0
B. 1 J
C. 2 J
D. 4 J
E. 16 J
ans: A
7. The work done by gravity during the descent of a projectile:
A. is positive
B. is negative
C. is zero
D. depends for its sign on the direction of the y axis
E. depends for its sign on the direction of both the x and y axes
ans: A
8. A baseball is hit high into the upper bleachers of left field. Over its entire flight the work done
by gravity and the work done by air resistance, respectively, are:
A. positive; positive
B. positive; negative
C. negative; positive
D. negative; negative
E. unknown since vital information is lacking
ans: D
9. A line drive to the shortstop is caught at the same height as it was originally hit. Over its
entire flight the work done by gravity and the work done by air resistance, respectively, are:
A. zero; positive
B. zero; negative
C. positive; negative
D. negative; positive
E. negative; negative
ans: B
Chapter 7:
KINETIC ENERGY AND WORK
87
10. A 2-kg object is moving at 3 m/s. A 4-N force is applied in the direction of motion and then
removed after the object has traveled an additional 5 m. The work done by this force is:
A. 12 J
B. 15 J
C. 18 J
D. 20 J
E. 38 J
ans: D
11. A sledge (including load) weighs 5000 N. It is pulled on level snow by a dog team exerting a
horizontal force on it. The coefficient of kinetic friction between sledge and snow is 0.05. How
much work is done by the dog team pulling the sledge 1000 m at constant speed?
A. 2.5 × 104 J
B. 2.5 × 105 J
C. 5.0 × 105 J
D. 2.5 × 106 J
E. 5.0 × 106 J
ans: B
12. Camping equipment weighing 6000 N is pulled across a frozen lake by means of a horizontal
rope. The coefficient of kinetic friction is 0.05. The work done by the campers in pulling the
equipment 1000 m at constant velocity is:
A. 3.1 × 104 J
B. 1.5 × 105 J
C. 3.0 × 105 J
D. 2.9 × 106 J
E. 6.0 × 106 J
ans: C
13. Camping equipment weighing 6000 N is pulled across a frozen lake by means of a horizontal
rope. The coefficient of kinetic friction is 0.05. How much work is done by the campers in
pulling the equipment 1000 m if its speed is increasing at the constant rate of 0.20 m/s2 ?
A. −1.2 × 106 J
B. 1.8 × 105 J
C. 3.0 × 105 J
D. 4.2 × 105 J
E. 1.2 × 106 J
ans: D
14. A 1-kg block is lifted vertically 1 m by a boy. The work done by the boy is about:
A. 1 ft · lb
B. 1 J
C. 10 J
D. 0.1 J
E. zero
ans: C
88
Chapter 7:
KINETIC ENERGY AND WORK
15. A 0.50-kg object moves in a horizontal circular track with a radius of 2.5 m. An external force
of 3.0 N, always tangent to the track, causes the object to speed up as it goes around. The
work done by the external force as the mass makes one revolution is:
A. 24 J
B. 47 J
C. 59 J
D. 94 J
E. 120 J
ans: B
16. A man pulls a 100-N crate up a frictionless 30◦ slope 5 m high, as shown. Assuming that the
crate moves at constant speed, the work done by the man is:
.....................
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....
.
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.
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.
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..
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....
...
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...........
.
.
.
.
....
.
.
.
.
.
.
..
◦
.......
.......
.......
... ... ... ... ... ... ... ... ... ... .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. ..
.. .. .. .. .. .. .. .. .. .. ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
....
.......
100 N
5m
... 30
.
A.
B.
C.
D.
E.
−500 J
−250 J
0
250 J
500 J
ans: E
17. A man pushes an 80-N crate a distance of 5.0 m upward along a frictionless slope that makes
an angle of 30◦ with the horizontal. His force is parallel to the slope. If the speed of the crate
decreases at a rate of 1.5 m/s2 , then the work done by the man is:
A. −200 J
B. 61 J
C. 140 J
D. 200 J
E. 260 J
ans: C
18. A man pushes an 80-N crate a distance of 5.0 m upward along a frictionless slope that makes
an angle of 30◦ with the horizontal. The force he exerts is parallel to the slope. If the speed of
the crate is constant, then the work done by the man is:
A. −200 J
B. 61 J
C. 140 J
D. 200 J
E. 260 J
ans: D
Chapter 7:
KINETIC ENERGY AND WORK
89
19. An 80-N crate slides with constant speed a distance of 5.0 m downward along a rough slope
that makes an angle of 30◦ with the horizontal. The work done by the force of gravity is:
A. −400 J
B. −200 J
C. −69 J
D. 200 J
E. 400 J
ans: D
20. A man pulls a sled along a rough horizontal surface by applying a constant force F at an angle
θ above the horizontal. In pulling the sled a horizontal distance d, the work done by the man
is:
A. F d
B. F d cos θ
C. F d sin θ
D. F d/ cos θ
E. F d/ sin θ
ans: B
21. A man wishes to pull a crate 15 m across a rough floor by exerting a force of 100 N. The
coefficient of kinetic friction is 0.25. For the man to do the least work, the angle between the
force and the horizontal should be:
A. 0
B. 14◦
C. 43◦
D. 66◦
E. 76◦
ans: A
22. A particle moves 5 m in the positive x direction while being acted upon by a constant force
F = (4 N)î + (2 N)ĵ − (4 N)k̂. The work done on the particle by this force is:
A. 20 J
B. 10 J
C. −20 J
D. 30 J
E. is impossible to calculate without knowing other forces
ans: A
23. A block is attached to the end of an ideal spring and moved from coordinate xi to coordinate
xf . The relaxed position is at x = 0. The work done by spring is positive if:
A. xi = 2 cm and xf = 4 cm
B. xi = −2 cm and xf = 4 cm
C. xi = −2 cm and xf = −4 cm
D. xi = 2 cm and xf = −4 cm
E. xi = −4 cm and xf = −2 cm
ans: E
90
Chapter 7:
KINETIC ENERGY AND WORK
24. An ideal spring, with a pointer attached to its end, hangs next to a scale. With a 100-N weight
attached, the pointer indicates “40” on the scale as shown. Using a 200-N weight instead results
in “60” on the scale. Using an unknown weight X instead results in “30” on the scale. The
weight of X is:
.. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. ..
.. .. .. .. .. .. .. ........................ .. .. .. .. .. .. .. .. .. ..
.....
..... ......................................
.
............
......
..... ..................................................................
..
.....
..... ...................................................................
.....
..............
..
..... ....................................................................
.
..............
......
...... .................................................................
...........
......
...... ...................................................................
.
............
......
..... ..................................................................
...........
......
...... ................................................................
........
...
..... ...................................
.......
.........................................................
....
•
0
•
40
100 N
A.
B.
C.
D.
E.
10 N
20 N
30 N
40 N
50 N
ans: E
25. Three identical ideal springs (X,Y,Z) are arranged as shown. When a 4.0-kg mass is hung on
X, the mass descends 3.0 cm. When a 6.0-kg mass is hung on Y, the mass descends:
.. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. ..
.. .. ......................... .. .. .. .. .. .. ......................... .. .. .. .. ..
...
...
..... ..................................
..... ..................................
.
.
...............
..............
.......
.......
...... .................................................................
...... .................................................................
.
.
..............
..............
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.......
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...........
...........
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.......
...... .................................................................
...... .................................................................
..............
.......
..............
.......
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.......
.....................................................................
.....................................................................
.............
.............
........
........
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...................................................................
.
.
.....
.....
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..... ...................................................................
.....
.....
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...
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......
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.
.....
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.....
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..
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.....
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..
.
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..............
.......
......................................................................
...........
.
.
.
.......
...... ...........................................................
..............
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.......
...................................................................
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....
..... ...............................
.......
............
•
•
X
Z
•
•
Y
•
A.
B.
C.
D.
E.
2.0 cm
4.0 cm
4.5 cm
6.0 cm
9.0 cm
ans: E
Chapter 7:
KINETIC ENERGY AND WORK
91
26. When a certain rubber band is stretched a distance x, it exerts a restoring force of magnitude
F = Ax, where A is a constant. The work done by a person in stretching this rubber band
from x = 0 to x = L, beginning and ending at rest, is:
A. AL2
B. A + 2L
C. A + 2L2
D. A/L
E. AL2 /2
ans: E
27. When a certain rubber band is stretched a distance x, it exerts a restoring force of magnitude
F = ax + bx2 , where a and b are constants. The work done in stretching this rubber band from
x = 0 to x = L is:
A. aL2 + bLx3
B. aL + 2bL2
C. a + 2bL
D. bL
E. aL2 /2 + bL3 /3
ans: E
28. An ideal spring is hung vertically from the ceiling. When a 2.0-kg mass hangs at rest from it
the spring is extended 6.0 cm from its relaxed length. A downward external force is now applied
to the mass to extend the spring an additional 10 cm. While the spring is being extended by
the force, the work done by the spring is:
A. −3.6 J
B. −3.3 J
C. −3.4 × 10−5 J
D. 3.3 J
E. 3.6 J
ans: A
29. An ideal spring is hung vertically from the ceiling. When a 2.0-kg block hangs at rest from it
the spring is extended 6.0 cm from its relaxed length. A upward external force is then applied
to the block to move it upward a distance of 16 cm. While the block is moving upward the
work done by the spring is:
A. −1.0 J
B. −0.52 J
C. −0.26 J
D. 0.52 J
E. 1.0 J
ans: A
92
Chapter 7:
KINETIC ENERGY AND WORK
30. Which of the following bodies has the largest kinetic energy?
A. Mass 3M and speed V
B. Mass 3M and speed 2V
C. Mass 2M and speed 3V
D. Mass M and speed 4V
E. All four of the above have the same kinetic energy
ans: C
31. Two trailers, X with mass 500 kg and Y with mass 2000 kg, are being pulled at the same speed.
The ratio of the kinetic energy of Y to that of X is:
A. 1:1
B. 2:1
C. 4:1
D. 9:1
E. 1500:1
ans: C
32. A 8000-N car is traveling at 12 m/s along a horizontal road when the brakes are applied. The
car skids to a stop in 4.0 s. How much kinetic energy does the car lose in this time?
A. 4.8 × 104 J
B. 5.9 × 104 J
C. 1.2 × 105 J
D. 5.8 × 105 J
E. 4.8 × 106 J
ans: B
33. The velocity of a particle moving along the x axis changes from vi to vf . For which values of
vi and vf is the total work done on the particle positive?
A. vi = 5 m/s, vf = 2 m/s
B. vi = 5 m/s, vf = −2 m/s
C. vi = −5 m/s, vf = −2 m/s
D. vi = −5 m/s, vf = 2 m/s
E. vi = 2 m/s, vf = −5 m/s
ans: E
34. An object is constrained by a cord to move in a circular path of radius 0.5 m on a horizontal
frictionless surface. The cord will break if its tension exceeds 16 N. The maximum kinetic
energy the object can have is:
A. 4 J
B. 8 J
C. 16 J
D. 32 J
E. 64 J
ans: A
Chapter 7:
KINETIC ENERGY AND WORK
93
35. The weight of an object on the moon is one-sixth of its weight on Earth. The ratio of the
kinetic energy of a body on Earth moving with speed V to that of the same body moving with
speed V on the moon is:
A. 6:1
B. 36:1
C. 1:1
D. 1:6
E. 1:36
ans: C
36. Which of the following is the correct combination of dimensions for energy?
A. MLT
B. LT2 /m
C. ML2 /T2
D. M2 L3 T
E. ML/T2
ans: C
37. The amount of work required to stop a moving object is equal to:
A. the velocity of the object
B. the kinetic energy of the object
C. the mass of the object times its acceleration
D. the mass of the object times its velocity
E. the square of the velocity of the object
ans: B
38. A 5.0-kg cart is moving horizontally at 6.0 m/s. In order to change its speed to 10.0 m/s, the
net work done on the cart must be:
A. 40 J
B. 90 J
C. 160 J
D. 400 J
E. 550 J
ans: C
94
Chapter 7:
KINETIC ENERGY AND WORK
39. A crate is initially at rest on a horizontal frictionless table. A constant horizontal force F is
applied. Which of the following five graphs is a correct plot of work W as a function of the
crate’s speed v?
W
W
...
.....
.
.
.
.
....
.....
.
.
.
..
.....
.
.
.
..
v
A
.
..
... .. .....
. ...
.......
.
.
....
.....
.
.
.
...
.....
.
.
.
.
..
v
B
W
W
..
..
....
....
..........
.......
.
.
.
.
.
.
....
....
.
.
.
.
.
.....
.....
v
C
..
...
W
.
..
..
.
..
...
.
.
..
.....
.
.
.
.
.
..........
v
D
............
.....
.
.
.
...
...
.
.
...
..
.
.
v
E
ans: D
40. An 8-N block slides down an incline. It has an initial speed of 7 m/s. The work done by the
resultant force on this block is:
A. 3 J
B. 6 J
C. 56 J
D. impossible to calculate without more information
E. none of these
ans: D
41. A 4-kg cart starts up an incline with a speed of 3 m/s and comes to rest 2 m up the incline.
The total work done on the car is:
A. 6 J
B. 8 J
C. 12 J
D. 18 J
E. impossible to calculate without more information
ans: D
42. Two objects with masses of m1 and m2 have the same kinetic energy and are both moving to
the right. The same constant force F is applied to the left to both masses. If m1 = 4m2 , the
ratio of the stopping distance of m1 to that of m2 is:
A. 1:4
B. 4:1
C. 1:2
D. 2:1
E. 1:1
ans: E
Chapter 7:
KINETIC ENERGY AND WORK
95
43. A Boston Red Sox baseball player catches a ball of mass m that is moving toward him with
speed v. While bringing the ball to rest, his hand moves back a distance d. Assuming constant
deceleration, the horizontal force exerted on the ball by his hand is:
A. mv/d
B. mvd
C. mv 2 /d
D. 2mv/d
E. mv 2 /(2d)
ans: E
44. A 0.50-kg object moves on a horizontal circular track with a radius of 2.5 m. An external force
of 3.0 N, always tangent to the track, causes the object to speed up as it goes around. If it
starts from rest its speed at the end of one revolution is:
A. 9.8 m/s
B. 14 m/s
C. 15 m/s
D. 19 m/s
E. 21 m/s
ans: B
45. A 0.50-kg object moves on a horizontal frictionless circular track with a radius of 2.5 m. An
external force of 3.0 N, always tangent to the track, causes the object to speed up as it goes
around. If it starts from rest, then at the end of one revolution the radial component of the
force of the track on it is:
A. 19 N
B. 38 N
C. 47 N
D. 75 N
E. 96 N
ans: B
46. A 2-kg block is attached to a horizonal ideal spring with a spring constant of 200 N/m. When
the spring has its equilibrium length the block is given a speed of 5 m/s. What is the maximum
elongation of the spring?
A. 0
B. 0.05 m
C. 5 m
D. 10 m
E. 100 m
ans: C
96
Chapter 7:
KINETIC ENERGY AND WORK
47. At time t = 0 a particle starts moving along the x axis. If its kinetic energy increases uniformly
with t the net force acting on it must be:
A. constant
B. proportional to t
C. inversely proportional
to t
√
D. proportional to t√
E. proportional to 1/ t
ans: E
48. At time t = 0 a 2-kg particle has a velocity of (4 m/s) î − (3 m/s) ĵ. At t = 3 s its velocity is
(2 m/s) î + (3 m/s) ĵ. During this time the work done on it was:
A. 4 J
B. −4 J
C. −12 J
D. −40 J
E. (4 J)î + (36 J)ĵ
ans: C
49. A particle starts from rest at time t = 0 and moves along the x axis. If the net force on it is
proportional to t, its kinetic energy is proportional to:
A. t
B. t2
C. t4
D. 1/t2
E. none of the above
ans: C
50. A 1.5-kg crate falls from a height of 2.0 m onto an industrial spring scale with a spring constant
of 1.5 × 105 N/m. At its greatest compression the reading on the scale is:
A. 15 N
B. 30 N
C. 1.5 × 103 N
D. 2.1 × 103 N
E. 3.0 × 103 N
ans: E
51. A particle moving along the x axis is acted upon by a single force F = F0 e−kx , where F0 and
k are constants. The particle is released from rest at x = 0. It will attain a maximum kinetic
energy of:
A. F0 /k
B. F0 /ek
C. kF0
D. 1/2(kF0 )2
E. kek F0
ans: A
Chapter 7:
KINETIC ENERGY AND WORK
97
52. The mechanical advantage of any machine is:
A. the efficiency of the machine
B. the work done by the machine
C. the ratio of the work done by the machine to the work expended on it
D. the ratio of the force exerted by the machine to the force applied to it
E. the ratio of the force applied to the machine to the force exerted by it
ans: D
53. In raising an object to a given height by means of an inclined plane, as compared with raising
the object vertically, there is a reduction in:
A. work required
B. distance pushed
C. friction
D. force required
E. value of the acceleration due to gravity
ans: D
54. A watt is:
3
A. kg · m/s
B. kg · m2 /s
C. kg · m2 /s3
D. kg · m/s
2
E. kg · m2 /s
ans: C
55. Power has the dimensions of:
A. ML2 /T2
B. MT/L2
C. ML/T2
D. ML2 /T3
E. none of these
ans: D
56. Which of the following five units represents a quantity that is NOT the same as the other four?
A. joule
B. erg
C. watt
D. foot·pound
E. newton·meter
ans: C
98
Chapter 7:
KINETIC ENERGY AND WORK
57. Which of the following five quantities is NOT an expression for energy? Here m is a mass,
g is the acceleration due to gravity, h and d are distances, F is a force, v is a speed, a is an
acceleration, P is power, and t is time.
A. mgh
B. F d
C. 1/2mv2
D. ma
E. P t
ans: D
58. A watt·second is a unit of:
A. force
B. power
C. displacement
D. speed
E. energy
ans: E
59. A watt per hour is a unit of:
A. energy
B. power
C. force
D. acceleration
E. none of these
ans: E
60. A kilowatt·hour is a unit of:
A. power
B. energy/time
C. work
D. power/time
E. force/distance
ans: C
Chapter 7:
KINETIC ENERGY AND WORK
99
61. A man moves the 10-g object shown in a vertical plane from position X to position Y along a
circular track of radius 20 m. The process takes 0.75 min. The work done by the man is about:
Y
•
........................................
........
......
......
.....
..........
.....
.
.
.
...... ..
.
...
.....
..
...
.
...
....
..
....
...
..
...
...
...
...
...
..
.
...
.
.
.
...
..
...
...
...
...
....
....
.....
....................
.......
..........
....
............................. .
object
A.
B.
C.
D.
E.
•••••••••••••••••••••••••
••••
.............
......
...
...
..........................
X
1J
2J
4J
6J
12 J
ans: C
62. A woman lifts a barbell 2.0 m in 5.0 s. If she lifts it the same distance in 10 s, the work done
by her is:
A. four times as great
B. two times as great
C. the same
D. half as great
E. one-fourth as great
ans: C
63. An escalator is used to move 20 people (60 kg each) per minute from the first floor of a department store to the second floor, 5 m above. Neglecting friction, the power required is
approximately:
....
.......
.......
.......
.
.
.
.
.
.
......
.......
.......
.......
.......
.
.
.
.
.
.........
.
......
..
.......
.......
.......
.......
.
.
.
.
.
.
.
.......
.......
...........
.......
.......
......
.
.
.
.
.
.......
.......
......
.......
.......
.
.
.
.
.
.
.......
......
◦
......
.......
......
............
30
A.
B.
C.
D.
E.
100
100 W
200 W
1000 W
2000 W
60, 000 W
ans: C
Chapter 7:
KINETIC ENERGY AND WORK
↑
|
|
|
5m
|
|
|
↓
64. A person holds an 80-N weight 2 m above the floor for 30 seconds. The power required to do
this is:
A. 80 W
B. 40 W
C. 20 W
D. 10 W
E. none of these
ans: E
65. A 50-N force is the only force on a 2-kg object that starts from rest. When the force has been
acting for 2 s the rate at which it is doing work is:
A. 75 W
B. 100 W
C. 1000 W
D. 2500 W
E. 5000 W
ans: D
66. A 50-N force is the only force a 2-kg crate that starts from rest. At the instant the object has
gone 2 m the rate at which the force is doing work is:
A. 2.5 W
B. 25 W
C. 75 W
D. 100 W
E. 500 W
ans: E
67. A particle starts from rest and is acted on by a net force that does work at a rate that is
proportional to the time t. The speed of the particle is proportional to:
√
t
A.
B. t
C. t2 √
D. 1/ t
E. 1/t
ans: A
Chapter 7:
KINETIC ENERGY AND WORK
101
Chapter 8:
POTENTIAL ENERGY AND CONSERVATION OF ENERGY
1. Only if a force on a particle is conservative:
A. is its work zero when the particle moves exactly once around any closed path
B. is its work always equal to the change in the kinetic energy of the particle
C. does it obey Newton’s second law
D. does it obey Newton’s third law
E. is it not a frictional force
ans: A
2. A nonconservative force:
A. violates Newton’s second law
B. violates Newton’s third law
C. cannot do any work
D. must be perpendicular to the velocity of the particle on which it acts
E. none of the above
ans: E
3. The sum of the kinetic and potential energies of a system of objects is conserved:
A. only when no external force acts on the objects
B. only when the objects move along closed paths
C. only when the work done by the resultant external force is zero
D. always
E. none of the above
ans: E
4. A force on a particle is conservative if:
A. its work equals the change in the kinetic energy of the particle
B. it obeys Newton’s second law
C. it obeys Newton’s third law
D. its work depends on the end points of every motion, not on the path between
E. it is not a frictional force
ans: D
5. Two particles interact by conservative forces. In addition, an external force acts on each
particle. They complete round trips, ending at the points where they started. Which of the
following must have the same values at the beginning and end of this trip?
A. the total kinetic energy of the two-particle system
B. the potential energy of the two-particle system
C. the mechanical energy of the two-particle system
D. the total linear momentum of the two-particle system
E. none of the above
ans: B
102
Chapter 8:
POTENTIAL ENERGY AND CONSERVATION OF ENERGY
6. Two objects interact with each other and with no other objects. Initially object A has a speed
of 5 m/s and object B has a speed of 10 m/s. In the course of their motion they return to their
initial positions. Then A has a speed of 4 m/s and B has a speed of 7 m/s. We can conclude:
A. the potential energy changed from the beginning to the end of the trip
B. mechanical energy was increased by nonconservative forces
C. mechanical energy was decreased by nonconservative forces
D. mechanical energy was increased by conservative forces
E. mechanical energy was decreased by conservative forces
ans: C
7. A good example of kinetic energy is provided by:
A. a wound clock spring
B. the raised weights of a grandfather’s clock
C. a tornado
D. a gallon of gasoline
E. an automobile storage battery
ans: C
8. No
A.
B.
C.
D.
E.
kinetic energy is possessed by:
a shooting star
a rotating propeller on a moving airplane
a pendulum at the bottom of its swing
an elevator standing at the fifth floor
a cyclone
ans: D
9. The wound spring of a clock possesses:
A. kinetic but no potential energy
B. potential but no kinetic energy
C. both potential and kinetic energy in equal amounts
D. neither potential nor kinetic energy
E. both potential and kinetic energy, but more kinetic energy than potential energy
ans: B
10. A body at rest in a system is capable of doing work if:
A. the potential energy of the system is positive
B. the potential energy of the system is negative
C. it is free to move in such a way as to decrease its kinetic energy
D. it is free to move in such a way as to decrease the potential energy of the system
E. it is free to move in such a way as to increase the potential energy of the system
ans: D
Chapter 8:
POTENTIAL ENERGY AND CONSERVATION OF ENERGY
103
11. Which one of the following five quantities CANNOT be used as a unit of potential energy?
A. watt·second
B. gram·cm/s2
C. joule
D. kg·m2 /s2
E. ft·lb
ans: B
12. Suppose that the fundamental dimensions are taken to be: force (F), velocity (V) and time
(T). The dimensions of potential energy are then:
A. F/T
B. FVT
C. FV/T
D. F/T2
E. FV2 /T2
ans: B
13. The graphs below show the magnitude of the force on a particle as the particle moves along the
positive x axis from the origin to x = x1 . The force is parallel to the x axis and is conservative.
The maximum magnitude F1 has the same value for all graphs. Rank the situations according
to the change in the potential energy associated with the force, least (or most negative) to
greatest (or most positive).
F
F
F1 .........
......
......
......
......
......
x1 x
1
A.
B.
C.
D.
E.
104
F
F1 ..............................................
...
...
...
...
x1 x
2
x1
.....
...... x
.
.
.
.
.....
......
.
.
.
.
.
..
F1 ....
3
1, 2, 3
1, 3, 2
2, 3, 1
3, 2, 1
2, 1, 3
ans: E
Chapter 8:
POTENTIAL ENERGY AND CONSERVATION OF ENERGY
14. A golf ball is struck by a golf club and falls on a green three meters above the tee. The potential
energy of the Earth-ball system is greatest:
A. just before the ball is struck
B. just after the ball is struck
C. just after the ball lands on the green
D. when the ball comes to rest on the green
E. when the ball reaches the highest point in its flight
ans: E
15. A ball is held at a height H above a floor. It is then released and falls to the floor. If air
resistance can be ignored, which of the five graphs below correctly gives the mechanical energy
E of the Earth-ball system as a function of the altitude y of the ball?
y
••••••••
. . . . . . . . . . . . .
... ... ... ... ... ... ... ... ... ... ... ... ...
E ........
.......
.....
....
....
...
...
...
...
y
H
A
E
ans: E
H
0
E ..
.....
.....
.....
.....
.....
.....
.....
.. y
H
B
.
..
.
.
...
.
.
..
....
.
.
.
.
.
............
y
H
D
E
.
.....
.
.
.
.
....
....
.
.
.
.
...
....
.
.
...
y
H
C
E
...........................................
H
y
E
16. A 6.0-kg block is released from rest 80 m above the ground. When it has fallen 60 m its kinetic
energy is approximately:
A. 4800 J
B. 3500 J
C. 1200 J
D. 120 J
E. 60 J
ans: B
Chapter 8:
POTENTIAL ENERGY AND CONSERVATION OF ENERGY
105
17. A 2-kg block is thrown upward from a point 20 m above Earth’s surface. At what height above
Earth’s surface will the gravitational potential energy of the Earth-block system have increased
by 500 J?
A. 5 m
B. 25 m
C. 46 m
D. 70 m
E. 270 m
ans: C
18. An
I.
II.
III.
IV.
V.
A.
B.
C.
D.
E.
elevator is rising at constant speed. Consider the following statements:
the upward cable force is constant
the kinetic energy of the elevator is constant
the gravitational potential energy of the Earth-elevator system is constant
the acceleration of the elevator is zero
the mechanical energy of the Earth-elevator system is constant
all five are true
only II and V are true
only IV and V are true
only I, II, and III are true
only I, II, and IV are true
ans: E
19. A projectile of mass 0.50 kg is fired with an initial speed of 10 m/s at an angle of 60◦ above
the horizontal. The potential energy of the projectile-Earth system (relative potential energy
when the projectile is at ground level) is:
A. 25 J
B. 18.75 J
C. 12.5 J
D. 6.25 J
E. none of these
ans: B
20. For a block of mass m to slide without friction up the rise of height h shown, it must have a
minimum initial kinetic energy of:
nv
..
.................................................
..
...........................................................................................................................................................
m
A.
B.
C.
D.
E.
106
........................................................................
....... ........
....
..
....
.
...
..
.
..
.
.
.
.
...
...
....
........
.....
.
..........
h
gh
mgh
gh/2
mgh/2
2mgh
ans: B
Chapter 8:
POTENTIAL ENERGY AND CONSERVATION OF ENERGY
21. A 2.2-kg block starts from rest on a rough inclined plane that makes an angle of 25◦ with the
horizontal. The coefficient of kinetic friction is 0.25. As the block goes 2.0 m down the plane,
the mechanical energy of the Earth-block system changes by:
A. 0
B. −9.8 J
C. 9.8 J
D. −18 J
E. 18 J
ans: B
22. A simple pendulum consists of a 2.0-kg mass attached to a string. It is released from rest at X
as shown. Its speed at the lowest point Y is about:
. . . . . . . . . . .. .. .. .. .. .. .. .. .. .. ..
... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
....
...
....
....
....
....
....
....
...
.... X
••••
••.•.•.••.•.••...•••..•••.••••••••
.
.....•
.
.
.
.
.
.
.
.
.
........
......
.......
........
.........
...
............
....................................................................
Y
A.
B.
C.
D.
E.
...
...
..
..........
....
1.85
m
.
...
..........
...
...
.
0.90 m/s
√
3.6 m/s
3.6 m/s
6.0 m/s
36 m/s
ans: D
23. The long pendulum shown is drawn aside until the ball has risen 0.50 m. It is then given an
initial speed of 3.0 m/s. The speed of the ball at its lowest position is:
.. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. ..
... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
....
...
....
....
....
....
....
....
...
....
••.•.•.••.•..••.•..•.•••••••
•
..•
.....•
•••••••
............... •
.
.
.
.
.
.
...... .....
......
.......
........
.........
............
..........................................................
A.
B.
C.
D.
E.
zero
0.89 m/s
3.1 m/s
3.7 m/s
4.3 m/s
ans: E
Chapter 8:
..
...
..
.........
.....
0.5. m
.......
........
....
..
.
POTENTIAL ENERGY AND CONSERVATION OF ENERGY
107
24. A particle moves along the x axis under the influence of a stationary object. The net force on
3
the particle is given by F = (8 N/m )x3 . If the potential energy is taken to be zero for x = 0
then the potential energy is given by:
4
A. (2 J/m )x4
B. (−2 J/m4 )x4
C. (24 J/m2 x2
2
D. (−24 J/m )x2
4
E. 5 J − (2 J/m )x4
ans: B
25. A 0.20-kg particle moves along the x axis under the influence of a stationary object. The
potential energy is given by
2
4
U (x) = (8.0 J/m )x2 + (2.0 J/m )x4 ,
where x is in coordinate of the particle. If the particle has a speed of 5.0 m/s when it is at
x = 1.0 m, its speed when it is at the origin is:
A. 0
B. 2.5 m/s
C. 5.7 m/s
D. 7.9 m/s
E. 11 m/s
ans: E
26. Which of the five graphs correctly shows the potential energy of a spring as a function of its
elongation x?
U
U
...........................................
x
...
....
.
.
...
.....
.
.
.
.
....
.....
.
.
.
..
A
108
Chapter 8:
x
.
..
..
.
..
...
.
.
..
.....
.
.
.
.
.
.........
B
U
ans: C
U
.......
.......
.
.
.
...
...
.
.
...
..
.
.
D
x
x
C
U.
...
...
...
...
....
.....
......
...........
x
E
POTENTIAL ENERGY AND CONSERVATION OF ENERGY
27. A force of 10 N holds an ideal spring with a 20-N/m spring constant in compression. The
potential energy stored in the spring is:
A. 0.5 J
B. 2.5 J
C. 5 J
D. 10 J
E. 200 J
ans: B
28. An ideal spring is used to fire a 15.0-g pellet horizontally. The spring has a spring constant of
20 N/m and is initially compressed by 7.0 cm. The kinetic energy of the pellet as it leaves the
spring is:
A. zero
B. 2.5 × 10−2 J
C. 4.9 × 10−2 J
D. 9.8 × 10−2 J
E. 1.4 J
ans: C
29. A 0.50-kg block attached to an ideal spring with a spring constant of 80 N/m oscillates on a
horizontal frictionless surface. The total mechanical energy is 0.12 J. The greatest extension
of the spring from its equilibrium length is:
A. 1.5 × 10−3 m
B. 3.0 × 10−3 m
C. 0.039 m
D. 0.054 m
E. 18 m
ans: D
30. A 0.50-kg block attached to an ideal spring with a spring constant of 80 N/m oscillates on a
horizontal frictionless surface. The total mechanical energy is 0.12 J. The greatest speed of the
block is:
A. 0.15 m/s
B. 0.24 m/s
C. 0.49 m/s
D. 0.69 m/s
E. 1.46 m/s
ans: D
31. A 0.50-kg block attached to an ideal spring with a spring constant of 80 N/m oscillates on a
horizontal frictionless surface. When the spring is 4.0 cm longer than its equilibrium length,
the speed of the block is 0.50 m/s. The greatest speed of the block is:
A. 0.23 m/s
B. 0.32 m/s
C. 0.55 m/s
D. 0.71 m/s
E. 0.93 m/s
ans: D
Chapter 8:
POTENTIAL ENERGY AND CONSERVATION OF ENERGY
109
32. A 0.5-kg block slides along a horizontal frictionless surface at 2 m/s. It is brought to rest by
compressing a very long spring of spring constant 800 N/m. The maximum spring compression
is:
A. 0
B. 3 cm
C. 5 cm
D. 80 cm
E. 80 m
ans: C
33. A block of mass m is initially moving to the right on a horizontal frictionless surface at a speed
v. It then compresses a spring of spring constant k. At the instant when the kinetic energy of
the block is equal to the potential energy of the spring, the spring is compressed a distance of:
0
A. v m/2k
B. (1/2)mv2
C. (1/4)mv2
D. mv2 /4k
0
E. (1/4) mv/k
ans: A
34. A 700-N man jumps out of a window into a fire net 10 m below. The net stretches 2 m before
bringing the man to rest and tossing him back into the air. The maximum potential energy of
the net, compared to its unstretched potential energy, is:
A. 300 J
B. 710 J
C. 850 J
D. 7000 J
E. 8400 J
ans: E
35. A toy cork gun contains a spring whose spring constant is 10.0 N/m. The spring is compressed
5.00 cm and then used to propel a 6.00-g cork. The cork, however, sticks to the spring for
1.00 cm beyond its unstretched length before separation occurs. The muzzle velocity of this
cork is:
spring
cork
.......
.
.......
......
.......
......
....... ..
. ......
....
.........
..................
.
.... .....
.
.
.
.
.
.
.
.
.
.
.
.. .
..
........................................................ ...................................................................................................................................................................................................................................................................................................................................................... .
..............
. ..
.......................................................... ....
........
.
.
.
.
.
.
.
.
.
.
.
.
... ...
....
. .. ..... ...... ....... ..... ...... ..... ....... .... ...... ....... ..... .... ..
.. ... ... ....... ... ...... .... ... ....... . ...
......
..
.........
.... .. .... ...... .. . .. .................................
.. ..............................................................................................................................................................................................................................................
...
....
... ... .... ....
.......
.
..
.
.
.
.
.
.
.
.
.
.
.
.
.........................
..
...... ........
....
.. ...
......
..
...........
...
..........
.. .............
.. .....
.....
A.
B.
C.
D.
E.
110
..
.......
....•
.
•
•
•
•
•...
•
...•
•
•
.•
..
..•
....
1.02 m/s
1.41 m/s
2.00 m/s
2.04 m/s
4.00 m/s
ans: C
Chapter 8:
POTENTIAL ENERGY AND CONSERVATION OF ENERGY
36. A small object of mass m, on the end of a light cord, is held horizontally at a distance r from
a fixed support as shown. The object is then released. What is the tension force of the cord
when the object is at the lowest point of its swing?
..............r..........••.•••.•.••••.•••.••.••• m
••••
...
...
...
...
...
..
...
..
.
...
.
..
...
....
...
.........
....
............
.......
.....
.. ........
.
.
.
.
.
..........
..
.............................
A.
B.
C.
D.
E.
mg/2
mg
2mg
3mg
mgr
ans: D
37. The string in the figure is 50 cm long. When the ball is released from rest, it swings along the
dotted arc. How fast is it going at the lowest point in its swing?
...
..
...
..
A.
B.
C.
D.
E.
...
..
.........
..........
.....50
..........cm
.........•••.•.••.••••.•••.•..•••
•••....••
.......
......
....... .......
.
. ...
.........
.....
2.0 m/s
2.2 m/s
3.1 m/s
4.4 m/s
6.0 m/s
ans: C
38. A block is released from rest at point P and slides along the frictionless track shown. At point
Q, its speed is:
P
...........................
↑ .....
...
|
...
|
...
Q
...
.......↑.|...............
...
.
h1
.
.
.
.
.
....
..
......
.....
.................
|
....
h
2
|
↓. . . . . . .
↓
. . . . . . . . . . . . . . . . . . |
.. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. ..
... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
ground level
A.
B.
C.
D.
E.
√
2g h1 − h2
2g(h1 − h2 )
(h
01 − h2 )/2g
2g(h1 − h2 )
(h1 − h2 )2 /2g
ans: D
Chapter 8:
POTENTIAL ENERGY AND CONSERVATION OF ENERGY
111
39. A small object of mass m starts from rest at the position shown and slides along the frictionless
loop-the-loop track of radius R. What is the smallest value of y such that the object will slide
without losing contact with the track?
....
...
... ..........
...
......
...
.
...
..
.........
.
................
......
............ .....
.............
......
......
......
......
............................
......
.....
.......
......
....
.........
.....
......
... ....
..
...
......
... .....
..
.
......
.
.
...
...
..
......
... ......
..
...
...
...... ...
.
.
.
.
.
.
.
.
.
.
.
.
....
..
..
....................
.
.
.
.
......
...
.......
.
.......
.
...
.... ..
.......
...
........
...
...
.........
..
...........
...
.....
............... ...........
...................................................................................................................................................................
.......
m
y
R
A.
B.
C.
D.
E.
R/4
R/2
R
2R
zero
ans: B
40. A small object slides along the frictionless loop-the-loop with a diameter of 3 m. What minimum
speed must it have at the top of the loop?
....
... ..........
......
...
....
.......
......
...... .....
.......
......
......
......
......
..................................
......
......
.....
......
.....
...
......
...
...
......
...
...
.
......
.
.
........
...
...... ..
.
......
..
.....................
....
.
...
......
........
...
......
..... ...
.......
.
...
.
........
.
.
...
.........
...
.
..........
.............. ..........
.....
.....................................................................................................................................................................
........
↑|
3m
↓|
A.
B.
C.
D.
E.
1.9 m/s
3.8 m/s
5.4 m/s
15 m/s
29 m/s
ans: B
41. A rectangular block is moving along a frictionless path when it encounters the circular loop as
shown. The block passes points 1, 2, 3, 4, 1 before returning to the horizontal track. At point
3:
•
3
..........
. ................... ....................
......
..............
......
........
..............
..
.
.
......
...
...
.
.
...
.
.
..
....
..
..
...
..
...
...
...
...
..
.
...
.
.
.
...
..
.....
...
...
..................
....
.....
..................
......
.
........
..
..
........ ..
........................................................................................................................................................................................................................................................................
..
..
•1
2•
1
•
A.
B.
C.
D.
E.
112
its mechanical energy is a minimum
the forces on it are balanced
it is not accelerating
its speed is a minimum
it experiences a net upward force
ans: D
Chapter 8:
POTENTIAL ENERGY AND CONSERVATION OF ENERGY
42. A ball of mass m, at one end of a string of length L, rotates in a vertical circle just fast enough
to prevent the string from going slack at the top of the circle. The speed of the ball at the
bottom of the circle is:
...................................
......
..........
.....
.....
....
...
...
...
.
...
..
.
...
.....
...
...
..
...
.....
...
.........
.
...
.
.
...
...
...
...
....
...
.....
.....
.
.
.
...................
.
.
.................................
A.
B.
C.
D.
E.
•......
....L
.....
••••••.•••• m
√
√2gL
√3gL
√4gL
√5gL
7gL
ans: D
43. A particle is released from rest at the point x = a and moves along the x axis subject to the
potential energy function U (x) shown. The particle:
U
...
.
...
..
.
...
..
...
...
.. .
...
.
...
..
...
.
...
...
..
....
... .....
.
.
.
.
.
....
..
....
.. .....
...
.
..... .....
.
.
.
.... ...
..........
............
.
x
a
A.
B.
C.
D.
E.
moves to
moves to
moves to
moves to
moves to
ans: B
b
c
d
e
a point to the left of x = e, stops, and remains at rest
a point to x = e, then moves to the left
infinity at varying speed
x = b, where it remains at rest
x = e and then to x = d, where it remains at rest
44. The potential energy of a particle moving along the x axis is given by
2
4
U (x) = (8.0 J/m )x2 + (2.0 J/m )x4 .
If the total mechanical energy is 9.0 J, the limits of motion are:
A. −0.96 m; +0.96 m
B. −2.2 m; +2.2 m
C. −1.6 m; +1.6 m
D. −0.96 m; +2.2 m
E. −0.96 m; +1.6 m
ans: A
Chapter 8:
POTENTIAL ENERGY AND CONSERVATION OF ENERGY
113
45. The potential energy of a 0.20-kg particle moving along the x axis is given by
2
4
U (x) = (8.0 J/m )x2 + (2.0 J/m )x4 .
When the particle is at x = 1.0 m it is traveling in the positive x direction with a speed of
5.0 m/s. It next stops momentarily to turn around at x =
A. 0
B. −1.1 m
C. 1.1 m
D. −2.3 m
E. 2.3 m
ans: C
46. Given a potential energy function U (x), the corresponding force Fn is in the positive x direction
if:
A. U is positive
B. U is negative
C. U is an increasing function of x
D. U is a decreasing function of x
E. it is impossible to obtain the direction of Fn from U
ans: D
47. As a particle moves along the x axis it is acted upon by a conservative force. The potential
energy is shown below as a function of the coordinate x of the particle. Rank the labeled
regions according to the magnitude of the force, least to greatest.
..
U (x)
..
.
.
.....................................
...
..
.
...
.
...
..
...
.
...
.
...
..
...
.
...
..
...
.
.
.........................
A
A.
B.
C.
D.
E.
114
B
C
D x
AB, BC, CD
AB, CD, BC
BC, CD, AB
BC, AB, CD
CD, BC, AB
ans: D
Chapter 8:
POTENTIAL ENERGY AND CONSERVATION OF ENERGY
48. The first graph shows the potential energy U (x) for a particle moving on the x axis. Which of
the other five graphs correctly gives the force F exerted on the particle?
U
F
... parabola
.
..
...
...
...
...
.
...
..
.
...
.
...
..
...
.
...
....
..... .......
..............
x
F
..
...
..
.. .
..
.............
.
.
x
.
.
...
.. .
..
...
.
..
... F
...
...
...
...
...
...
...
...
x
...
...
...
...
...
...
...
..
......................... x
.....
....
.
.
.
...
..
.
...
A
B
F.
...
...
...
...
...
...
...
...
...
x
...
...
...
...
...
...
...
.
D
C
F
...
..
...
...
.
....
.
..
......
.................... x
E
ans: D
Chapter 8:
POTENTIAL ENERGY AND CONSERVATION OF ENERGY
115
49. The diagram shows a plot of the potential energy as a function of x for a particle moving along
the x axis. The points of stable equilibrium are:
U
...
.
...
...................
...
.....
...
.
...
.
...
...
......
.
.
...
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
...
.
.
.
.
...
...
...
...
.
...
.
...
.
.... ...
...
......
...
...
x
a b
A.
B.
C.
D.
E.
c
d
e
only a
only b
only c
only d
b and d
ans: B
50. The diagram shows a plot of the potential energy as a function of x for a particle moving along
the x axis. The points of unstable equilibrium are:
U
...
...
.....
....... .........
...
.....
...
.
...
.
...
...
.....
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
...
.
.
.
.
...
.
.
.
.
...
...
..
.
...
... ..
...
.... ...
...
.......
...
..
x
a b
A.
B.
C.
D.
E.
116
c
d
e
only a
only b
only c
only d
b and d
ans: D
Chapter 8:
POTENTIAL ENERGY AND CONSERVATION OF ENERGY
51. The diagram shows a plot of the potential energy as a function of x for a particle moving along
the x axis. Of the labeled points, the points of neutral equilibrium are:
U
...
.
...
...................
...
.....
...
.
...
.
...
...
......
.
.
...
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
...
.
.
.
.
...
...
...
...
.
...
.
...
.
.... ...
...
......
...
...
x
a b
A.
B.
C.
D.
E.
c
d
e
only a
only b
only c
only d
b and d
ans: C
52. The potential energy of a body of mass m is given by U = −mgx + 12 kx2 . The corresponding
force is:
A. −mgx2 /2 + kx3 /6
B. mgx2 /2 − kx3 /6
C. −mg + kx/2
D. −mg + kx
E. mg − kx
ans: E
53. The potential energy of a 0.20-kg particle moving along the x axis is given by
2
4
U (x) = (8.0 J/m )x2 + (2.0 J/m )x4 .
When the particle is at x = 1.0 m the magnitude of its acceleration is:
A. 0
B. −8 m/s2
2
C. 8 m/s
2
D. −40 m/s
2
E. 40 m/s
ans: D
Chapter 8:
POTENTIAL ENERGY AND CONSERVATION OF ENERGY
117
54. The potential energy for the interaction between the two atoms in a diatomic molecule is
U = A/x12 − B/x6 , where A and B are constants and x is the interatomic distance. The
magnitude of the force of one atom on the other is:
F
A.
B.
C.
D.
E.
••••••••••
•••••••••••••••••••••••••••••
•••••••••••••••••••••••••••••••••••••....................................................... F
••••••••••••••••••••••••••••
••••••••••
←−−−−−−−−− x −−−−−−−−−→
••••••
••••••••••••••••••••••
•••••••
..
..........................................................
..
12A/|x|13 − 6B/|x|7
−13A/|x|13 + 7B/|x|7
−11A/|x|11 + 5B/|x|5
72A/|x|12 − 72B/|x|6
A/|x|13 − B/|x|7
ans: A
55. The thermal energy of a system consisting of a thrown ball, Earth, and the air is most closely
associated with:
A. the gravitational interaction of Earth and the ball
B. the kinetic energy of the ball as a whole
C. motions of the individual particles within the ball
D. motions of individual particles within the ball and the air
E. the kinetic energy of Earth as a whole
ans: D
56. Three identical blocks move either on a horizontal surface, up a plane, or down a plane, as
shown below. They start with different speeds and continue to move until brought to rest by
friction. They all move the same distance. Rank the three situations according to the initial
speeds, least to greatest.
nv
..
...
.....................................
..
nv
. . . . . . . . . . . . . . . . . . . . . . . .
... ... ... ... ... .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. ... ... ... ...
... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... .... .... ... ... ... ...
... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... .. .. .. .. .. ..
(1)
A.
B.
C.
D.
E.
118
.
.............
..........
...... ..... ................
.......
..........
......
.......
...
...........
......
.
.
.
.
.
.
... .........................
......
...................
.......
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
......
......... ....
...
......... .....
.......... .....
...
................
...
.................... .
.
...
.
.
.
.
.
.
.
.
.
...
.... . . .
.. .......................
.......... .. .. .
......... .. .. .
................... .
.
.
.
.
.
.
... . . .
.............. ..
.. ...... .
...... .
...
(2)
nv
.
..........
...... .....
.......
...
...
.......
...
.........
......
.
.
.
...
.
.............
.
......
... ..........................
.......
........... .
.
.
.
.
.
.
.
.
.
.
.
.
.
......
................
...
.......... ..
...
................
.............. ..
.
.................... .
.......
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
. ...
...
.... . . .
..........
.. ........................
.............
.......... .. .. .
......... .. .. .
................... .
.
.
.
.
.
.
... . . .
.............. ..
.. ...... .
...... .
...
(3)
The same for all cases
1, 2, 3
1, then 2 and 3 tie
3, 1, 2
2, 1, 3
ans: D
Chapter 8:
POTENTIAL ENERGY AND CONSERVATION OF ENERGY
57. Objects A and B interact with each other via both conservative and nonconservative forces.
Let KA and KB be the kinetic energies, U be the potential energy, and Eint be the thermal
energy. If no external agent does work on the objects then:
A. KA + U is conserved
B. KA + U + Eint is conserved
C. KA + KB + Eint is conserved
D. KA + KB + U is conserved
E. KA + KB + U + Eint is conserved
ans: E
58. A block slides across a rough horizontal table top. The work done by friction changes:
A. only the kinetic energy
B. only the potential energy
C. only the internal energy
D. only the kinetic and potential energies
E. only the kinetic and internal energies
ans: E
59. A 25-g ball is released from rest 80 m above the surface of Earth. During the fall the total
internal energy of the ball and air increases by 15 J. Just before it hits the surface its speed is
A. 19 m/s
B. 36 m/s
C. 40 m/s
D. 45 m/s
E. 53 m/s
ans: A
60. A 5-kg projectile is fired over level ground with a velocity of 200 m/s at an angle of 25◦ above
the horizontal. Just before it hits the ground its speed is 150 m/s. Over the entire trip the
change in the internal energy of the projectile and air is:
A. +19, 000 J
B. −19, 000 J
C. +44, 000 J
D. −44, 000 J
E. 0
ans: C
61. A 0.75-kg block slides on a rough horizontal table top. Just before it hits a horizontal ideal
spring its speed is 3.5 m/s. It compresses the spring 5.7 cm before coming to rest. If the spring
constant is 1200 N/m, the internal energy of the block and the table top must have:
A. not changed
B. decreased by 1.9 J
C. decreased by 2.6 J
D. increased by 1.9 J
E. increased by 2.6 J
ans: C
Chapter 8:
POTENTIAL ENERGY AND CONSERVATION OF ENERGY
119
Chapter 9:
CENTER OF MASS AND LINEAR MOMENTUM
1. Which one of the following statements is true?
A. the center of mass of an object must lie within the object
B. all the mass of an object is actually concentrated at its center of mass
C. the center of mass of an object cannot move if there is zero net force on the object
D. the center of mass of a cylinder must lie on its axis
E. none of the above
ans: E
2. The x and y coordinates of the center of mass of the three-particle system shown below are:
y (m)
4m
3m
6 kg
••••••••••••••••••••••••
••••••
2m
••• 5 kg
•••••••••••••••••••••••••••
1m
4 kg
•••••••••••••••••••••••••
••••
1m
A.
B.
C.
D.
E.
2m
3m
4 m x (m)
0, 0
1.3 m, 1.7 m
1.4 m, 1.9 m
1.9 m, 2.5 m
1.4 m, 2.5 m
ans: C
3. The center of mass of a uniform disk of radius R is located:
A. on the rim
B. a distance R/2 from the center
C. a distance R/3 from the center
D. a distance 2R/3 from the center
E. at the center
ans: E
4. The center of mass of the system consisting of Earth, the Sun, and the planet Mars is:
A. closer to Earth than to either of the other bodies
B. closer to the Sun than to either of the other bodies
C. closer to Mars than to either of the other bodies
D. at the geometric center of the triangle formed by the three bodies
E. at the center of the line joining Earth and Mars
ans: B
120
Chapter 9:
CENTER OF MASS AND LINEAR MOMENTUM
5. The center of mass of Earth’s atmosphere is:
A. a little less than halfway between Earth’s surface and the outer boundary of the atmosphere
B. near the surface of Earth
C. near the outer boundary of the atmosphere
D. near the center of Earth
E. none of the above
ans: D
6. A thick uniform wire is bent into the shape of the letter “U” as shown. Which point indicates
the location of the center of mass of this wire?
• A
• B
D •
•
C
• E
ans: B
7. A machinist starts with three identical square plates but cuts one corner from one of them, two
corners from the second, and three corners from the third. Rank the three plates according to
the x coordinate of their centers of mass, from smallest to largest.
y
y
y
x
1
A.
B.
C.
D.
E.
x
2
x
3
1, 2, 3
1 and 2 tie, then 3
1, then 2 and 3 tie
3, 2, 1
1 and 3 tie, then 2
ans: E
Chapter 9:
CENTER OF MASS AND LINEAR MOMENTUM
121
8. Block A, with a mass of 4 kg, is moving with a speed of 2.0 m/s while block B, with a mass of
8 kg, is moving in the opposite direction with a speed of 3 m/s. The center of mass of the two
block-system is moving with a velocity of:
A. 1.3 m/s in the same direction as A
B. 1.3 m/s in the same direction as B
C. 2.7 m/s in the same direction as A
D. 1.0 m/s in the same direction as B
E. 5.0 m/s in the same direction as A
ans: B
9. At the same instant that a 0.50-kg ball is dropped from 25 m above Earth, a second ball, with a
mass of 0.25 kg, is thrown straight upward from Earth’s surface with an initial speed of 15 m/s.
They move along nearby lines and pass each other without colliding. At the end of 2.0 s the
height above Earth’s surface of the center of mass of the two-ball system is:
A. 2.9 m
B. 4.0 m
C. 5.0 m
D. 7.1 m
E. 10.4 m
ans: D
10. At the same instant that a 0.50-kg ball is dropped from 25 m above Earth, a second ball, with a
mass of 0.25 kg, is thrown straight upward from Earth’s surface with an initial speed of 15 m/s.
They move along nearby lines and pass without colliding. At the end of 2.0 s the velocity of
the center of mass of the two-ball system is:
A. 11 m/s, down
B. 11 m/s, up
C. 15 m/s, down
D. 15 m/s, up
E. 20 m/s, down
ans: C
11. At the same instant that a 0.50-kg ball is dropped from 25 m above Earth, a second ball, with a
mass of 0.25 kg, is thrown straight upward from Earth’s surface with an initial speed of 15 m/s.
They move along nearby lines and pass without colliding. At the end of 2.0 s the magnitude of
the acceleration of the center of mass of the two-ball system is:
A. 0.25g
B. 0.50g
C. 0.75g
D. g
E. g/0.75
ans: D
122
Chapter 9:
CENTER OF MASS AND LINEAR MOMENTUM
12. A light rope passes over a light frictionless pulley attached to the ceiling. An object with a large
mass is tied to one end and an object with a smaller mass is tied to the other end. Starting from
rest the heavier object moves downward and the lighter object moves upward with the same
magnitude acceleration. Which of the following statements is true for the system consisting of
the two masses?
A. The center of mass remains at rest.
B. The net external force is zero.
C. The velocity of the center of mass is a constant.
D. The acceleration of the center of mass is g, downward.
E. None of the above statements are true.
ans: E
13. Two 4.0-kg blocks are tied together with a compressed spring between them. They are thrown
from the ground with an initial velocity of 35 m/s, 45◦ above the horizontal. At the highest
point of the trajectory they become untied and spring apart. About how far below the highest
point is the center of mass of the two-block system 2.0 s later, before either fragment has hit
the ground?
A. 12 m
B. 20 m
C. 31 m
D. Can’t tell because the velocities of the fragments are not given.
E. Can’t tell because the coordinates of the highest point are not given.
ans: B
14. The center of mass of a system of particles has a constant velocity if:
A. the forces exerted by the particles on each other sum to zero
B. the external forces acting on particles of the system sum to zero
C. the velocity of the center of mass is initially zero
D. the particles are distributed symmetrically around the center of mass
E. the center of mass is at the geometric center of the system
ans: B
15. The center of mass of a system of particles remains at the same place if:
A. it is initially at rest and the external forces sum to zero
B. it is initially at rest and the internal forces sum to zero
C. the sum of the external forces is less than the maximum force of static friction
D. no friction acts internally
E. none of the above
ans: A
16. A man sits in the back of a canoe in still water. He then moves to the front of the canoe and
sits there. Afterwards the canoe:
A. is forward of its original position and moving forward
B. is forward of its original position and moving backward
C. is rearward of its original position and moving forward
D. is rearward of its original position and moving backward
E. is rearward of its original position and not moving
ans: E
Chapter 9:
CENTER OF MASS AND LINEAR MOMENTUM
123
17. A 640-N hunter gets a rope around a 3200-N polar bear. They are stationary, 20 m apart, on
frictionless level ice. When the hunter pulls the polar bear to him, the polar bear will move:
A. 1.0 m
B. 3.3 m
C. 10 m
D. 12 m
E. 17 m
ans: B
18. Two boys, with masses of 40 kg and 60 kg, respectively, stand on a horizontal frictionless surface
holding the ends of a light 10-m long rod. The boys pull themselves together along the rod.
When they meet the 60-kg boy will have moved what distance?
A. 4 m
B. 5 m
C. 6 m
D. 10 m
E. need to know the forces they exert
ans: A
19. The center of mass of a system of particles obeys an equation similar to Newton’s second law
F = macom , where:
A. F is the net internal force and m is the total mass of the system
B. F is the net internal force and m is the mass acting on the system
C. F is the net external force and m is the total mass of the system
D. F is the force of gravity and m is the mass of Earth
E. F is the force of gravity and m is the total mass of the system
ans: C
20. A large wedge with a mass of 10 kg rests on a horizontal frictionless surface, as shown. A
block with a mass of 5.0 kg starts from rest and slides down the inclined surface of the wedge,
which is rough. At one instant the vertical component of the block’s velocity is 3.0 m/s and
the horizontal component is 6.0 m/s. At that instant the velocity of the wedge is:
5.0 kg
......
....... .....
.......
...
....
.......
...
.......
.......
.
.
...............
.
.
.
.....
....
...
.......
.
.
.
.
...
.
.
.
...
.......
... ............
.......
.......
.
.
.
.
.
.
......
.......
.......
.......
.......
.
.
.
.
.
.
.
.......
.......
.......
.......
......
.
.
.
.
.
..
10 kg
A.
B.
C.
D.
E.
124
3.0 m/s to the left
3.0 m/s to the right
6.0 m/s to the right
6.0 m/s to the left
17 m/s to the right
ans: B
Chapter 9:
CENTER OF MASS AND LINEAR MOMENTUM
21. A 2.0-kg block is attached to one end of a spring with a spring constant of 100 N/m and a
4.0-kg block is attached to the other end. The blocks are placed on a horizontal frictionless
surface and set into motion. At one instant the 2.0-kg block is observed to be traveling to the
right with a speed of 0.50 m/s and the 4.0-kg block is observed to be traveling to the left with
a speed of 0.30 m/s. Since the only forces on the blocks are the force of gravity, the normal
force of the surface, and the force of the spring, we conclude that:
A. the spring is compressed at the time of the observation
B. the spring is not compressed at the time of observation
C. the motion was started with the masses at rest
D. the motion was started with at least one of masses moving
E. the motion was started by compressing the spring
ans: D
22. A 2.0-kg mass is attached to one end of a spring with a spring constant of 100 N/m and a 4.0-kg
mass is attached to the other end. The masses are placed on a horizontal frictionless surface
and the spring is compressed 10 cm. The spring is then released with the masses at rest and
the masses oscillate. When the spring has its equilibrium length for the first time the 2.0-kg
mass has a speed of 0.36 m/s. The mechanical energy that has been lost to the instant is:
A. zero
B. 0.31 J
C. 0.61 J
D. 0.81 J
E. 1.2 J
ans: B
23. Momentum may be expressed in:
A. kg/m
B. gram·s
C. N·s
D. kg/(m·s)
E. N/s
ans: C
24. The momentum of an object at a given instant is independent of its:
A. inertia
B. mass
C. speed
D. velocity
E. acceleration
ans: E
Chapter 9:
CENTER OF MASS AND LINEAR MOMENTUM
125
25. Two bodies, A and B, have equal kinetic energies. The mass of A is nine times that of B. The
ratio of the momentum of A to that of B is:
A. 1:9
B. 1:3
C. 1:1
D. 3:1
E. 9:1
ans: D
26. Two objects, P and Q, have the same momentum. Q has more kinetic energy than P if it:
A. weighs more than P
B. is moving faster than P
C. weighs the same as P
D. is moving slower than P
E. is moving at the same speed as P
ans: B
27. A particle moves along the x axis. Its momentum is graphed below as a function of time. Rank
the numbered regions according to the magnitude of the force acting on the particle, least to
greatest.
p
2
............................................. 3
.
........
.
........
..
........
.
1 ..
......
.
.....
.
.
.....
.
.
..... 4
.
.
.
.....
..
.....
.
.
.....
.....
.....
.
t
A.
B.
C.
D.
E.
1, 2, 3,
2, 3, 4,
1, 4, 3,
1, 3, 4,
2, 4, 3,
ans: B
4
1
2
2
1
28. A 1.0-kg ball moving at 2.0 m/s perpendicular to a wall rebounds from the wall at 1.5 m/s.
The change in the momentum of the ball is:
A. zero
B. 0.5 N · s away from wall
C. 0.5 N · s toward wall
D. 3.5 N · s away from wall
E. 3.5 N · s toward wall
ans: D
126
Chapter 9:
CENTER OF MASS AND LINEAR MOMENTUM
29. If the total momentum of a system is changing:
A. particles of the system must be exerting forces on each other
B. the system must be under the influence of gravity
C. the center of mass must have constant velocity
D. a net external force must be acting on the system
E. none of the above
ans: D
30. When you step on the accelerator to increase the speed of your car, the force that accelerates
the car is:
A. the force of your foot on the accelerator
B. the force of friction of the road on the tires
C. the force of the engine on the drive shaft
D. the normal force of the road on the tires
E. none of the above
ans: B
31. A 2.5-kg stone is released from rest and falls toward Earth. After 4.0 s, the magnitude of its
momentum is:
A. 98 kg · m/s
B. 78 kg · m/s
C. 39 kg · m/s
D. 24 kg · m/s
E. zero
ans: A
32. A 64-kg woman stands on frictionless level ice with a 0.10-kg stone at her feet. She kicks the
stone with her foot so that she acquires a velocity of 0.0017 m/s in the forward direction. The
velocity acquired by the stone is:
A. 1.1 m/s forward
B. 1.1 m/s backward
C. 0.0017 m/s forward
D. 0.0017 m/s backward
E. none of these
ans: B
33. A man is marooned at rest on level frictionless ice. In desperation, he hurls his shoe to the
right at 15 m/s. If the man weighs 720 N and the shoe weighs 4.0 N, the man moves to the left
with a speed of:
A. 0
B. 2.1 × 10−2 m/s
C. 8.3 × 10−2 m/s
D. 15 m/s
E. 2.7 × 103 m/s
ans: C
Chapter 9:
CENTER OF MASS AND LINEAR MOMENTUM
127
34. Two spacemen are floating together with zero speed in a gravity-free region of space. The mass
of spaceman A is 120 kg and that of spaceman B is 90 kg. Spaceman A pushes B away from
him with B attaining a final speed of 0.5 m/s. The final recoil speed of A is:
A. zero
B. 0.38 m/s
C. 0.5 m/s
D. 0.67 m/s
E. 1.0 m/s
ans: B
35. A projectile in flight explodes into several fragments. The total momentum of the fragments
immediately after this explosion:
A. is the same as the momentum of the projectile immediately before the explosion
B. has been changed into kinetic energy of the fragments
C. is less than the momentum of the projectile immediately before the explosion
D. is more than the momentum of the projectile immediately before the explosion
E. has been changed into radiant energy
ans: A
36. A rifle of mass M is initially at rest but free to recoil. It fires a bullet of mass m and velocity
v (relative to the ground). After firing, the velocity of the rifle (relative to the ground) is:
A. −mv
B. −M v/m
C. −mv/M
D. −v
E. mv/M
ans: C
37. Bullets from two revolvers are fired with the same velocity. The bullet from gun #1 is twice as
heavy as the bullet from gun #2. Gun #1 weighs three times as much as gun #2. The ratio
of the momentum imparted to gun #1 to that imparted to gun #2 is:
A. 2:3
B. 3:2
C. 2:1
D. 3:1
E. 6:1
ans: C
128
Chapter 9:
CENTER OF MASS AND LINEAR MOMENTUM
38. A 5-kg object can move along the x axis. It is subjected to a force F in the positive x direction;
a graph of F as a function of time t is shown below. Over the time the force is applied the
change in the velocity of the object is:
F (N)
4
2
A.
B.
C.
D.
E.
....
... .....
.
.. ...
... ....
...
..
...
...
...
..
...
..
...
...
..
...
..
...
..
1
2
3
4
t(s)
0.8 m/s
1.1 m/s
1.6 m/s
2.3 m/s
4.0 m/s
ans: A
39. Force:
A. equals the negative integral (with respect to distance) of the potential energy function
B. is the ability to do work
C. is the rate of change of doing work
D. equals the time rate of change of momentum
E. has dimensions of momentum multiplied by time
ans: D
40. Cart A, with a mass of 0.20 kg, travels on a horizontal air track at 3.0 m/s and hits cart B,
which has a mass of 0.40 kg and is initially traveling away from A at 2.0 m/s. After the collision
the center of mass of the two cart system has a speed of:
A. zero
B. 0.33 m/s
C. 2.3 m/s
D. 2.5 m/s
E. 5.0 m/s
ans: B
Chapter 9:
CENTER OF MASS AND LINEAR MOMENTUM
129
41. A 500-kg sack of coal is dropped on a 2000-kg railroad flatcar which was initially moving at
3 m/s as shown. After the sack rests on the flatcar, the speed of the flatcar is:
..
.
.
.
.
.. . 500 kg
.. .. .. .. .. .. .. .. .. ..
....................
... ..
... .....
...
...
...
....
............................
2000 kg
...
...
... .........
..... ................................
... ... ... ...
.......
.......
A.
B.
C.
D.
E.
Santa Fe
..
..............................................
..
3 m/s
...
...
... .........
..... ................................
... ... ... ...
.......
.......
0.6 m/s
1.2 m/s
1.8 m/s
2.4 m/s
3.6 m/s
ans: D
42. A cart loaded with sand slides forward along a horizontal frictionless track. As the cart moves,
sand trickles out at a constant rate through a hole in the back of the cart. The acceleration of
the cart is:
A. constant and in the forward direction
B. constant and in the backward direction
C. variable and in the forward direction
D. variable and in the backward direction
E. zero
ans: E
43. The thrust of a rocket is:
A. a gravitational force acting on the rocket
B. the force of the exiting fuel gases on the rocket
C. any force that is external to the rocket-fuel system
D. a force that arises from the reduction in mass of the rocket-fuel system
E. none of the above
ans: B:
44. At one instant of time a rocket is traveling in outer space at 2500 m/s and is exhausting fuel
at a rate of 100 kg/s. If the speed of the fuel as it leaves the rocket is 1500 m/s, relative to the
rocket, the thrust is:
A. 0
B. 1.0 × 105 N
C. 1.5 × 105 N
D. 2.9 × 105 N
E. 2.5 × 105 N
ans: C
130
Chapter 9:
CENTER OF MASS AND LINEAR MOMENTUM
45. A rocket exhausts fuel with a velocity of 1500 m/s, relative to the rocket. It starts from rest
in outer space with fuel comprising 80 per cent of the total mass. When all the fuel has been
exhausted its speed is:
A. 3600 m/s
B. 2400 m/s
C. 1200 m/s
D. 880 m/s
E. 400 m/s
ans: B
46. A 1000-kg space probe is motionless in space. To start moving, its main engine is fired for 5 s
during which time it ejects exhaust gases at 5000 m/s. At the end of this process it is moving
at 20 m/s. The approximate mass of the ejected gas is:
.........................................................................................................................
.....................
....
.. ......
....
1000
kg
.
.........
.........................................................................................................................................
......
..
........................................
.
20 m/s
A.
B.
C.
D.
E.
...
...........
...........
.
........... .....................
.
...........
........... ..................... ...................
...
....
........... ....................
.
...
...........
...........
....
........... .....................
....
....
........... ..................... ...................
...........
.
........... .....................
...........
.
...........
....
........
....................................................
..
5000 m/s
0.8 kg
4 kg
5 kg
20 kg
25 kg
ans: B
47. The physical quantity “impulse” has the same dimensions as that of:
A. force
B. power
C. energy
D. momentum
E. work
ans: D
48. The law of conservation of momentum applies to a system of colliding objects only if:
A. there is no change in kinetic energy of the system
B. the coefficient of restitution is one
C. the coefficient of restitution is zero
D. the net external impulse is zero
E. the collisions are all elastic
ans: D
Chapter 9:
CENTER OF MASS AND LINEAR MOMENTUM
131
49. Sphere X, of mass 2 kg, is moving to the right at 10 m/s. Sphere Y, of mass 4 kg, is moving to
the left at 10 m/s. The two spheres collide head-on. The magnitude of the impulse of X on Y
is:
A. twice the magnitude of the impulse of Y on X
B. half the magnitude of the impulse of Y on X
C. one-fourth the magnitude of the impulse of Y on X
D. four times the magnitude of the impulse of Y on X
E. the same as the magnitude of the impulse of Y on X
ans: E
50. Two bodies of unequal mass, placed at rest on a frictionless surface, are acted on by equal
horizontal forces for equal times. Just after these forces are removed, the body of greater mass
will have:
A. the greater speed
B. the greater acceleration
C. the smaller momentum
D. the greater momentum
E. the same momentum as the other body
ans: E
51. A 0.2-kg rubber ball is dropped from the window of a building. It strikes the sidewalk below
at 30 m/s and rebounds up at 20 m/s. The impulse on the ball during the collision is:
A. 10 N · s upward
B. 10 N · s downward
C. 2.0 N · s upward
D. 2.0 N · s downward
E. 9.8 N · s upward
ans: A
52. A 10-kg block of ice is at rest on a frictionless horizontal surface. A 1.0-N force is applied in
an easterly direction for 1.0 s. During this time interval, the block:
A. acquires a speed of 1 m/s
B. moves 10 cm
C. acquires a momentum of 1.0 kg · m/s
D. acquires a kinetic energy of 0.1 J
E. none of the above
ans: C
132
Chapter 9:
CENTER OF MASS AND LINEAR MOMENTUM
53. A uniform narrow bar, resting on ice, is given a transverse horizontal impulse J at one end as
shown. The center of mass of the bar COM will then:
•
COM
A.
B.
C.
D.
E.
....
...........
..
..
.
...
...
...
..
.
.
......................................
J
.....
.......
.. ......
....
...
...
...
..
remain at rest
move in a circle
move in a straight line
move in a parabola
move along some other curve
ans: C
54. What magnitude impulse will give a 2.0-kg object a momentum change of magnitude + 50 kg ·
m/s?
A. +25 N · s
B. −25 N · s
C. +50 N · s
D. −50 N · s
E. +100 N · s
ans: C
55. A student’s life was saved in an automobile accident because an airbag expanded in front of
his head. If the car had not been equipped with an airbag, the windshield would have stopped
the motion of his head in a much shorter time. Compared to the windshield, the airbag:
A. causes a much smaller change in momentum
B. exerts a much smaller impulse
C. causes a much smaller change in kinetic energy
D. exerts a much smaller force
E. does much more work
ans: D
Chapter 9:
CENTER OF MASS AND LINEAR MOMENTUM
133
56. A ball hits a wall and rebounds with the same speed, as diagramed below. The changes in the
components of the momentum of the ball are:
y
...
..
...
.........
...
..............
...
... ..
...
.
.
.
...
...
...
...
...
...
...
...
...
...
...
.
...
..
...
...
...
...
...
...
... . .....
.
.............. .....
...... .
... ... ... ... ... ... ... .......... ... ... ... ... ... ...
... ... ... ... ... ... ... ... ... ... ... ... ... ...
θ θ
A.
B.
C.
D.
E.
∆px
∆px
∆px
∆px
∆px
ans:
> 0,
< 0,
= 0,
= 0,
> 0,
C
∆py
∆py
∆py
∆py
∆py
x
>0
>0
>0
<0
<0
57. A golf ball of mass m is hit by a golf club so that the ball leaves the tee with speed v. The
club is in contact with the ball for time T . The magnitude of the average force on the club on
the ball during the time T is:
A. mvT
B. mv/T
C. (1/2)mv2 T
D. mv2 /(2T )
E. mT 2 /(2v)
ans: B
58. A 640-N acrobat falls 5.0 m from rest into a net. The net tosses him back up with the same
speed he had just before he hit the net. The magnitude of the average upward force exerted
on him by the net during this collision is:
A. 32 N
B. 64 N
C. 320 N
D. 640 N
E. impossible to determine from given data
ans: E
59. Whenever an object strikes a stationary object of equal mass:
A. the two objects cannot stick together
B. the collision must be elastic
C. the first object must stop
D. momentum is not necessarily conserved
E. none of the above
ans: E
134
Chapter 9:
CENTER OF MASS AND LINEAR MOMENTUM
60. For a two-body collision involving objects with different masses, a frame of reference which has
the same velocity relative to the laboratory as does the center of mass of the two objects is:
A. a frame for which the momentum of the incident object is zero
B. a frame for which the momentum of the target object is zero
C. a frame for which the average momentum of the two objects is zero
D. a frame for which the total momentum of the two objects is zero
E. none of the above
ans: D
61. An
A.
B.
C.
D.
E.
inelastic collision is one in which:
momentum is not conserved but kinetic energy is conserved
total mass is not conserved but momentum is conserved
neither kinetic energy nor momentum is conserved
momentum is conserved but kinetic energy is not conserved
the total impulse is equal to the change in kinetic energy
ans: D
62. A 4.0-N puck is traveling at 3.0 m/s. It strikes a 8.0-N puck, which is stationary. The two
pucks stick together. Their common final speed is:
A. 1.0 m/s
B. 1.5 m/s
C. 2.0 m/s
D. 2.3 m/s
E. 3.0 m/s
ans: A
63. A 3.00-g bullet traveling horizontally at 400 m/s hits a 3.00-kg wooden block, which is initially
at rest on a smooth horizontal table. The bullet buries itself in the block without passing
through. The speed of the block after the collision is:
A. 1.33 m/s
B. 0.40 m/s
C. 12.0 m/s
D. 40.0 m/s
E. 160 m/s
ans: B
64. A 2-kg cart, traveling on a horizontal air track with a speed of 3 m/s, collides with a stationary
4-kg cart. The carts stick together. The impulse exerted by one cart on the other has a
magnitude of:
A. 0
B. 4 N · s
C. 6 N · s
D. 9 N · s
E. 12 N · s
ans: B
Chapter 9:
CENTER OF MASS AND LINEAR MOMENTUM
135
65. A 3-g bullet is fired horizontally into a 10-kg block of wood suspended by a rope from the
ceiling. The block swings in an arc, rising 3 mm above its lowest position. The velocity of the
bullet was:
A. unknown since the heat generated in the collision was not given
B. 8.0 × 102 m/s
C. 24.0 m/s
D. 8.00 m/s
E. 2.4 × 104 m/s
ans: B
66. A 3.0-kg and a 2.0-kg cart approach each other on a horizontal air track. They collide and
stick together. After the collision their total kinetic energy is 40 J. The speed of their center
of mass is:
A. zero
B. 2.8 m/s
C. 4.0 m/s
D. 5.2 m/s
E. 6.3 m/s
ans: C
67. Blocks A and B are moving toward each other. A has a mass of 2.0 kg and a velocity of 50 m/s,
while B has a mass of 4.0 kg and a velocity of −25 m/s. They suffer a completely inelastic
collision. The kinetic energy lost during the collision is:
A. 0
B. 1250 J
C. 3750 J
D. 5000 J
E. 5600 J
ans: C
68. For a completely inelastic two-body collision the kinetic energy retained by the objects is the
same as:
A. the total kinetic energy before the collision
B. the difference in the kinetic energies of the objects before the collision
2
, where M is the total mass and vcom is the velocity of the center of mass
C. 12 M vcom
D. the kinetic energy of the more massive body before the collision
E. the kinetic energy of the less massive body before the collision
ans: C
69. A 75-kg man is riding in a 30-kg cart at 2.0 m/s. He jumps off in such a way as to land on the
ground with no horizontal velocity. The resulting change in speed of the cart is:
A. zero
B. 2.0 m/s
C. 3.0 m/s
D. 5.0 m/s
E. 7.0 m/s
ans: D
136
Chapter 9:
CENTER OF MASS AND LINEAR MOMENTUM
70. An
A.
B.
C.
D.
E.
elastic collision is one in which:
momentum is not conserved but kinetic energy is conserved
total mass is not conserved but momentum is conserved
kinetic energy and momentum are both conserved
momentum is conserved but kinetic energy is not conserved
the total impulse is equal to the change in kinetic energy
ans: C
71. Object A strikes the stationary object B head-on in an elastic collision. The mass of A is fixed,
you may choose the mass of B appropriately. Then:
A. for B to have the greatest recoil speed, choose mB = mA
B. for B to have the greatest recoil momentum, choose mB
mA
C. for B to have the greatest recoil kinetic energy, choose mB
mA
D. for B to have the least recoil speed, choose mB = mA
E. for B to have the greatest recoil kinetic energy, choose mB = mA
ans: E
72. Block A, with a mass of 2.0 kg, moves along the x axis with a velocity of 5.0 m/s in the positive
x direction. It suffers an elastic collision with block B, initially at rest, and the blocks leave the
collision along the x axis. If B is much more massive than A, the speed of A after the collision
is:
A. 0
B. +5.0 m/s
C. −5.0 m/s
D. +10 m/s
E. −10 m/s
ans: C
73. A very massive object traveling at 10 m/s strikes a very light object, initially at rest, and the
light object moves off in the direction of travel of the heavy object. If the collision is elastic,
the speed of the lighter object is:
A. 5.0 m/s
B. 10 m/s
C. 15 m/s
D. 20 m/s
E. Can’t tell from the information given.
ans: D
74. Sphere A has mass m and is moving with velocity v. It makes a head-on elastic collision with
a stationary sphere B of mass 2m. After the collision their speeds (vA and vB ) are:
A. 0, v/2
B. −v/3, 2v/3
C. −v, v
D. −2v/3, v/3
E. none of these
ans: B
Chapter 9:
CENTER OF MASS AND LINEAR MOMENTUM
137
75. Blocks A and B are moving toward each other along the x axis. A has a mass of 2.0 kg and
a velocity of 50 m/s, while B has a mass of 4.0 kg and a velocity of −25 m/s. They suffer an
elastic collision and move off along the x axis. The kinetic energy transferred from A to B
during the collision is:
A. 0
B. 2500 J
C. 5000 J
D. 7500 J
E. 10000 J
ans: A
76. When a particle suffers a head-on elastic collision with another particle, initially at rest, the
greatest fraction of kinetic energy is transferred if:
A. the incident particle is initially traveling very fast
B. the incident particle is traveling very slowly
C. the incident particle is much more massive than the target particle
D. the incident particle is much less massive than the target particle
E. the incident and target particle have the same mass
ans: E
77. Two objects, X and Y, are held at rest on a horizontal frictionless surface and a spring is
compressed between them. The mass of X is 2/5 times the mass of Y. Immediately after the
spring is released, X has a kinetic energy of 50 J and Y has a kinetic energy of:
A. 20 J
B. 8 J
C. 310 J
D. 125 J
E. 50 J
ans: D
78. Two carts (A and B), having spring bumpers, collide as shown. Cart A has a mass of 2 kg and
is initially moving to the right. Cart B has a mass of 3 kg and is initially stationary. When the
separation between the carts is a minimum:
..
.................................................
..
.......
..... .......
....
..
...
.................
A.
B.
C.
D.
E.
138
A
.......
..... .......
....
..
...
.................
..........................................
..................................................................
........................
.........................................
.................................................................
............................
.......
..... .......
..
.....
...
.................
B
.......
..... .......
..
.....
...
.................
cart B is still at rest
cart A has come to rest
the carts have the same momentum
the carts have the same kinetic energy
the kinetic energy of the system is at a minimum
ans: E
Chapter 9:
CENTER OF MASS AND LINEAR MOMENTUM
79. Two identical carts travel at 1 m/s in opposite directions on a common horizontal surface. They
collide head-on and are reported to rebound, each with a speed of 2 m/s. Then:
A. momentum was not conserved; therefore, the report must be false
B. if some other form of energy were changed to kinetic during the collision, the report could
be true
C. if the collision were elastic, the report could be true
D. if friction were present, the report could be true
E. if the duration of the collision were long enough, the report could be true
ans: B
80. A block moves at 5.0 m/s in the positive x direction and hits an identical block, initially at
rest. A small amount of gunpowder had been placed on one of the blocks. The explosion does
not harm the blocks but it doubles their total kinetic energy. After the explosion the blocks
move along the x axis and the incident block has a speed in of:
A. 1.8 m/s
B. 5.0 m/s
C. 6.8 m/s
D. 7.1 m/s
E. 11.8 m/s
ans: A
81. A stream of gas consists of n molecules. Each molecule has mass m and speed v. The stream
is reflected elastically from a rigid surface as shown. The magnitude of the change in the total
momentum of the stream is:
.......
...... ..
... .
......................
v
....
•
•
•
•
•
•
•
•
•
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v....................................
30◦
...
•
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. . . .. . . . . . . . . . . . . . . . . . .
.•
. . . . . . . . . . . . . . . . . . ... . . .•
..... ..... ..... ..... ..... ..... ..... ..... ..... ..... ..... ..... ..... ..... ..... ..... ..... ..... ..... ..... ..... ..... ..... ..... ..... ..... ..... ..... ..... ..... ..... ..... ..... ..... ..... ..... ..... ..... ..... ..... ..... ..... ..... ..... .....
A.
B.
C.
D.
E.
•
2mnv
2mnv sin 30◦
mnv sin 30◦
mnv cos 30◦
mnv
ans: B
Chapter 9:
CENTER OF MASS AND LINEAR MOMENTUM
139
Chapter 10:
ROTATION
1. A radian is about:
A. 25◦
B. 37◦
C. 45◦
D. 57◦
E. 90◦
ans: D
2. One revolution is the same as:
A. 1 rad
B. 57 rad
C. π/2 rad
D. π rad
E. 2π rad
ans: E
3. One revolution per minute is about:
A. 0.0524 rad/s
B. 0.105 rad/s
C. 0.95 rad/s
D. 1.57 rad/s
E. 6.28 rad/s
ans: B
4. If a
A.
B.
C.
D.
E.
wheel turns with constant angular speed then:
each point on its rim moves with constant velocity
each point on its rim moves with constant acceleration
the wheel turns through equal angles in equal times
the angle through which the wheel turns in each second increases as time goes on
the angle through which the wheel turns in each second decreases as time goes on
ans: C
5. If a
A.
B.
C.
D.
E.
wheel is turning at 3.0 rad/s, the time it takes to complete one revolution is about:
0.33 s
0.67 s
1.0 s
1.3 s
2.1 s
ans: E
140
Chapter 10:
ROTATION
6. If wheel turning at a constant rate completes 100 revolutions in 10 s its angular speed is:
A. 0.31 rad/s
B. 0.63 rad/s
C. 10 rad/s
D. 31 rad/s
E. 63 rad/s
ans: E
7. The angular speed of the second hand of a watch is:
A. (π/1800) rad/s
B. (π/60) m/s
C. (π/30) m/s
D. (2π) m/s
E. (60) m/s
ans: C
8. The angular speed of the minute hand of a watch is:
A. (60/π) m/s
B. (1800/π) m/s
C. (π) m/s
D. (π/1800) m/s
E. (π/60) m/s
ans: D
9. A flywheel is initially rotating at 20 rad/s and has a constant angular acceleration. After 9.0 s
it has rotated through 450 rad. Its angular acceleration is:
A. 3.3 rad/s
B. 4.4 rad/s
C. 5.6 rad/s
D. 6.7 rad/s
E. 11 rad/s
ans: D
10. Ten seconds after an electric fan is turned on, the fan rotates at 300 rev/min. Its average
angular acceleration is:
A. 3.14 rad/s2
B. 30 rad/s2
2
C. 30 rev/s
2
D. 50 rev/min
E. 1800 rev/s2
ans: A
Chapter 10:
ROTATION
141
2
11. A wheel rotates with a constant angular acceleration of π rad/s . During a certain time interval
its angular displacement is π rad. At the end of the interval its angular velocity is 2π rad/s. Its
angular velocity at the beginning of the interval is:
A. zero
B. 1 rad/s
C. π √
rad/s
D. π 2 rad/s
E. 2π rad/s
ans: D
12. A flywheel rotating at 12 rev/s is brought to rest in 6 s. The magnitude of the average angular
acceleration in rad/s2 of the wheel during this process is:
A. 1/π
B. 2
C. 4
D. 4π
E. 72
ans: D
13. A phonograph turntable, initially rotating at 0.75 rev/s, slows down and stops in 30 s. The
magnitude of its average angular acceleration in rad/s2 for this process is:
A. 1.5
B. 1.5π
C. π/40
D. π/20
E. 0.75
ans: D
14. The angular velocity of a rotating wheel increases by 2 rev/s every minute. The angular acceleration in rad/s2 of this wheel is:
A. 4π2
B. 2π
C. 1/30
D. π/15
E. 4π
ans: D
15. A wheel initially has an angular velocity of 18 rad/s. It has a constant angular acceleration of
2
2.0 rad/s and is slowing at first. What time elapses before its angular velocity is 18 rad/s in
the direction opposite to its initial angular velocity?
A. 3.0 s
B. 6.0 s
C. 9.0 s
D. 18 s
E. 36 s
ans: D
142
Chapter 10:
ROTATION
16. A wheel initially has an angular velocity of 36 rad/s but after 6.0 s its angular velocity is
24 rad/s. If its angular acceleration is constant its value is:
A.
B.
C.
D.
E.
2
2.0 rad/s
−2.0 rad/s2
2
3.0 rad/s
2
−3.0 rad/s
2
6.0 rad/s
ans: B
17. A wheel initially has an angular velocity of −36 rad/s but after 6.0 s its angular velocity is
−24 rad/s. If its angular acceleration is constant the value is:
A.
B.
C.
D.
E.
2
2.0 rad/s
−2.0 rad/s2
2
3.0 rad/s
2
−3.0 rad/s
2
−6.0 rad/s
ans: A
2
18. A wheel initially has an angular velocity of 18 rad/s but it is slowing at a rate of 2.0 rad/s .
By the time it stops it will have turned through:
A. 81 rad
B. 160 rad
C. 245 rad
D. 330 rad
E. 410 rad
ans: A
2
19. A wheel starts from rest and has an angular acceleration of 4.0 rad/s . When it has made
10 rev its angular velocity is:
A. 16 rad/s
B. 22 rad/s
C. 32 rad/s
D. 250 rad/s
E. 500 rad/s
ans: B
2
20. A wheel starts from rest and has an angular acceleration of 4.0 rad/s . The time it takes to
make 10 rev is:
A. 0.50 s
B. 0.71 s
C. 2.2 s
D. 2.8 s
E. 5.6 s
ans: E
Chapter 10:
ROTATION
143
4
21. A wheel starts from rest and has an angular acceleration that is given by α(t) = (6 rad/s )t2 .
The angle through which it turns in time t is given by:
A. [(1/8)t4 ] rad
B. [(1/4)t4 ] rad
C. [(1/2)t4 ] rad
D. (t4 ) rad
E. 12 rad
ans: C
4
22. A wheel starts from rest and has an angular acceleration that is given by α(t) = (6.0 rad/s )t2 .
The time it takes to make 10 rev is:
A. 2.8 s
B. 3.3 s
C. 4.0 s
D. 4.7 s
E. 5.3 s
ans: B
23. A wheel starts from rest and has an angular acceleration that is given by α(t) = (6.0 rad/s4 )t2 .
After it has turned through 10 rev its angular velocity is:
A. 63 rad/s
B. 75 rad/s
C. 89 rad/s
D. 130 rad/s
E. 210 rad/s
ans: B
24. A wheel is spinning at 27 rad/s but is slowing with an angular acceleration that has a magnitude
4
given by (3.0 rad/s )t2 . It stops in a time of:
A. 1.7 s
B. 2.6 s
C. 3.0 s
D. 4.4 s
E. 7.3 s
ans: C
25. If the angular velocity vector of a spinning body points out of the page then, when viewed from
above the page, the body is spinning:
A. clockwise about an axis that is perpendicular to the page
B. counterclockwise about an axis that is perpendicular to the page
C. about an axis that is parallel to the page
D. about an axis that is changing orientation
E. about an axis that is getting longer
ans: B
144
Chapter 10:
ROTATION
26. The angular velocity vector of a spinning body points out of the page. If the angular acceleration
vector points into the page then:
A. the body is slowing down
B. the body is speeding up
C. the body is starting to turn in the opposite direction
D. the axis of rotation is changing orientation
E. none of the above
ans: A
27. A child, riding on a large merry-go-round, travels a distance of 3000 m in a circle of diameter
40 m. The total angle through which she revolves is:
A. 50 rad
B. 75 rad
C. 150 rad
D. 314 rad
E. none of these
ans: C
28. The figure shows a cylinder of radius 0.7 m rotating about its axis at 10 rad/s. The speed of
the point P is:
...............................
........
......
......
....
....
...
...
..
...
....
..
...
..
...
..
...
..
...
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.
.
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.
.
.
...
...
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...
....
....
......
......
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...............................
P.......•......
•
A.
B.
C.
D.
E.
......
.............
.....
...
..
...
.
..
...
....
.
.
...
...
7.0 m/s
14π rad/s
7.0π rad/s
0.70 m/s
none of these
ans: A
Chapter 10:
ROTATION
145
29. The fan shown has been turned on and is now slowing as it rotates clockwise. The direction of
the acceleration of the point X on the fan tip could be:
•
....
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A.
B.
C. ↓
D. ←
E. →
ans: D
30. A wheel of diameter 3.0 cm has a 4.0-m cord wrapped around its periphery. Starting from rest,
2
the wheel is given a constant angular acceleration of 2.0 rad/s . The cord will unwind in:
A. 0.82 s
B. 2.0 s
C. 8.0 s
D. 16 s
E. 130 s
ans: D
31. A particle moves in a circular path of radius 0.10 m with a constant angular speed of 5 rev/s.
The acceleration of the particle is:
2
A. 0.10π m/s
2
B. 0.50 m/s
C. 500π m/s2
2
D. 1000π2 m/s
2
E. 10π2 m/s
ans: E
32. A car travels north at constant velocity. It goes over a piece of mud, which sticks to the tire.
The initial acceleration of the mud, as it leaves the ground, is:
A. vertically upward
B. horizontally to the north
C. horizontally to the south
D. zero
E. upward and forward at 45◦ to the horizontal
ans: A
146
Chapter 10:
ROTATION
33. Wrapping paper is being from a 5.0-cm radius tube, free to rotate on its axis. If it is pulled at
the constant rate of 10 cm/s and does not slip on the tube, the angular velocity of the tube is:
A. 2.0 rad/s
B. 5.0 rad/s
C. 10 rad/s
D. 25 rad/s
E. 50 rad/s
ans: A
34. String is wrapped around the periphery of a 5.0-cm radius cylinder, free to rotate on its axis.
The string is pulled straight out at a constant rate of 10 cm/s and does not slip on the cylinder.
As each small segment of string leaves the cylinder, its acceleration changes by:
A. 0
2
B. 0.010 m/s
C. 0.020 m/s2
D. 0.10 m/s2
2
E. 0.20 m/s
ans: E
35. A flywheel of diameter 1.2 m has a constant angular acceleration of 5.0 rad/s2 . The tangential
acceleration of a point on its rim is:
A. 5.0 rad/s2
B. 3.0 m/s2
C. 5.0 m/s2
2
D. 6.0 m/s
2
E. 12 m/s
ans: B
36. For a wheel spinning with constant angular acceleration on an axis through its center, the ratio
of the speed of a point on the rim to the speed of a point halfway between the center and the
rim is:
A. 1
B. 2
C. 1/2
D. 4
E. 1/4
ans: B
37. For a wheel spinning on an axis through its center, the ratio of the tangential acceleration of a
point on the rim to the tangential acceleration of a point halfway between the center and the
rim is:
A. 1
B. 2
C. 1/2
D. 4
E. 1/4
ans: B
Chapter 10:
ROTATION
147
38. For a wheel spinning on an axis through its center, the ratio of the radial acceleration of a
point on the rim to the radial acceleration of a point halfway between the center and the rim
is:
A. 1
B. 2
C. 1/2
D. 4
E. 1/4
ans: B
39. Two wheels are identical but wheel B is spinning with twice the angular speed of wheel A. The
ratio of the magnitude of the radial acceleration of a point on the rim of B to the magnitude
of the radial acceleration of a point on the rim of A is:
A. 1
B. 2
C. 1/2
D. 4
E. 1/4
ans: D
40. A wheel starts from rest and spins with a constant angular acceleration. As time goes on the
acceleration vector for a point on the rim:
A. decreases in magnitude and becomes more nearly tangent to the rim
B. decreases in magnitude and becomes more early radial
C. increases in magnitude and becomes more nearly tangent to the rim
D. increases in magnitude and becomes more nearly radial
E. increases in magnitude but retains the same angle with the tangent to the rim
ans: D
41. The magnitude of the acceleration of a point on a spinning wheel is increased by a factor of 4
if:
A. the magnitudes of the angular velocity and the angular acceleration are each multiplied by
a factor of 4
B. the magnitude of the angular velocity is multiplied by a factor of 4 and the angular acceleration is not changed
C. the magnitudes of the angular velocity and the angular acceleration are each multiplied by
a factor of 2
D. the magnitude of the angular velocity is multiplied by a factor of 2 and the angular acceleration is not changed
E. the magnitude of the angular velocity is multiplied by a factor of 2 and the magnitude of
the angular acceleration is multiplied by a factor of 4
ans: E
148
Chapter 10:
ROTATION
42. Three identical balls are tied by light strings to the same rod and rotate around it, as shown
below. Rank the balls according to their rotational inertia, least to greatest.
1 m••••••••••••••••••••••
••••••••••• ball 1
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2m
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• ball 2
3m
A.
B.
C.
D.
E.
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• ball 3
1, 2, 3
3, 2, 1
3, then 1 and 2 tie
1, 3, 2
All are the same
ans: A
43. Four identical particles, each with mass m, are arranged in the x, y plane as shown. They are
connected by light sticks to form a rigid body. If m = 2.0 kg and a = 1.0 m, the rotational
inertia of this array about the y axis is:
y
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a
...................................
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........
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A.
B.
C.
D.
E.
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4.0 kg · m2
12 kg · m2
9.6 kg · m2
4.8 kg · m2
none of these
ans: B
Chapter 10:
ROTATION
149
44. Three identical balls, with masses of M , 2M , and 3M , are fastened to a massless rod of length
L as shown. The rotational inertia about the left end of the rod is:
←−−− L/2 −−−→←−−− L/2 −−−→
3M
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...............................
........
.
.........................................
.
A.
B.
C.
D.
E.
M L2 /2
M L2
3M L2 /2
6M L2
3M L2 /4
ans: E
45. The rotational inertia of a thin cylindrical shell of mass M , radius R, and length L about its
central axis (X—X ) is:
..............................................................................................................................................................
X
••••••••
••• •••
•• ••
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••••••••••••
..............................................................................................................................................................
........
...
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...
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...
..
...
..
..
....
..
...
....
...
..
...
...
..
.
...
.......
←−−−−−−−− L −−−−−−−−→
A.
B.
C.
D.
E.
↑|
R
↓|
X
M R2 /2
M L2 /2
M L2
M R2
none of these
ans: D
46. The rotational inertia of a wheel about its axle does not depend upon its:
A. diameter
B. mass
C. distribution of mass
D. speed of rotation
E. material composition
ans: D
150
Chapter 10:
ROTATION
47. Consider four objects, each having the same mass and the same radius:
1. a solid sphere
2. a hollow sphere
3. a flat disk in the x, y plane
4. a hoop in the x, y plane
The order of increasing rotational inertia about an axis through the center of mass and parallel
to the z axis is:
A. 1, 2, 3, 4
B. 4, 3, 2, 1
C. 1, 3, 2, 4
D. 4, 2, 3, 1
E. 3, 1, 2, 4
ans: C
48. A and B are two solid cylinders made of aluminum. Their dimensions are shown. The ratio of
the rotational inertia of B to that of A about the common axis X—X is:
↑
R
↓
X
..........................................................
... ....
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........................................................
A
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←
− L−
→
...........................................................................................................
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...................................................................................................................
..
B
........
...
...
...
...
...
...
...
..
..
..
...
..
....
....
..
...
....
...
..
...
...
....
..
...
...
...
.
.
.
.
....
↑|
2R
↓|
X
←−−− 2L −−−→
A.
B.
C.
D.
E.
2
4
8
16
32
ans: E
49. Two uniform circular disks having the same mass and the same thickness are made from
different materials. The disk with the smaller rotational inertia is:
A. the one made from the more dense material
B. the one made from the less dense material
C. neither – both rotational inertias are the same
D. the disk with the larger angular velocity
E. the disk with the larger torque
ans: A
Chapter 10:
ROTATION
151
50. A uniform solid cylinder made of lead has the same mass and the same length as a uniform solid
cylinder made of wood. The rotational inertia of the lead cylinder compared to the wooden
one is:
A. greater
B. less
C. same
D. unknown unless the radii are given
E. unknown unless both the masses and the radii are given
ans: B
51. To
A.
B.
C.
increase the rotational inertia of a solid disk about its axis without changing its mass:
drill holes near the rim and put the material near the axis
drill holes near the axis and put the material near the rim
drill holes at points on a circle near the rim and put the material at points between the
holes
D. drill holes at points on a circle near the axis and put the material at points between the
holes
E. do none of the above (the rotational inertia cannot be changed without changing the mass)
ans: B
52. The rotational inertia of a disk about its axis is 0.70 kg · m2 . When a 2.0-kg weight is added to
its rim, 0.40 m from the axis, the rotational inertia becomes:
A. 0.38 kg · m2
B. 0.54 kg · m2
C. 0.70 kg · m2
D. 0.86 kg · m2
E. 1.0 kg · m2
ans: E
53. When a thin uniform stick of mass M and length L is pivoted about its midpoint, its rotational
inertia is M L2 /12. When pivoted about a parallel axis through one end, its rotational inertia
is:
A. M L2 /12
B. M L2 /6
C. M L2 /3
D. 7M L2 /12
E. 13M L2 /12
ans: C
54. The rotational inertia of a solid uniform sphere about a diameter is (2/5)M R2 , where M is its
mass and R is its radius. If the sphere is pivoted about an axis that is tangent to its surface,
its rotational inertia is:
A. M R2
B. (2/5)M R2
C. (3/5)M R2
D. (5/2)M R2
E. (7/5)M R2
ans: E
152
Chapter 10:
ROTATION
55. A solid uniform sphere of radius R and mass M has a rotational inertia about a diameter
that is given by (2/5)M R2 . A light string of length 3R is attached to the surface and used to
suspend the sphere from the ceiling. Its rotational inertia about the point of attachment at
the ceiling is:
A. (2/5)M R2
B. 9M R2
C. 16M R2
D. (47/5)M R2
E. (82/5)M R2
ans: E
56. A force with a given magnitude is to be applied to a wheel. The torque can be maximized by:
A. applying the force near the axle, radially outward from the axle
B. applying the force near the rim, radially outward from the axle
C. applying the force near the axle, parallel to a tangent to the wheel
D. applying the force at the rim, tangent to the rim
E. applying the force at the rim, at 45◦ to the tangent
ans: D
57. The meter stick shown below rotates about an axis through the point marked •, 20 cm from one
end. Five forces act on the stick: one at each end, one at the pivot point, and two 40 cm from
one end, as shown. The magnitudes of the forces are all the same. Rank the forces according
to the magnitudes of the torques they produce about the pivot point, least to greatest.
F1
.
........
.........
....
..
...
...
...
F2
...
................
... .
...
...
.
.
...
...
F3
F
.
........
4
.........
...
...
................
....
... .
.. .....
... ....
.......
..
..........................................................
•
..
F5
0 cm 20 cm 40 cm 60 cm 80 cm 100 cm
A.
B.
C.
D.
E.
F1 , F2 ,
F1 and
F2 and
F2 , F5 ,
F2 and
ans: E
F3 , F4 , F5
F2 tie, then F3 , F4 , F5
F5 tie, then F4 , F1 , F3
F1 and F3 tie, then F4
F5 tie, then F4 , then F1 and F3 tie
Chapter 10:
ROTATION
153
58. A rod is pivoted about its center. A 5-N force is applied 4 m from the pivot and another 5-N
force is applied 2 m from the pivot, as shown. The magnitude of the total torque about the
pivot (in N·m) is:
..............
..........
5N
....... ..
.......
......
...
......
◦ ...................
30
...
.......
.......
.......
.......
.
.
.
.
.
...
.. .......
........
...............
2.0 m
•
4.0 m
.....
.......
.......
.......
.......
.
◦
.
.
.
.
.
...
.......
......
30
5N
A.
B.
C.
D.
E.
0
5
8.7
15
26
ans: D
59. τ = Iα for an object rotating about a fixed axis, where τ is the net torque acting on it, I is its
rotational inertia, and α is its angular acceleration. This expression:
A. is the definition of torque
B. is the definition of rotational inertia
C. is the definition of angular acceleration
D. follows directly from Newton’s second law
E. depends on a principle of physics that is unrelated to Newton’s second law
ans: D
60. A meter stick on a horizontal frictionless table top is pivoted at the 80-cm mark. It is initially
at rest. A horizontal force F1 is applied perpendicularly to the end of the stick at 0 cm, as
shown. A second horizontal force F2 (not shown) is applied at the 100-cm end of the stick. If
the stick does not rotate:
F1
..
........
..........
...
...
..
...
..
•
0 cm 20 cm 40 cm 60 cm 80 cm 100 cm
A.
B.
C.
D.
E.
154
|F2 | > |F1 |
|F2 | < |F1 |
|F2 | = |F1 |
|F2 | > |F1 |
|F2 | > |F1 |
ans: A
for
for
for
for
for
Chapter 10:
all orientations of
all orientations of
all orientations of
some orientations
some orientations
ROTATION
F2
F2
F2
of F2 and |F2 | < |F1 | for others
of F2 and |F2 | = |F1 | for others
61. A uniform disk, a thin hoop, and a uniform sphere, all with the same mass and same outer
radius, are each free to rotate about a fixed axis through its center. Assume the hoop is
connected to the rotation axis by light spokes. With the objects starting from rest, identical
forces are simultaneously applied to the rims, as shown. Rank the objects according to their
angular accelerations, least to greatest.
hoop
disk
..............................
......
.....
.....
...
...
...
...
....
..
...
..
...
...
..
..
...
.
.
...
..
.
.
...
.....
...
.....
.......
.............................................................................
......
•
A.
B.
C.
D.
E.
sphere
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
..
•
•
•
•
•
•
•
•
•
•
..•
.•
.•
.•
.•
.•
.•
.•
.•
.•
.•
.•
.•
.•
..........................................
•
•
•
•
•
•
•
•
•
•
F
.....
.....................
.........
......
......
....
...
...
..
...
.
.
.
..
...
..
...
.
...
..
..
...
.
.
...
..
.
.
....
....
......
.
.........
......
.........................................................................
...
•
F
F
disk, hoop, sphere
hoop, disk, sphere
hoop, sphere, disk
hoop, disk, sphere
sphere, disk, hoop
ans: D
62. A disk is free to rotate on a fixed axis. A force of given magnitude F , in the plane of the disk,
is to be applied. Of the following alternatives the greatest angular acceleration is obtained if
the force is:
A. applied tangentially halfway between the axis and the rim
B. applied tangentially at the rim
C. applied radially halfway between the axis and the rim
D. applied radially at the rim
E. applied at the rim but neither radially nor tangentially
ans: B
63. A cylinder is 0.10 m in radius and 0.20 m in length. Its rotational inertia, about the cylinder
axis on which it is mounted, is 0.020 kg · m2 . A string is wound around the cylinder and pulled
with a force of 1.0 N. The angular acceleration of the cylinder is:
2
A. 2.5 rad/s
B. 5.0 rad/s2
2
C. 10 rad/s
2
D. 15 rad/s
2
E. 20 rad/s
ans: B
Chapter 10:
ROTATION
155
64. A disk with a rotational inertia of 2.0 kg · m2 and a radius of 0.40 m rotates on a frictionless
fixed axis perpendicular to the disk faces and through its center. A force of 5.0 N is applied
tangentially to the rim. The angular acceleration of the disk is:
2
A. 0.40 rad/s
B. 0.60 rad/s2
C. 1.0 rad/s2
2
D. 2.5 rad/s
2
E. 10 rad/s
ans: C
65. A disk with a rotational inertia of 5.0 kg · m2 and a radius of 0.25 m rotates on a frictionless
fixed axis perpendicular to the disk and through its center. A force of 8.0 N is applied along
the rotation axis. The angular acceleration of the disk is:
A. 0
2
B. 0.40 rad/s
C. 0.60 rad/s2
2
D. 1.0 rad/s
2
E. 2.5 rad/s
ans: A
66. A disk with a rotational inertia of 5.0 kg·m2 and a radius of 0.25 m rotates on a frictionless fixed
axis perpendicular to the disk and through its center. A force of 8.0 N is applied tangentially to
the rim. If the disk starts at rest, then after it has turned through half a revolution its angular
velocity is:
A. 0.57 rad/s
B. 0.64 rad/s
C. 0.80 rad/s
D. 1.6 rad/s
E. 3.2 rad/s
ans: D
67. A thin circular hoop of mass 1.0 kg and radius 2.0 m is rotating about an axis through its center
2
and perpendicular to its plane. It is slowing down at the rate of 7.0 rad/s . The net torque
acting on it is:
A. 7.0 N · m
B. 14.0 N · m
C. 28.0 N · m
D. 44.0 N · m
E. none of these
ans: C
156
Chapter 10:
ROTATION
68. A certain wheel has a rotational inertia of 12 kg · m2 . As it turns through 5.0 rev its angular
velocity increases from 5.0 rad/s to 6.0 rad/s. If the net torque is constant its value is:
A. 0.016 N · m
B. 0.18 N · m
C. 0.57 N · m
D. 2.1 N · m
E. 3.6 N · m
ans: D
69. A 16-kg block is attached to a cord that is wrapped around the rim of a flywheel of diameter
0.40 m and hangs vertically, as shown. The rotational inertia of the flywheel is 0.50 kg · m2 .
When the block is released and the cord unwinds, the acceleration of the block is:
..... ..... ..... ..... ..... ..... ..... ..... ..... ..... ..... ..... ..... ..... .....
...... ...... ...... ...... ......... ...... ...... ...... ...... ........ ...... ...... ...... ...... ......
.
...
...
...
...
...
...
....
... ..................................... ..
.
.........
........
...
...... ..
... ........
.... .....
...
.
...
.
...
...
...
..
.
...
...
..
..
.
...
.
.
...
.
.
...
.
....
...
.
..
.
...
.
.
...
.
..
..
.
.
.
...
.
.
....
..
.
...
.
...
.
...
.
........................
...
..
.
...
.
.
.
...
..
...
..
....
...
.....
...
......
.....
.
.
.
.
........
.
.
...................................
↑
|
|
0.4 m
|
|
↓
•
16 kg
A.
B.
C.
D.
E.
0.15g
0.56g
0.84g
g
1.3g
ans: B
70. A 8.0-cm radius disk with a rotational inertia of 0.12 kg · m2 is free to rotate on a horizontal
axis. A string is fastened to the surface of the disk and a 10-kg mass hangs from the other end.
The mass is raised by using a crank to apply a 9.0-N·m torque to the disk. The acceleration of
the mass is:
2
A. 0.50 m/s
2
B. 1.7 m/s
C. 6.2 m/s2
2
D. 12 m/s
2
E. 20 m/s
ans: A
Chapter 10:
ROTATION
157
71. A 0.70-kg disk with a rotational inertia given by M R2 /2 is free to rotate on a fixed horizontal
axis suspended from the ceiling. A string is wrapped around the disk and a 2.0-kg mass hangs
from the free end. If the string does not slip, then as the mass falls and the cylinder rotates,
the suspension holding the cylinder pulls up on the cylinder with a force of:
A. 6.9 N
B. 9.8 N
C. 16 N
D. 26 N
E. 29 N
ans: B
72. A small disk of radius R1 is mounted coaxially with a larger disk of radius R2 . The disks
are securely fastened to each other and the combination is free to rotate on a fixed axle that
is perpendicular to a horizontal frictionless table top, as shown in the overhead view below.
The rotational inertia of the combination is I. A string is wrapped around the larger disk and
attached to a block of mass m, on the table. Another string is wrapped around the smaller
disk and is pulled with a force F as shown. The acceleration of the block is:
........................................
...........
........
........
.......
......
......
......
.
.....
.
.
....
...
.
.
2
...
..
.
.
...
...
...
.
.
................................
...
.
.
.
.
.
.
.
.
.
......
...
.....
.
.
.
....
.
....
...
...
.
...
.
...
...
..
...
.
.
...
..
...
.....
..
...
...
...
..
...
...
..
..
..
...
...
.
.
...
...
...
..
..
.
.
...
.
.
...
.
.
.
.
...
...
....
...
...
...
...... 1
...
...
...
.....
........
...
...............................................................................................................
. .....
...
.
.
...
...
...
...
....
....
.....
.....
......
......
.
.......
.
.
.
.
.........
....
..................................................
m
R
R
A.
B.
C.
D.
E.
158
R1 F/mR2
R1 R2 F/(I
R1 R2 F/(I
R1 R2 F/(I
R1 R2 F/(I
ans: C
− mR22 )
+ mR22 )
− mR1 R2 )
+ mR1 R2 )
Chapter 10:
ROTATION
•
F
73. A small disk of radius R1 is fastened coaxially to a larger disk of radius R2 . The combination
is free to rotate on a fixed axle, which is perpendicular to a horizontal frictionless table top,
as shown in the overhead view below. The rotational inertia of the combination is I. A string
is wrapped around the larger disk and attached to a block of mass m, on the table. Another
string is wrapped around the smaller disk and is pulled with a force F as shown. The tension
in the string pulling the block is:
...........
.................. .........................
.........
.......
......
.......
.....
.....
.
.
.
.
....
....
....
2
....
...
.
.
...
...
.
...
.........................
.
.
.
..
.
.
.
.
.
.
...
......
.....
.
..
.
.
...
.
.
.
.
....
...
...
.
.
.
....
...
...
...
.
....
.
...
..
...
..
....
...
..
....
....
...
..
..
..
...
...
..
..
.
...
...
.
..
.
.
.
.
...
...
.
.
.
.
.
.
...
...
.
.
.
.
.
.
.
.
...
.... 1
..
......
....
...
........
......
..
...
...............................................................................................................
...
. ....
...
...
.
....
.
....
....
....
.....
.....
......
......
.......
.......
.........
.
.
.
.
.
.
.
............................................
m
R
R
A.
B.
C.
D.
E.
R1 F/R2
mR1 R2 F/(I
mR1 R2 F/(I
mR1 R2 F/(I
mR1 R2 F/(I
ans: C
•
F
− mR22 )
+ mR22 )
− mR1 R2 )
+ mR1 R2 )
74. A block is attached to each end of a rope that passes over a pulley suspended from the ceiling.
The blocks do not have the same mass. If the rope does not slip on the pulley, then at any
instant after the blocks start moving, the rope:
A. pulls on both blocks, but exerts a greater force on the heavier block
B. pulls on both blocks, but exerts a greater force on the lighter block
C. pulls on both blocks and exerts the same magnitude force on both
D. does not pull on either block
E. pulls only on the lighter block
ans: A
75. A pulley with a radius of 3.0 cm and a rotational inertia of 4.5 × 10−3 kg · m2 is suspended from
the ceiling. A rope passes over it with a 2.0-kg block attached to one end and a 4.0-kg block
attached to the other. The rope does not slip on the pulley. When the speed of the heavier
block is 2.0 m/s the kinetic energy of the pulley is:
A. 0.15 J
B. 0.30 J
C. 1.0 J
D. 10 J
E. 20 J
ans: D
Chapter 10:
ROTATION
159
76. A pulley with a radius of 3.0 cm and a rotational inertia of 4.5 × 10−3 kg · m2 is suspended from
the ceiling. A rope passes over it with a 2.0-kg block attached to one end and a 4.0-kg block
attached to the other. The rope does not slip on the pulley. At any instant after the blocks
start moving, the object with the greatest kinetic energy is:
A. the heavier block
B. the lighter block
C. the pulley
D. either block (the two blocks have the same kinetic energy)
E. none (all three objects have the same kinetic energy)
ans: C
77. A disk with a rotational inertia of 5.0 kg · m2 and a radius of 0.25 m rotates on a fixed axis
perpendicular to the disk and through its center. A force of 2.0 N is applied tangentially to the
rim. As the disk turns through half a revolution the work done by the force is:
A. 1.6 J
B. 2.5 J
C. 6.3 J
D. 10 J
E. 40 J
ans: A
78. A circular saw is powered by a motor. When the saw is used to cut wood, the wood exerts a
torque of 0.80 N · m on the saw blade. If the blade rotates with a constant angular velocity of
20 rad/s the work done on the blade by the motor in 1.0 min is:
A. 0
B. 480 J
C. 960 J
D. 1400 J
E. 1800 J
ans: C
2
79. A disk has a rotational inertia of 6.0 kg · m2 and a constant angular acceleration of 2.0 rad/s .
If it starts from rest the work done during the first 5.0 s by the net torque acting on it is:
A. 0
B. 30 J
C. 60 J
D. 300 J
E. 600 J
ans: D
80. A disk starts from rest and rotates around a fixed axis, subject to a constant net torque. The
as the work done during the first 5 s.
work done by the torque during the second 5 s is
A. the same
B. twice as much
C. half as much
D. four times as much
E. one-fourth as much
ans: D
160
Chapter 10:
ROTATION
81. A disk starts from rest and rotates about a fixed axis, subject to a constant net torque. The
as the work done during the
work done by the torque during the second revolution is
first revolution.
A. the same
B. twice as much
C. half as much
D. four times as much
E. one-fourth as much
ans: A
Chapter 10:
ROTATION
161
Chapter 11:
ROLLING, TORQUE, AND ANGULAR MOMENTUM
1. A wheel rolls without sliding along a horizontal road as shown. The velocity of the center of
the wheel is represented by −→. Point P is painted on the rim of the wheel. The instantaneous
velocity of point P is:
...................................
.........
.......
......
.....
......
....
....
...
...
...
.
.
.
.
.
.
.
.
.
.
...
.
.
.
.
.
.
.
.
.
.
.
...
..................
......
..
.
.
.
.
...
.
.
..
.
..
...
....
..
....
..
..
...
.......................................................
...
..
...
...
..
.
...
..
.
...
.
.
.
...
.
...
...
....
...
.....
....
......
.....
.
.
.
.
........
.
.
.
......
. . . . . . . . . ................................... . . . . . . . . .
... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
.. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. ..
v
P
•
A.
B.
C.
D.
E.
→
←
↑
zero
ans: E
2. A wheel of radius 0.5 m rolls without sliding on a horizontal surface as shown. Starting from
2
rest, the wheel moves with constant angular acceleration 6 rad/s . The distance traveled by
the center of the wheel from t = 0 to t = 3 s is:
.........
.............. ......................
.......
......
......
.....
....
....
.
.
.
.
...
...
......................................
...
..
......
.
.
.
.
.
.
.
.
.
.
...
.
..
....
...
....
..
..
..
...
.......................................................
....
..
...
...
...
....
...
.
.
.
...
.
.
...
..
...
...
....
...
.....
.....
......
.....
.
.
.
........
.
.
.
.
.....
. . . . . . . . . ................................. . . . . . . . . .
.. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. ..
.. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. ..
•
A.
B.
C.
D.
E.
v
zero
27 m
13.5 m
18 m
none of these
ans: C
3. Two wheels roll side-by-side without sliding, at the same speed. The radius of wheel 2 is twice
the radius of wheel 1. The angular velocity of wheel 2 is:
A. twice the angular velocity of wheel 1
B. the same as the angular velocity of wheel 1
C. half the angular velocity of wheel 1
D. more than twice the angular velocity of wheel 1
E. less than half the angular velocity of wheel 1
ans: C
162
Chapter 11:
ROLLING, TORQUE, AND ANGULAR MOMENTUM
4. A forward force on the axle accelerates a rolling wheel on a horizontal surface. If the wheel
does not slide the frictional force of the surface on the wheel is:
A. zero
B. in the forward direction
C. in the backward direction
D. in the upward direction
E. in the downward direction
ans: D
5. When the speed of a rear-drive car is increasing on a horizontal road the direction of the
frictional force on the tires is:
A. forward for all tires
B. backward for all tires
C. forward for the front tires and backward for the rear tires
D. backward for the front tires and forward for the rear tires
E. zero
ans: D
6. A solid wheel with mass M , radius R, and rotational inertia M R2 /2, rolls without sliding on
a horizontal surface. A horizontal force F is applied to the axle and the center of mass has an
acceleration a. The magnitudes of the applied force F and the frictional force f of the surface,
respectively, are:
A. F = M a, f = 0
B. F = M a, f = M a/2
C. F = 2M a, f = M a
D. F = 2M a, f = M a/2
E. F = 3M a/2, f = M a/2
ans: E
7. The coefficient of static friction between a certain cylinder and a horizontal floor is 0.40. If the
rotational inertia of the cylinder about its symmetry axis is given by I = (1/2)M R2 , then the
magnitude of the maximum acceleration the cylinder can have without sliding is:
A. 0.1g
B. 0.2g
C. 0.4g
D. 0.8g
E. g
ans: D
8. A thin-walled hollow tube rolls without sliding along the floor. The ratio of its translational
kinetic energy to its rotational kinetic energy (about an axis through its center of mass) is:
A. 1
B. 2
C. 3
D. 1/2
E. 1/3
ans: A
Chapter 11:
ROLLING, TORQUE, AND ANGULAR MOMENTUM
163
9. A sphere and a cylinder of equal mass and radius are simultaneously released from rest on the
same inclined plane and roll without sliding down the incline. Then:
A. the sphere reaches the bottom first because it has the greater inertia
B. the cylinder reaches the bottom first because it picks up more rotational energy
C. the sphere reaches the bottom first because it picks up more rotational energy
D. they reach the bottom together
E. none of the above are true
ans: E
10. A hoop, a uniform disk, and a uniform sphere, all with the same mass and outer radius, start
with the same speed and roll without sliding up identical inclines. Rank the objects according
to how high they go, least to greatest.
A. hoop, disk, sphere
B. disk, hoop, sphere
C. sphere, hoop, disk
D. sphere, disk, hoop
E. hoop, sphere, disk
ans: A
11. A hoop rolls with constant velocity and without sliding along level ground. Its rotational
kinetic energy is:
A. half its translational kinetic energy
B. the same as its translational kinetic energy
C. twice its translational kinetic energy
D. four times its translational kinetic energy
E. one-third its translational kinetic energy
ans: B
12. Two identical disks, with rotational inertia I (= 12 M R2 ), roll without sliding across a horizontal
floor with the same speed and then up inclines. Disk A rolls up its incline without sliding. On
the other hand, disk B rolls up a frictionless incline. Otherwise the inclines are identical. Disk
A reaches a height 12 cm above the floor before rolling down again. Disk B reaches a height
above the floor of:
A. 24 cm
B. 18 cm
C. 12 cm
D. 8 cm
E. 6 cm
ans: D
164
Chapter 11:
ROLLING, TORQUE, AND ANGULAR MOMENTUM
13. A yo-yo, arranged as shown, rests on a frictionless surface. When a force F is applied to the
string as shown, the yo-yo:
..............................
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... ... ... ... ... ... ... ... .. .. .. .. .. .. .. .. .. .. .. .. ..
.. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. ..
A.
B.
C.
D.
E.
moves to
moves to
moves to
moves to
moves to
ans: B
the
the
the
the
the
F
left and rotates counterclockwise
right and rotates counterclockwise
left and rotates clockwise
right and rotates clockwise
right and does not rotate
14. When we apply the energy conservation principle to a cylinder rolling down an incline without
sliding, we exclude the work done by friction because:
A. there is no friction present
B. the angular velocity of the center of mass about the point of contact is zero
C. the coefficient of kinetic friction is zero
D. the linear velocity of the point of contact (relative to the inclined surface) is zero
E. the coefficient of static and kinetic friction are equal
ans: D
15. Two uniform cylinders have different masses and different rotational inertias. They simultaneously start from rest at the top of an inclined plane and roll without sliding down the plane.
The cylinder that gets to the bottom first is:
A. the one with the larger mass
B. the one with the smaller mass
C. the one with the larger rotational inertia
D. the one with the smaller rotational inertia
E. neither (they arrive together)
ans: E
16. A 5.0-kg ball rolls without sliding from rest down an inclined plane. A 4.0-kg block, mounted
on roller bearings totaling 100 g, rolls from rest down the same plane. At the bottom, the block
has:
A. greater speed than the ball
B. less speed than the ball
C. the same speed as the ball
D. greater or less speed than the ball,depending on the angle of inclination
E. greater or less speed than the ball, depending on the radius of the ball
ans: A
Chapter 11:
ROLLING, TORQUE, AND ANGULAR MOMENTUM
165
17. A cylinder of radius R = 6.0 cm is on a rough horizontal surface. The coefficient of kinetic
friction between the cylinder and the surface is 0.30 and the rotational inertia for rotation
about the axis is given by M R2 /2, where M is its mass. Initially it is not rotating but its
center of mass has a speed of 7.0 m/s. After 2.0 s the speed of its center of mass and its angular
velocity about its center of mass, respectively, are:
A. 1.1 m/s, 0
B. 1.1 m/s, 19 rad/s
C. 1.1 m/s, 98 rad/s
D. 1.1 m/s, 200 rad/s
E. 5.9 m/s, 98 rad/s
ans: D
18. The fundamental dimensions of angular momentum are:
A. mass·length·time−1
B. mass·length−2 ·time−2
C. mass2 ·time−1
D. mass·length2 ·time−2
E. none of these
ans: E
19. Possible units of angular momentum are:
A. kg·m/s
B. kg·m2 /s2
C. kg·m/s2
D. kg·m2 /s
E. none of these
ans: D
20. The unit kg·m2 /s can be used for:
A. angular momentum
B. rotational kinetic energy
C. rotational inertia
D. torque
E. power
ans: A
21. The newton·second is a unit of:
A. work
B. angular momentum
C. power
D. linear momentum
E. none of these
ans: D
166
Chapter 11:
ROLLING, TORQUE, AND ANGULAR MOMENTUM
22. A 2.0-kg block travels around a 0.50-m radius circle with an angular velocity of 12 rad/s. The
magnitude of its angular momentum about the center of the circle is:
A. 6.0 kg · m2 /s
B. 12 kg · m2 /s
C. 48 kg/m2 · s
D. 72 kg · m2 /s2
2
E. 576 kg/m · s2
ans: A
23. The angular momentum vector of Earth about its rotation axis, due to its daily rotation, is
directed:
A. tangent to the equator toward the east
B. tangent to the equator toward the west
C. north
D. south
E. toward the Sun
ans: C
24. A 6.0-kg particle moves to the right at 4.0 m/s as shown. The magnitude of its angular momentum about the point O is:
6 kg
A.
B.
C.
D.
E.
4 m/s
...
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zero
288 kg · m2 /s
144 kg · m2 /s
24 kg · m2 /s
249 kg · m2 /s
ans: C
Chapter 11:
ROLLING, TORQUE, AND ANGULAR MOMENTUM
167
25. Two objects are moving in the x, y plane as shown. The magnitude of their total angular
momentum (about the origin O) is:
2 m/s
y
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3 m/s
↑
6 kg
|
1m
|
3 kg
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O
←−−−−− 2 m −−−−−→
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A.
B.
C.
D.
E.
zero
6 kg · m2 /s
12 kg · m2 /s
30 kg · m2 /s
78 kg · m2 /s
ans: D
26. A 2.0-kg block starts from rest on the positive x axis 3.0 m from the origin and thereafter has an
2
2
acceleration given by a = (4.0 m/s ) î − (3.0 m/s ) ĵ. At the end of 2.0 s its angular momentum
about the origin is:
A. 0
B. (−36 kg · m2 /s) k̂
C. (+48 kg · m2 /s) k̂
D. (−96 kg · m2 /s) k̂
E. (+96 kg · m2 /s) k̂
ans: B
27. A 15-g paper clip is attached to the rim of a phonograph record with a radius of 30 cm, spinning
at 3.5 rad/s. The magnitude of its angular momentum is:
A. 1.4 × 10−3 kg · m2 /s
B. 4.7 × 10−3 kg · m2 /s
C. 1.6 × 10−2 kg · m2 /s
D. 3.2 × 10−1 kg · m2 /s
E. 1.1 kg · m2 /s
ans: B
28. As a 2.0-kg block travels around a 0.50-m radius circle it has an angular speed of 12 rad/s.
The circle is parallel to the xy plane and is centered on the z axis, 0.75 m from the origin. The
magnitude of its angular momentum around the origin is:
A. 6.0 kg · m2 /s
B. 9.0 kg · m2 /s
C. 11 kg · m2 /s
D. 14 kg · m2 /s
E. 20 kg · m2 /s
ans: C
168
Chapter 11:
ROLLING, TORQUE, AND ANGULAR MOMENTUM
29. As a 2.0-kg block travels around a 0.50-m radius circle it has an angular speed of 12 rad/s. The
circle is parallel to the xy plane and is centered on the z axis, a distance of 0.75 m from the
origin. The z component of the angular momentum around the origin is:
A. 6.0 kg · m2 /s
B. 9.0 kg · m2 /s
C. 11 kg · m2 /s
D. 14 kg · m2 /s
E. 20 kg · m2 /s
ans: A
30. As a 2.0-kg block travels around a 0.50-m radius circle it has an angular speed of 12 rad/s.
The circle is parallel to the xy plane and is centered on the z axis, 0.75 m from the origin. The
component in the xy plane of the angular momentum around the origin has a magnitude of:
A. 0
B. 6.0 kg · m2 /s
C. 9.0 kg · m2 /s
D. 11 kg · m2 /s
E. 14 kg · m2 /s
ans: C
31. A uniform disk has radius R and mass M . When it is spinning with angular velocity ω about
an axis through its center and perpendicular to its face its angular momentum is Iω. When it
is spinning with the same angular velocity about a parallel axis a distance h away its angular
momentum is:
A. Iω
B. (I + M h2 )ω
C. I − M h2 )ω
D. (I + M R2 )ω
E. (I − M R2 )ω
ans: B
32. A pulley with radius R and rotational inertia I is free to rotate on a horizontal fixed axis
through its center. A string passes over the pulley. A block of mass m1 is attached to one end
and a block of mass m2 is attached to the other. At one time the block with mass m1 is moving
downward with speed v. If the string does not slip on the pulley, the magnitude of the total
angular momentum, about the pulley center, of the blocks and pulley, considered as a system,
is given by:
A. (m1 − m2 )vR + Iv/R
B. (m1 + m2 )vR + Iv/R
C. (m1 − m2 )vR + Iv/R2
D. (m1 + m2 )vR + Iv/R2
E. none of the above
ans: B
Chapter 11:
ROLLING, TORQUE, AND ANGULAR MOMENTUM
169
33. A single force acts on a particle situated on the positive x axis. The torque about the origin is
in the negative z direction. The force might be:
A. in the positive y direction
B. in the negative y direction
C. in the positive x direction
D. in the negative x direction
E. in the positive z direction
ans: B
34. A rod rests on frictionless ice. Forces that are equal in magnitude and opposite in direction
are then simultaneously applied to its ends as shown. The quantity that vanishes is its:
...
.......
..........
...
....
..
...
...
.
... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ......
.
.
.
.... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...
.. ..... ..... ..... ..... ..... ..... ..... ..... ..... ..... ..... ..... ..... ..... ..... ..... ..... ..... .....
.
.
.
. .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... ...
.. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. ..
.... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...
.. .. .. .. .. .. .. .. .. .. .. .. .. .. .. ... ... ... ... ...
..... .... .... .... .... .... .... .... .... .... .... .... .... .... .... ... ... ... ... ...
...
...
...
...
...
..
....... ..
........
...
F
F
A.
B.
C.
D.
E.
angular momentum
angular acceleration
total linear momentum
kinetic energy
rotational inertia
ans: C
35. A 2.0-kg stone is tied to a 0.50-m long string and swung around a circle at a constant angular
velocity of 12 rad/s. The net torque on the stone about the center of the circle is:
A. 0
B. 6.0 N · m
C. 12 N · m
D. 72 N · m
E. 140 N · m
ans: A
36. A 2.0-kg stone is tied to a 0.50-m long string and swung around a circle at a constant angular
velocity of 12 rad/s. The circle is parallel to the xy plane and is centered on the z axis, 0.75 m
from the origin. The magnitude of the torque about the origin is:
A. 0
B. 6.0 N · m
C. 14 N · m
D. 72 N · m
E. 108 N · m
ans: E
170
Chapter 11:
ROLLING, TORQUE, AND ANGULAR MOMENTUM
37. A 2.0-kg block starts from rest on the positive x axis 3.0 m from the origin and thereafter
2
2
has an acceleration given by a = (4.0 m/s ) î − (3.0 m/s ) ĵ. The torque, relative to the origin,
acting on it at the end of 2.0 s is:
A. 0
B. (−18 N · m) k̂
C. (+24 N · m) k̂
D. (−144 N · m) k̂
E. (+144 N · m) k̂
ans: B
38. A uniform disk, a thin hoop, and a uniform sphere, all with the same mass and same outer
radius, are each free to rotate about a fixed axis through its center. Assume the hoop is
connected to the rotation axis by light spokes. With the objects starting from rest, identical
forces are simultaneously applied to the rims, as shown. Rank the objects according to their
angular momenta after a given time t, least to greatest.
hoop
disk
.......................
........
......
.....
....
...
...
...
...
....
...
..
..
...
.
...
..
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..
.
.
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..
.
....
.
...
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..
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......... ...................................................
..
•
A.
B.
C.
D.
E.
sphere
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..
•
F
•
F
F
all tie
disk, hoop, sphere
hoop, disk, sphere
hoop, sphere, disk
hoop, disk, sphere
ans: A
39. A single force acts on a particle P. Rank each of the orientations of the force shown below
according to the magnitude of the time rate of change of the particle’s angular momentum
about the point O, least to greatest.
O•
..
...........................................................
.
•
P
1
A.
B.
C.
D.
E.
•.......................................................
P
O•
2
...
......
.........
....
...
...
...
.
O•
•
P
3
..
................
.... ..
....
.
.
..
...
....
O•
•
P
4
1, 2, 3, 4
1 and 2 tie, then 3, 4
1 and 2 tie, then 4, 3
1 and 2 tie, then 3 and 4 tie
All are the same
ans: C
Chapter 11:
ROLLING, TORQUE, AND ANGULAR MOMENTUM
171
40. A pulley with radius R is free to rotate on a horizontal fixed axis through its center. A string
passes over the pulley. Mass m1 is attached to one end and mass m2 is attached to the other.
The portion of the string attached to m1 has tension T1 and the portion attached to m2 has
tension T2 . The magnitude of the total external torque, about the pulley center, acting on the
masses and pulley, considered as a system, is given by:
A. |m1 − m2 |gR
B. (m1 + m2 )gR
C. |m1 − m2 |gR + (T1 + T2 )R
D. (m1 + m2 )gR + (T1 − T2 )R
E. |m1 − m2 |gR + (T2 − T1 )R
ans: A
41. An ice skater with rotational inertia I0 is spinning with angular speed ω 0 . She pulls her arms
in, thereby increasing her angular speed to 4ω0 . Her rotational inertia is then:
A. I0
B. I0 /2
C. 2I0
D. I0 /4
E. 4I0
ans: D
42. A man, with his arms at his sides, is spinning on a light frictionless turntable. When he extends
his arms:
A. his angular velocity increases
B. his angular velocity remains the same
C. his rotational inertia decreases
D. his rotational kinetic energy increases
E. his angular momentum remains the same
ans: E
43. A man, holding a weight in each hand, stands at the center of a horizontal frictionless rotating
turntable. The effect of the weights is to double the rotational inertia of the system. As he is
rotating, the man opens his hands and drops the two weights. They fall outside the turntable.
Then:
A. his angular velocity doubles
B. his angular velocity remains about the same
C. his angular velocity is halved
D. the direction of his angular momentum vector changes
E. his rotational kinetic energy increases
ans: B
172
Chapter 11:
ROLLING, TORQUE, AND ANGULAR MOMENTUM
44. A uniform sphere of radius R rotates about a diameter with an angular momentum of magnitude
L. Under the action of internal forces the sphere collapses to a uniform sphere of radius R/2.
The magnitude of its new angular momentum is:
A. L/4
B. L/2
C. L
D. 2L
E. 4L
ans: C
45. When a man on a frictionless rotating stool extends his arms horizontally, his rotational kinetic
energy:
A. must increase
B. must decrease
C. must remain the same
D. may increase or decrease depending on his initial angular velocity
E. may increase or decrease depending on his angular acceleration
ans: B
46. When a woman on a frictionless rotating turntable extends her arms out horizontally, her
angular momentum:
A. must increase
B. must decrease
C. must remain the same
D. may increase or decrease depending on her initial angular velocity
E. tilts away from the vertical
ans: C
47. Two disks are mounted on low-friction bearings on a common shaft. The first disc has rotational
inertia I and is spinning with angular velocity ω. The second disc has rotational inertia 2I
and is spinning in the same direction as the first disc with angular velocity 2ω as shown. The
two disks are slowly forced toward each other along the shaft until they couple and have a final
common angular velocity of:
.
............................................
..
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.
.
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...
..
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.
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.
.
.
.
.
.
.
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..
.. ..
...
...
...
..
.......
.
.
.
.
..
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..
..
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.
.
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.
.
.
..
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..
.
.
..
.
.
.
.
.
.
.
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.
........
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..
.
.
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.
.....
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..
..
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.
...
...
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...
...
..
..
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..
.
.... ...
.
........................................ ...
..
.......................................
..
A.
B.
C.
D.
E.
ω
2ω
I
2I
5ω/3
√
ω 03
ω 7/3
ω
3ω
ans: A
Chapter 11:
ROLLING, TORQUE, AND ANGULAR MOMENTUM
173
48. A wheel with rotational inertia I, mounted on a vertical shaft with negligible rotational inertia,
is rotating with angular speed ω0 . A nonrotating wheel with rotational inertia 2I is suddenly
dropped onto the same shaft as shown. The resultant combination of the two wheels and shaft
will rotate at:
.......
......................... ....................................
..........
........
........
......
......
.....
.
.
.
.
...
..
...
...
.
.
.
.
.
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..
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..
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.
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.
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.
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.
.
.
.
.
.
..... .
... ......... ................
....... ..... .
.. .......... .................................................................... ............. ....
..........
...
...
..........
....................
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....
....
...
...
.
.
.
.
.
.
.
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.
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.
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.
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..
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.
...
...
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...
....
......
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.
.
.
.
.
.
.
.
.....
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...
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..
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..
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.
...
.
.
..
.
..............
...
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......
.
.
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.
..................
... ....
.
... ....... .................
.
.
.
.
.
.
.
.
..
..... ........
... .
....... .
...... ............ ................................. .................. ..........
..
........
.
..
........... ................................................ ..................
........................................................
..
..
...
...
..
...
...
..
.
.....
...................
A.
B.
C.
D.
E.
ω0 /2
2ω0
ω0 /3
3ω0
ω0 /4
ans: C
49. A phonograph record is dropped onto a freely spinning turntable. Then:
A. neither angular momentum nor mechanical energy is conserved because of the frictional
forces between record and turntable
B. the frictional force between record and turntable increases the total angular momentum
C. the frictional force between record and turntable decreases the total angular momentum
D. the total angular momentum remains constant
E. the sum of the angular momentum and rotational kinetic energy remains constant
ans: D
50. A playground merry-go-round has a radius R and a rotational inertia I. When the merry-goround is at rest, a child with mass m runs with speed v along a line tangent to the rim and
jumps on. The angular velocity of the merry-go-round is then:
A. mv/I
B. v/R
C. mRv/I
D. 2mRv/I
E. mRv/(mR2 + I)
ans: E
174
Chapter 11:
ROLLING, TORQUE, AND ANGULAR MOMENTUM
51. A playground merry-go-round has a radius of 3.0 m and a rotational inertia of 600 kg · m2 . It
is initially spinning at 0.80 rad/s when a 20-kg child crawls from the center to the rim. When
the child reaches the rim the angular velocity of the merry-go-round is:
A. 0.62 rad/s
B. 0.73 rad/s
C. 0.80 rad/s
D. 0.89 rad/s
E. 1.1 rad/s
ans: A
52. Two pendulum bobs of unequal mass are suspended from the same fixed point by strings of
equal length. The lighter bob is drawn aside and then released so that it collides with the other
bob on reaching the vertical position. The collision is elastic. What quantities are conserved
in the collision?
A. Both kinetic energy and angular momentum of the system
B. Only kinetic energy
C. Only angular momentum
D. Angular speed of lighter bob
E. None of the above
ans: A
53. A particle, held by a string whose other end is attached to a fixed point C, moves in a circle
on a horizontal frictionless surface. If the string is cut, the angular momentum of the particle
about the point C:
A. increases
B. decreases
C. does not change
D. changes direction but not magnitude
E. none of these
ans: C
54. A block with mass M , on the end of a string, moves in a circle on a horizontal frictionless table
as shown. As the string is slowly pulled through a small hole in the table:
...................................................................................................
..
..
...
...
...
...
..
..
.
.
..
.
.
.
.
..
..
.........
...
...
.
...
...
...
..
...
...
.
...
............
...
...
.
.
.
.
.
. ..... .
...
...
.. ... .. ...
...
...
.. .... .......
...
...
.........
..
..
.
.
.
.
.
.
.
..
.
...
...
...
...
...
...
............... .
...
...
..
..
.
.
.
.
..
..
...
...
...
...
..
..
........................................................................... ..
M
.•.
.. ..
...
...
...
...
...
...
...
...
..
......... pull
.
A.
B.
C.
D.
E.
the angular momentum of the block remains constant
the angular momentum of the block decreases
the kinetic energy of the block remains constant
the kinetic energy of the block decreases
none of the above
ans: A
Chapter 11:
ROLLING, TORQUE, AND ANGULAR MOMENTUM
175
Chapter 12:
EQUILIBRIUM AND ELASTICITY
1. A net torque applied to a rigid object always tends to produce:
A. linear acceleration
B. rotational equilibrium
C. angular acceleration
D. rotational inertia
E. none of these
ans: C
2. The conditions that the net force and the net torque both vanish:
A. hold for every rigid body in equilibrium
B. hold only for elastic solid bodies in equilibrium
C. hold for every solid body
D. are always sufficient to calculate the forces on a solid object in equilibrium
E. are sufficient to calculate the forces on a solid object in equilibrium only if the object is
elastic
ans: A
3. For an object in equilibrium the net torque acting on it vanishes only if each torque is calculated
about:
A. the center of mass
B. the center of gravity
C. the geometrical center
D. the point of application of the force
E. the same point
ans: E
4. For
A.
B.
C.
D.
E.
a body to be in equilibrium under the combined action of several forces:
all the forces must be applied at the same point
all of the forces form pairs of equal and opposite forces
the sum of the components of all the forces in any direction must equal zero
any two of these forces must be balanced by a third force
the lines of action of all the forces must pass through the center of gravity of the body
ans: C
5. For
A.
B.
C.
D.
E.
a body to be in equilibrium under the combined action of several forces:
all the forces must be applied at the same point
all of the forces form pairs of equal and opposite forces
any two of these forces must be balanced by a third force
the sum of the torques about any point must equal zero
the lines of action of all the forces must pass through the center of gravity of the body
ans: D
176
Chapter 12:
EQUILIBRIUM AND ELASTICITY
6. To determine if a rigid body is in equilibrium the vector sum of the gravitational forces acting
on the particles of the body can be replaced by a single force acting at:
A. the center of mass
B. the geometrical center
C. the center of gravity
D. a point on the boundary
E. none of the above
ans: C
7. The center of gravity coincides with the center of mass:
A. always
B. never
C. if the center of mass is at the geometrical center of the body
D. if the acceleration due to gravity is uniform over the body
E. if the body has a uniform distribution of mass
ans: D
8. The location of which of the following points within an object might depend on the orientation
of the object?
A. Its center of mass
B. Its center of gravity
C. Its geometrical center
D. Its center of momentum
E. None of the above
ans: B
9. A cylinder placed so it can roll on a horizontal table top, with its center of gravity above its
geometrical center, is:
A. in stable equilibrium
B. in unstable equilibrium
C. in neutral equilibrium
D. not in equilibrium
E. none of the above
ans: B
10. A cylinder placed so it can roll on a horizontal table top, with its center of gravity below its
geometrical center, is:
A. in stable equilibrium
B. in unstable equilibrium
C. in neutral equilibrium
D. not in equilibrium
E. none of the above
ans: A
Chapter 12:
EQUILIBRIUM AND ELASTICITY
177
11. A cube balanced with one edge in contact with a table top and with its center of gravity directly
equilibrium with respect to rotation about the edge and in
above the edge is in
equilibrium with respect to rotation about a horizontal axis that is perpendicular to the edge.
A. stable, stable
B. stable, unstable
C. unstable, stable
D. unstable, unstable
E. unstable, neutral
ans: C
12. A meter stick on a horizontal frictionless table top is pivoted at the 80-cm mark. A force F1
is applied perpendicularly to the end of the stick at 0 cm, as shown. A second force F2 (not
shown) is applied perpendicularly at the 100-cm end of the stick. The forces are horizontal. If
the stick does not move, the force exerted by the pivot on the stick:
F1
...
........
.. .....
....
...
...
...
..
pivot
...
...
...
...
...
...
...
..
..............
...
•
0 cm 20 cm 40 cm 60 cm 80 cm 100 cm
A.
B.
C.
D.
E.
must be
must be
must be
must be
must be
ans: E
zero
in the same direction as F1 and have magnitude |F2 | − |F1 |
directed opposite to F1 and have magnitude |F2 | − |F1 |
in the same direction as F1 and have magnitude |F2 | + |F1 |
directed opposite to F1 and have magnitude |F2 | + |F1 |
13. A meter stick on a horizontal frictionless table top is pivoted at the 80-cm mark. A force F1
is applied perpendicularly to the end of the stick at 0 cm, as shown. A second force F2 (not
shown) is applied perpendicularly at the 60-cm mark. The forces are horizontal. If the stick
does not move, the force exerted by the pivot on the stick:
F1
..
.......
..........
...
....
..
...
...
pivot
...
...
...
...
...
...
...
..
..............
..
•
0 cm 20 cm 40 cm 60 cm 80 cm 100 cm
A.
B.
C.
D.
E.
178
must be
must be
must be
must be
must be
ans: B
zero
in the same direction as F1 and have magnitude |F2 | − |F1 |
directed opposite to F1 and have magnitude |F2 | − |F1 |
in the same direction as F1 and have magnitude |F2 | + |F1 |
directed opposite to F1 and have magnitude |F2 | + |F1 |
Chapter 12:
EQUILIBRIUM AND ELASTICITY
14. Three identical uniform rods are each acted on by two or more forces, all perpendicular to
the rods and all equal in magnitude. Which of the rods could be in static equilibrium if an
additional force is applied at the center of mass of the rod?
...
........
....... ..
...
....
..
...
..
•
...
........
....... ..
...
....
..
...
..
•
•.......
...
...
...
....... ..
.........
..
..
........
..........
...
....
..
...
..
•
•.......
...
...
...
.........
.........
...
1
A.
B.
C.
D.
E.
2
..
........
..........
...
....
..
...
..
•
•.......
...
...
...
....... ..
.........
..
..
........
..........
...
....
..
...
..
•
3
Only 1
Only 2
Only 3
Only 1 and 2
All three
ans: C
15. A 160-N child sits on a light swing and is pulled back and held with a horizontal force of 100 N.
The magnitude of the tension force of each of the two supporting ropes is:
A. 60 N
B. 94 N
C. 120 N
D. 190 N
E. 260 N
ans: B
16. The diagram shows a stationary 5-kg uniform rod (AC), 1 m long, held against a wall by a
rope (AE) and friction between the rod and the wall. To use a single equation to find the
force exerted on the rod by the rope at which point should you place the reference point for
computing torque?
...
..
....
..
....
..
..
.........
...... ..
...... .....
.
.
.
.
.
.
..
......
....
......
..
......
......
....
......
.
.
.
.
.
.
.
.
....
......
..
......
......
....
......
..
......
.
.
.
.
.
....
....
.
.
.
.
.
.
.
.
......
....
......
..
......
....
......
......
.
.
.
.
.
.
.
..
....
......
..
......
....
..
....
...
...
..
....
...
E•
D
•
•
A
•
B
C
•
ans: C
Chapter 12:
EQUILIBRIUM AND ELASTICITY
179
17. A picture P of weight W is hung by two strings as shown. The magnitude of the tension force
of each string is T . The total upward pull of the strings on the picture is:
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
.. .. .... .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. ..... .. ..
....
..
....
....
...
....
....
...
....
....
.
.
.
.
.
.
.
.
.
. ..
.. ...
... ......
.... ....
....
...
..
....
..
..
...
.
•
T
θ
•
T
•
θ
•
P
A.
B.
C.
D.
E.
2W cos θ
T sin θ
T cos θ
2T sin θ
2T cos θ
ans: D
18. A picture can be hung on a wall with string in three different ways, as shown. The magnitude
of the tension force of the string is:
•
•
.. ..
... ...
... ...
... ...
... ...
... ...
... ...
... ...
... ...
.....
... ....
... .....
...
...
.
.
.
...
...
...
...
...
...
...
.
.
...
..
.
...
.
...
...
.
.
.
•
•
••
I
A.
B.
C.
D.
E.
•
...
...... ...........
......
......
......
......
......
......
......
......
.
.
.
.
...
...
•
II
•
III
least in I
greatest in I
greatest in II
least in III
greatest in III
ans: E
19. A uniform plank is supported by two equal 120-N forces at X and Y, as shown. The support
at X is then moved to Z (half-way to the plank center). The supporting forces at Y and Z are
then:
X
Z
Y
•
.....
.....
.
.
.
.... .. .. ..
.
.
......
......
......
.......
. . . .
...
... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ..
...
... ... ... ...
... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
.
A.
B.
C.
D.
E.
180
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
FY = 240 N, FZ = 120 N
FY = 200 N, FZ = 40 N
FY = 40 N, FZ = 200 N
FY = 80 N, FZ = 160 N
FY = 160 N, FZ = 80 N
ans: D
Chapter 12:
EQUILIBRIUM AND ELASTICITY
.
.
.
.
.
.
.
.
.
.
.
.
20. A uniform rod AB is 1.2 m long and weighs 16 N. It is suspended by strings AC and BD as
shown. A block P weighing 96 N is attached at E, 0.30 m from A. The magnitude of the tension
force of the string BD is:
.. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. ..
... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
C
•
•
E
A•
A.
B.
C.
D.
E.
D
•B
•
•
P
8.0 N
24 N
32 N
48 N
80 N
ans: C
21. A 5.0-m weightless strut, hinged to a wall, is used to support an 800-N block as shown. The
horizontal and vertical components of the force of the hinge on the strut are:
.
.......
.
......
.
.......
.
......
.
......
.
.
.
.
.
.
.
.
......
.
.......
.
.
.
....
.
.......
.
......
.
.......
.
.
.
.
.
..
.
......
.
.......
.
.......
.
.......
.
.......
.
........................
.
.
.
.
.
... .......... ....
.. . .
....... .......... ....
....... .......
.
.
.
.
.
. .....
.
.......
.
......
•
hinge
A.
B.
C.
D.
E.
3m
••••••
•••••
•
•
•••
•••
•
•
•••
•••
•
•
••
••••
•
•
•••
•••
•
•
•
••••
800 N
FH = 800 N, FY = 800 N
FH = 600 N, FY = 800 N
FH = 800 N, FY = 600 N
FH = 1200 N, FY = 800 N
FH = 0, FY = 800 N
ans: B
22. A uniform plank is 6.0 m long and weighs 80 N. It is balanced on a sawhorse at its center. An
additional 160 N weight is now placed on the left end of the plank. To keep the plank balanced,
it must be moved what distance to the left?
A. 6.0 m
B. 2.0 m
C. 1.5 m
D. 1.0 m
E. 0.50 m
ans: B
Chapter 12:
EQUILIBRIUM AND ELASTICITY
181
23. A uniform 240-g meter stick can be balanced by a 240-g weight placed at the 100-cm mark if
the fulcrum is placed at the point marked:
A. 75 cm
B. 60 cm
C. 50 cm
D. 40 cm
E. 80 cm
ans: A
24. A ladder leans against a wall. If the ladder is not to slip, which one of the following must be
true?
.
......
.
......
.
.
.
.
.
.
.
......
.
......
.
......
......
.
......
.
......
.
......
.
......
......
.
......
.
......
......
.
......
.
......
......
.....................................................................................................................................
••••••
••••••
••••••
••••••
••••••
••••••
••••••
••••••
••••••
••••••
••••••
•
A.
B.
C.
D.
E.
The coefficient of friction between the ladder and the wall must not be zero
The coefficient of friction between the ladder and the floor must not be zero
Both A and B
Either A or B
Neither A nor B
ans: B
25. An 80-N uniform plank leans against a frictionless wall as shown. The magnitude of the torque
(about point P) applied to the plank by the wall is:
..
......
.......
.
.
.
.....
..
......
.
.
.
.
...
..
......
.
......
..
......
.
.
.
.
.
.
.
.
......
..
......
.
.
.
....
..
......
.
......
..
......
.
.
.
.
.
.
..
.
......
..
.
.
.
.
.
.
.. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .
...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... .......
••••• ↑|
••••••
•
•
•
•••••
|
|
•••••
•
•
•
•
•
•
•
•
•
4m
••••
•••••
•
•
•
|
•
•
|
•••••
•
•
•
•
••••P
•
•
•
↓|
••••
←−−−− 3 m −−−−→
A.
B.
C.
D.
E.
182
40 N · m
60 N · m
120 N · m
160 N · m
240 N · m
ans: C
Chapter 12:
EQUILIBRIUM AND ELASTICITY
26. An 800-N man stands halfway up a 5.0-m long ladder of negligible weight. The base of the
ladder is 3.0 m from the wall as shown. Assuming that the wall-ladder contact is frictionless,
the wall pushes against the ladder with a force of magnitude:
..
......
..
......
.
.
.
.
.
...
..
......
.
.
.....
.
.
.
.
..
..... .....
..
........
......
..
.
.
.
.
.
.
..
......
..
......
.
.
.
.
....
..
......
.
.
.
.
.
..
..
......
.
......
.
.
......
.......
.
.
.
.....
..
......
. . . . . . . . . . . . . . . . . . .
..................................................................................................................
••••
••••
••••
..
•••• .
••••
••••
••••
••••
••••
••••
••••
••••
••••
••••
••••
3m
•
A.
B.
C.
D.
E.
150 N
300 N
400 N
600 N
800 N
ans: B
27. A uniform ladder is 10 m long and weighs 400 N. It rests with its upper end against a frictionless
vertical wall. Its lower end rests on the ground and is prevented from slipping by a peg driven
into the ground. The ladder makes a 30◦ angle with the horizontal. The magnitude of the
force exerted on the peg by the ladder is:
...
.......
...
.......
...
.......
..
.......
...
.......
.
.
.
......
...
.......
...
.......
..
.......
...
.......
.
.
.
......
...
.......
..
◦
...
...
...
.......
... ... ... ... .... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
....... ....... ....... ....... ....... ....... ....... ....... ....... ....... ....... ....... ....... ....... ....... ....... ....... ....... .......
•••
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•
•
•
•
•
•
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•
•
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•
•
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•
•••••••
peg •••• •••••••••••••• 30
••••••
A.
B.
C.
D.
E.
zero
200 N
400 N
470 N
670 N
ans: D
Chapter 12:
EQUILIBRIUM AND ELASTICITY
183
28. A window washer attempts to lean a ladder against a frictionless wall. He finds that the ladder
slips on the ground when it is placed at an angle of less than 75◦ to the ground but remains in
place when the angle is greater than 75◦ . The coefficient of static friction between the ladder
and the ground:
A. is about 0.13
B. is about 0.27
C. is about 1.0
D. depends on the mass of the ladder
E. depends on the length of the ladder
ans: A
29. The 600-N ball shown is suspended on a string AB and rests against a frictionless vertical wall.
The string makes an angle of 30◦ with the wall. The magnitude of the tension force of the
string is:
..
.....
.....
.
...
..
◦ .......
..
... .....
..... ......
............... ....................
.. .......
... ..
.................................. ....
......
.... ..
.....
... ..
.
.
.
.... .
...
......
...
......
....
..
...
......
...
......
.
. .. .
...
.
.
....
.... ...
......
.........
...... ....
.....................
...
....
....
.
...
30
600 N
A.
B.
C.
D.
E.
184
•
•A
•
B
690 N
1200 N
2100 N
2400 N
none of these
ans: A
Chapter 12:
EQUILIBRIUM AND ELASTICITY
30. The 600-N ball shown is suspended on a string AB and rests against a frictionless vertical wall.
The string makes an angle of 30◦ with the wall. The ball presses against the wall with a force
of mangitude:
.
.....
.
...
.
...
..
◦ ......
.
... .......
.... ... ...
................. ...................
. .......
.. ... .
............................... ....
..... ..
.......
....
... ...
.
.
......
...
......
..
.. ..
...
....
....
...
......
...
......
.
....
...
.
.
. .
....
... ...
.....
...... ....
........
.......................
...
.....
.
...
.
..
30
600 N
A.
B.
C.
D.
E.
•
•A
•
B
120 N
300 N
350 N
600 N
690 N
ans: C
31. The uniform rod shown below is held in place by the rope and wall. Suppose you know the
weight of the rod and all dimensions. Then you can solve a single equation for the force of the
rope on the rod, provided you write expressions for the torques about the point:
...
...
.
....
.
.
.
. .....
...
.
.... ................
.........
.........
....
........
.
.
.........
...
.........
.........
....
.........
.
.
.........
. ..
.........
........
....
......
.
.
.
..
.
...
....
..
...
...
•1
•
A.
B.
C.
D.
E.
2
•
3
•
4
1
2
3
4
1, 2, or 3
ans: B
Chapter 12:
EQUILIBRIUM AND ELASTICITY
185
32. A 240-N weight is hung from two ropes as shown. The tension force of the horizontal rope has
magnitude:
. . . . . . . . . . . . . . . . . . . . .
..... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... .........
.
.
...
......
.
.......
.......
.....
.......
.
.
.
.
.
.
....
......
..
.......
...
.......
.......
....
.......
.
.
.
.
.
.
.
.
....
........
◦
....... ...
.
.............................................................. .........
.
...
....
.
...
....
.
.....
.....
.
.. .
....
..
...
....
.
.
....
...
•
•
A.
B.
C.
D.
E.
•
30
•
240 N
0
656 N
480 N
416 N
176 N
ans: D
33. A 960-N block is suspended as shown. The beam AB is weightless and is hinged to the wall at
A. The tension force of the cable BC has magnitude:
.
.......
.
......
.
.......
.
...................
. ........
......
.......
.
......
.
.
.
.
.
.
.......
.
.......
.
......
......
.......
.
.......
.......
......
.
.
.
.......
....
.......
.
......
.......
.......
.
.
.
.
.......
.
...
.......
.
......
.......................
.......
...
.
.
.......
.
.
.
.. ........... ..
.
.
.
....
.
...... .......... ...
..
.
...
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
....
...
.
.
.
..
.....
.
................................................
.......
..
..
.
..
.
.
.
.
.
.
...
.
.....
.
.
...
.......
....
.
.
.
.
.
.
.
.
..
........................................................
.
.
.
.
.
.
.
.......
C
↑ •
|
3m
|
↓
•••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••B
•••
A ←−−−− 4 m −−−−→
960 N
A.
B.
C.
D.
E.
186
720 N
1200 N
1280 N
1600 N
none of these
ans: D
Chapter 12:
EQUILIBRIUM AND ELASTICITY
34. A horizontal beam of weight W is supported by a hinge and cable as shown. The force exerted
on the beam by the hinge has a vertical component that must be:
.
.......
.
.......
.
.
.
.
.
.
..
..
...... ............
.......
.......
......
.......
.
.
.
.......
.....
.......
.
......
.......
.......
.
.
.
.
.......
....
......
.
.......
.......
.......
.
.
.
.
.
......
...
.......
.
.......
.......
......
.
.
.......
.
.
.
.
. .................
.......
.
.
......
...... ........... ....
..
.
...
....... .......... .....
.
.
.
.
.
.
.
....
..... ..............
.
....
.......
..
.
......
....... ..
.
.........
.......
...
.
.
.
.
.
..
.
.......
.
......
•
cable
hinge
••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••
W
A.
B.
C.
D.
E.
nonzero and up
nonzero and down
nonzero but not enough information given to know whether up or down
zero
equal to W
ans: A
35. A 400-N uniform vertical boom is attached to the ceiling by a hinge, as shown. An 800-N
weight W and a horizontal guy wire are attached to the lower end of the boom as indicated.
The pulley is massless and frictionless. The tension force T of the horizontal guy wire has
magnitude:
.. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. ..
... ... ... ... ... ... ... ... ... ..... ... ... ... ... ... ... ... ... ..... ....... ...... ... ... ... ... ...
. ... .. .
...
.... ..... .... ....
.
... ..... ...
....................
....... .......
...... .... .........
...
...
.
....
.
.
...
..
..
.
.
.....
...
....
.....
...
. ..
.
......
.. ...
.
... ....
.... ......
...
...
.. ........... ............
...
.........
...
....
...
...
...
...
...
...
...
...
...
...
...
...
...
.
◦ ..............
...
.....
...
.
pulley
•
•
W = 800 N
A.
B.
C.
D.
E.
60
••• hinge
•••
•••
•••
••• boom (400 N)
•••
•••
•••
•••
•••
•
guy wire
340 N
400 N
690 N
800 N
1200 N
ans: B
Chapter 12:
EQUILIBRIUM AND ELASTICITY
187
36. A picture is to be hung from the ceiling by means of two wires. Order the following arrangements
of the wires according to the tension force of wire B, from least to greatest.
. . . . . . . . . . . . . . .
... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
.. .. .. .. .. .. .. .. .. .. .. .. .. .. ..
A
A.
B.
C.
D.
E.
B
. . . . . . . . . . . . . . .
... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
.. .. .. .. .. .. .. .. .. .. .. .. .. .. ..
A
B
• cm
• cm
I
II
. . . . . . . . . . . . . . .
... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
.. .. .. .. .. .. .. .. .. .. .. .. .. .. ..
A
B
• cm
III
I, II, III
III, II, I
I and II tie, then III
II, I, III
all tie
ans: D
37. The pull P is just sufficient to keep the 14-N block and the weightless pulleys in equilibrium
as shown. The magnitude T of the tension force of the upper cable is:
... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
.. .. .. .. .. .. .. .. ... .. .. .. .. .. .. .. ..
....
...
....
.
.
....
.
.
.
...... ... ..........
.
.
...
.....
....
...
...
.
.....
...
......
........
.
.
.
... ................... ....
..
...
.................
.....
..... .... .......
..
...
...
..
.....
.
....
..
...
.......
....
.......
.
.
... .......
...
..
... ................ .....
...
..
..
..........
...
...
....... .. .......
...
...
... ... .....
...
...
...
....
.
...
.
..
....
.....
......
....
..
..
.
.....
..... ........................ .....
....
....
...
...
...
..
...
...
...
...
...
....
....
....
...
...
...
.........
........
...
T
•
•
•
•
14 lb
A.
B.
C.
D.
E.
188
P
14 N
28 N
16 N
9.33 N
18.7 N
ans: C
Chapter 12:
EQUILIBRIUM AND ELASTICITY
38. The ideal mechanical advantage (i.e. the ratio of the weight W to the pull P for equilibrium)
of the combination of pulleys shown is:
. . . . . . . . . . . . . . .
... ... ... ... .... ... ... ... ... ... .... ... .... ... ...
...
...
...
...
...
...
...
...
...
.
.
...
.
.
.
...................
.
.
.
.
.
...
.
.
..
... ... .....
.
...
.
.
...
.
...
....
.
.....
..
..
...
.
.....
.
.
....
.
.
...
.......
.
.
.. .
...
....
.... .................... ....
.
...
.
.
.
..... ..
.
........
...
.... ......................... ....
...
......
...
......
..
...
...
.
.
...
.
.
...
..
.
...
.
.
.
...
..... .. .....
..................
...
....
..
... ..................... ....
... ..
........
....
...
...
...
.
...
...
..
.
..... ... ......
..................
...
...
...
...
..
•
• •
•
P
•
•
•
W
A.
B.
C.
D.
E.
1
2
3
4
5
ans: D
39. Stress can be measured in:
A. N/m2
B. N·m2
C. N/m
D. N·m
E. none of these (it is unitless)
ans: A
40. Strain can be measured in:
A. N/m2
B. N·m2
C. N/m
D. N·m
E. none of these (it is unitless)
ans: E
41. Young’s modulus can be correctly given in:
A. N·m
B. N/m2
C. N·m/s
D. N/m
E. joules
ans: B
Chapter 12:
EQUILIBRIUM AND ELASTICITY
189
42. Young’s modulus is a proportionality constant that relates the force per unit area applied
perpendicularly at the surface of an object to:
A. the shear
B. the fractional change in volume
C. the fractional change in length
D. the pressure
E. the spring constant
ans: C
43. Young’s modulus can be used to calculate the strain for a stress that is:
A. just below the ultimate strength
B. just above the ultimate strength
C. well below the yield strength
D. well above the yield strength
E. none of the above
ans: C
44. The ultimate strength of a sample is the stress at which the sample:
A. returns to its original shape when the stress is removed
B. remains underwater
C. breaks
D. bends 180◦
E. does none of these
ans: C
45. A certain wire stretches 0.90 cm when outward forces with magnitude F are applied to each
end. The same forces are applied to a wire of the same material but with three times the
diameter and three times the length. The second wire stretches:
A. 0.10 cm
B. 0.30 cm
C. 0.90 cm
D. 2.7 cm
E. 8.1 cm
ans: B
46. A force of 5000 N is applied outwardly to each end of a 5.0-m long rod with a radius of 34.0 cm
and a Young’s modulus of 125 × 108 N/m2 . The elongation of the rod is:
A. 0.0020 mm
B. 0.0040 mm
C. 0.14 mm
D. 0.55 mm
E. 1.42 mm
ans: D
190
Chapter 12:
EQUILIBRIUM AND ELASTICITY
47. A 4.0-m long steel beam with a cross-sectional area of 1.0 × 10−2 m2 and a Young’s modulus
2
of 2.0 × 1011 N/m is wedged horizontally between two vertical walls. In order to wedge the
beam, it is compressed by 0.020 mm. If the coefficient of static friction between the beam and
the walls is 0.70 the maximum mass (including its own) it can bear without slipping is:
A. 0
B. 3.6 kg
C. 36 kg
D. 71 kg
E. 710 kg
ans: E
48. Two supports, made of the same material and initially of equal length, are 2.0 m apart. A stiff
board with a length of 4.0 m and a mass of 10 kg is placed on the supports, with one support
at the left end and the other at the midpoint. A block is placed on the board a distance of
0.50 m from the left end. As a result the board is horizontal. The mass of the block is:
A. zero
B. 2.3 kg
C. 6.6 kg
D. 10 kg
E. 20 kg
ans: E
49. The bulk modulus is a proportionality constant that relates the pressure acting on an object
to:
A. the shear
B. the fractional change in volume
C. the fractional change in length
D. Young’s modulus
E. the spring constant
ans: B
2
50. A cube with edges exactly 2 cm long is made of material with a bulk modulus of 3.5×109 N/m .
When it is subjected to a pressure of 3.0 × 105 Pa its volume is:
A. 7.31 cm3
B. 7.99931 cm3
C. 8.00069 cm3
D. 8.69 cm3
E. none of these
ans: B
2
51. A cube with 2.0-cm sides is made of material with a bulk modulus of 4.7 × 105 N/m . When
it is subjected to a pressure of 2.0 × 105 Pa the length of its any of its sides is:
A. 0.85 cm
B. 1.15 cm
C. 1.66 cm
D. 2.0 cm
E. none of these
ans: C
Chapter 12:
EQUILIBRIUM AND ELASTICITY
191
52. To shear a cube-shaped object, forces of equal magnitude and opposite directions might be
applied:
A. to opposite faces, perpendicular to the faces
B. to opposite faces, parallel to the faces
C. to adjacent faces, perpendicular to the faces
D. to adjacent faces, neither parallel or perpendicular to the faces
E. to a single face, in any direction
ans: B
53. A shearing force of 50 N is applied to an aluminum rod with a length of 10 m, a cross-sectional
2
area of 1.0 × 10−5 m, and a shear modulus of 2.5 × 1010 N/m . As a result the rod is sheared
through a distance of:
A. zero
B. 1.9 mm
C. 1.9 cm
D. 19 cm
E. 1.9 m
ans: B
192
Chapter 12:
EQUILIBRIUM AND ELASTICITY
Chapter 13:
GRAVITATION
1. In the formula F = Gm1 m2 /r2 , the quantity G:
A. depends on the local value of g
B. is used only when Earth is one of the two masses
C. is greatest at the surface of Earth
D. is a universal constant of nature
E. is related to the Sun in the same way that g is related to Earth
ans: D
2. The magnitude of the acceleration of a planet in orbit around the Sun is proportional to:
A. the mass of the planet
B. the mass of the Sun
C. the distance between the planet and the Sun
D. the reciprocal of the distance between the planet and the Sun
E. the product of the mass of the planet and the mass of the Sun
ans: B
3. Suitable units for the gravitational constant G are:
A. kg·m/s2
B. m/s2
C. N·s/m
D. kg·m/s
E. m3 /(kg·s2 )
ans: E
4. The gravitational constant G has the derived units:
A. N·m
B. N·m/kg
C. N·kg/m
D. N·m2 /kg2
E. N·kg2 /m2
ans: D
5. Earth exerts a gravitational force on the Moon, keeping it in its orbit. The reaction to this
force, in the sense of Newton’s third law, is:
A. the centripetal force on the Moon
B. the nearly circular orbit of the Moon
C. the gravitational force on Earth by the Moon
D. the tides due to the Moon
E. the apple hitting Newton on the head.
ans: C
Chapter 13:
GRAVITATION
193
6. A particle might be placed
1. inside a uniform spherical shell of mass M , but not at the center
2. inside a uniform spherical shell of mass M , at the center
3. outside a uniform spherical shell of mass M , a distance r from the center
4. outside a uniform solid sphere of mass M , a distance 2r from the center
Rank these situations according to the magnitude of the gravitational force on the particle,
least to greatest.
A. All tie
B. 1, 2, 3, 4
C. 1 and 2 tie, then 3 and 4 tie
D. 1 and 2 tie, then 3, then 4
E. 1 and 2 tie, then 4, then 3
ans: D
7. Three particles, two with mass m and one with mass M , might be arranged in any of the
four configurations known below. Rank the configurations according to the magnitude of the
gravitational force on M , least to greatest.
•m
d
•
M
d
•
m
d
•
m
•
m
1
A.
B.
C.
D.
E.
1, 2, 3,
2, 1, 3,
2, 1, 4,
2, 3, 4,
2, 3, 2,
ans: B
d
•
M
2
d
•
m
•
M
d
•
m
3
d •m
d
•
•
m
M
4
..
....
....
...
....
.
.
.
..
....
...
..............................................................
4
4
3
2
4
8. Four particles, each with mass m are arranged symmetrically about the origin on the x axis.
A fifth particle, with mass M , is on the y axis. The direction of the gravitational force on M
is:
y
•M
•
m
A.
B.
C.
D.
E.
194
↑
↓
←
→
none of these directions
ans: B
Chapter 13:
GRAVITATION
•
m
•
m
•
m
x
9. Let F1 be the magnitude of the gravitational force exerted on the Sun by Earth and F2 be the
magnitude of the force exerted on Earth by the Sun. Then:
A. F1 is much greater than F2
B. F1 is slightly greater than F2
C. F1 is equal to F2
D. F1 is slightly less than F2
E. F1 is much less than F2
ans: C
10. Let
is:
A.
B.
C.
D.
E.
M denote the mass of Earth and let R denote its radius. The ratio g/G at Earth’s surface
R2 /M
M/R2
M R2
M/R
R/M
ans: B
11. Venus has a mass of about 0.0558 times the mass of Earth and a diameter of about 0.381 times
the diameter of Earth. The acceleration of a body falling near the surface of Venus is about:
2
A. 0.21 m/s
2
B. 1.4 m/s
2
C. 2.8 m/s
2
D. 3.8 m/s
2
E. 25 m/s
ans: D
12. The approximate value of g at an altitude above Earth equal to one Earth diameter is:
2
A. 9.8 m/s
B. 4.9 m/s2
C. 2.5 m/s2
2
D. 1.9 m/s
2
E. 1.1 m/s
ans: E
13. A rocket ship is coasting toward a planet. Its captain wishes to know the value of g at the
surface of the planet. This may be inferred by:
A. measuring the apparent weight of one of the crew
B. measuring the apparent weight of an object of known mass in the ship
C. measuring the diameter of the planet
D. measuring the density of the planet
E. observing the ship’s acceleration and correcting for the distance from the center of the
planet.
ans: E
Chapter 13:
GRAVITATION
195
14. To measure the mass of a planet with the same radius as Earth, an astronaut drops an object
from rest (relative to the planet) from an altitude of one radius above the surface. When the
object hits its speed is 4 times what it would be if the same experiment were carried out for
Earth. In units of Earth masses, the mass of the planet is:
A. 2
B. 4
C. 8
D. 16
E. 32
ans: D
15. Suppose you have a pendulum clock that keeps correct time on Earth (acceleration due to
gravity = 9.8 m/s2 ). Without changing the clock, you take it to the Moon (acceleration due to
gravity = 1.6 m/s2 ). For every hour interval (on Earth) the Moon clock will record:
A. (9.8/1.6) h
B. 0
1h
9.8/1.6 h
C.
D. 0
(1.6/9.8) h
1.6/9.8 h
E.
ans: E
16. The mass of an object:
A. is slightly different at different locations on Earth
B. is a vector
C. is independent of the acceleration due to gravity
D. is the same for all objects of the same size and shape
E. can be measured directly and accurately on a spring scale
ans: C
17. An astronaut on the Moon simultaneously drops a feather and a hammer. The fact that they
land together shows that:
A. no gravity forces act on a body in a vacuum
B. the acceleration due to gravity on the Moon is less than on Earth
C. in the absence of air resistance all bodies at a given location fall with the same acceleration
D. the feather has a greater weight on the Moon than on Earth
E. G = 0 on the Moon
ans: C
18. The mass of a hypothetical planet is 1/100 that of Earth and its radius is 1/4 that of Earth.
If a person weighs 600 N on Earth, what would he weigh on this planet?
A. 24 N
B. 48 N
C. 96 N
D. 192 N
E. 600 N
ans: C
196
Chapter 13:
GRAVITATION
19. An object at the surface of Earth (at a distance R from the center of Earth) weighs 90 N. Its
weight at a distance 3R from the center of Earth is:
A. 10 N
B. 30 N
C. 90 N
D. 270 N
E. 810 N
ans: A
20. An object is raised from the surface of Earth to a height of two Earth radii above Earth. Then:
A. its mass increases and its weight remains constant
B. both its mass and weight remain constant
C. its mass remains constant and its weight decreases
D. both its mass and its weight decrease
E. its mass remains constant and its weight increases
ans: C
21. A spring scale, calibrated in newtons, is used to weigh sugar. If it were possible to weigh sugar
at the following locations, where will the buyer get the most sugar to a newton?
A. At the north pole
B. At the equator
C. At the center of Earth
D. On the Moon
E. On Jupiter
ans: C
22. Of
A.
B.
C.
D.
E.
the following where would the weight of an object be the least?
2000 miles above Earth’s surface
At the north pole
At the equator
At the center of Earth
At the south pole
ans: D
23. If Earth were to rotate only 100 times per year about its axis:
A. airplanes flying west to east would make better time
B. we would fly off Earth’s surface
C. our apparent weight would slightly increase
D. Earth’s atmosphere would float into outer space
E. our apparent weight would slightly decrease
ans: C
Chapter 13:
GRAVITATION
197
24. An
A.
B.
C.
D.
E.
astronaut in an orbiting spacecraft feels “weightless” because she:
is beyond the range of gravity
is pulled outward by centrifugal force
has no acceleration
has the same acceleration as the spacecraft
is outside Earth’s atmosphere
ans: D
25. Each of the four corners of a square with edge a is occupied by a point mass m. There is a
fifth mass, also m, at the center of the square. To remove the mass from the center to a point
far away the work that must be done by an external agent is given by:
A. 4Gm2 /a
2
/a
B. −4Gm
√
2Gm2 /a
C. 4 √
D. −4 2Gm2 /a
E. 4Gm2 /a2
ans: C
26. Two particles, each of mass m, are a distance d apart. To bring a third particle, with mass
2m, from far away to a resting point midway between the two particles the work done by an
external agent is given by:
A. 4Gm2 /d
B. −4Gm2 /d
C. 8Gm2 /d2
D. −8Gm2 /d2
E. zero
ans: D
27. The escape speed at the surface of Earth is approximately 8 km/s. What is the mass, in units
of Earth’s mass, of a planet with twice the radius of Earth for which the escape speed is twice
that for Earth?
A. 2
B. 4
C. 8
D. 1/2
E. 1/4
ans: C
28. Neglecting air resistance, a 1.0-kg projectile has an escape velocity of about 11 km/s at the
surface of Earth. The corresponding escape velocity for a 2.0 kg projectile is:
A. 3.5 km/s
B. 5.5 km/s
C. 7.1 km/s
D. 10 km/s
E. 11 km/s
ans: E
198
Chapter 13:
GRAVITATION
29. Neglecting air resistance, the escape speed from a certain planet for an empty space vehicle is
1.12 × 104 m/s. What is the corresponding escape speed for the fully loaded vehicle, which has
triple the mass of the empty one?
A. 3.73 × 103 m/s
B. 1.12 × 104 m/s
C. 3.36 × 104 m/s
D. 9.98 × 104 m/s
E. 1.40 × 1012 m/s
ans: B
30. An object is dropped from an altitude of one Earth radius above Earth’s surface. If M is the
mass of Earth and R is its radius the speed of the object just before it hits Earth is given by:
0
A. 0GM/R
B. 0GM/2R
C. 02GM/R
D. 0GM/R2
E.
GM/2R2
ans: A
31. A projectile is fired straight upward from Earth’s surface with a speed that is half the escape
speed. If R is the radius of Earth, the highest altitude reached, measured from the surface, is:
A. R/4
B. R/3
C. R/2
D. R
E. 2R
ans: B
32. The mass density of a certain planet has spherical symmetry but varies in such a way that the
mass inside every spherical surface with center at the center of the planet is proportional to
the radius of the surface. If r is the distance from the center of the planet to a point mass
inside the planet, the gravitational force on the mass is:
A. not dependent on r
B. proportional to r2
C. proportional to r
D. proportional to 1/r
E. proportional to 1/r2
ans: D
Chapter 13:
GRAVITATION
199
33. A spherical shell has inner radius R1 , outer radius R2 , and mass M , distributed uniformly
throughout the shell. The magnitude of the gravitational force exerted on the shell by a point
mass particle of m, located a distance d from the center, inside the inner radius, is:
A. 0
B. GM m/R12
C. GM m/d2
D. GM m/(R22 − d2 )
E. GM m/(R1 − d)2
ans: A
34. A spherical shell has inner radius R1 , outer radius R2 , and mass M , distributed uniformly
throughout the shell. The magnitude of the gravitational force exerted on the shell by a point
mass m, located a distance d from the center, outside the outer radius, is:
A. 0
B. GM m/R12
C. GM m/d2
D. GM m/(R22 − d2 )
E. GM m/(R1 − d)2
ans: C
35. A spherical shell has inner radius R1 , outer radius R2 , and mass M , distributed uniformly
throughout the shell. The magnitude of the gravitational force exerted on the shell by a point
particle of mass m located a distance d from the center, outside the inner radius and inside the
outer radius, is:
A. 0
B. GM m/d2
C. GM m/(R23 − d3 )
D. GM m(d3 − R13 )/d2 (R23 − R13 )
E. GM m/(d3 − R13 )
ans: D
36. An
A.
B.
C.
D.
E.
artificial satellite of Earth releases a bomb. Neglecting air resistance, the bomb will:
strike Earth under the satellite at the instant of release
strike Earth under the satellite at the instant of impact
strike Earth ahead of the satellite at the instant of impact
strike Earth behind the satellite at the instant of impact
never strike Earth
ans: E
37. An astronaut finishes some work on the outside of his satellite, which is in circular orbit around
Earth. He leaves his wrench outside the satellite. The wrench will:
A. fall directly down to Earth
B. continue in orbit at reduced speed
C. continue in orbit with the satellite
D. fly off tangentially into space
E. spiral down to Earth
ans: C
200
Chapter 13:
GRAVITATION
38. The elliptical orbit of a planet around the Sun is shown on the diagram. Which of the following
statements is true?
E
•
•D
.....................................................
..............
.........
........
.........
.......
......
......
......
......
.....
.
.
.
....
...
.
.
...
..
.
...
.
...
...
.
...
....
..
...
...
...
.
...
...
...
...
...
..
.
...
.
...
...
....
...
...
....
....
.....
.
.
.
.
.
......
.......
......
......
........
........
...........
.............................................................
A•
A.
B.
C.
D.
E.
•B
•C
the eccentricity of the orbit is less than zero
the eccentricity of the orbit is greater than 1
the sun might be at point C
the sun might be at point D
the sun might be at point B
ans: E
39. Consider the statement: “Earth moves in a stable orbit around the Sun and is therefore in
equilibrium”. The statement is:
A. false, because no moving body can be in equilibrium
B. true, because Earth does not fall into or fly away from the Sun
C. false, because Earth is rotating on its axis and no rotating body can be in equilibrium
D. false, because Earth has a considerable acceleration
E. true, because if it were not in equilibrium then buildings and structures would not be stable
ans: D
40. A planet travels in an elliptical orbit about a star X as shown. The magnitude of the acceleration
of the planet is:
Q
•
.....................................................
..............
.........
.........
.......
.......
......
......
......
.
.
.
.
.
.....
....
.
...
.
.
...
..
.
.
...
...
...
.
..
...
.
..
....
..
...
..
•
•
•
•
•
•
•
...
..
•
•
•
•
•
•
•
•
•
•
•
•
•
•
...
..
...
..
.
.
...
.
.
.
...
...
...
....
...
...
.....
....
......
.....
.
......
.
.
.
...
.......
.......
.........
.............
.........
....................................................
P•
W•
•X
V
A.
B.
C.
D.
E.
•R
•
•S
•
U
•
T
greatest at point Q
greatest at point S
greatest at point U
greatest at point W
the same at all points
ans: D
Chapter 13:
GRAVITATION
201
41. In planetary motion the line from the star to the planet sweeps out equal areas in equal times.
This is a direct consequence of:
A. the conservation of energy
B. the conservation of momentum
C. the conservation of angular momentum
D. the conservation of mass
E. none of the above
ans: C
42. The speed of a comet in an elliptical orbit about the Sun:
A. decreases while it is receding from the Sun
B. is constant
C. is greatest when farthest from the Sun
D. varies sinusoidally with time
E. equals L/(mr), where L is its angular momentum, m is its mass, and r is its distance from
the Sun
ans: A
43. A planet travels in an elliptical orbit about a star as shown. At what pair of points is the speed
of the planet the same?
Q
•
.........................................
..................
..........
........
.......
......
.....
...
.
.
....
.
...
...
.
.
...
...
.
...
..
.
...
..
.....
..
..
..
...
.
...
..
...
..
.
.
...
.
.
.
...
..
...
...
...
...
....
...
.....
.....
.
......
.
.
.
.
..
......
........
.......
..........
.......
.........
.................
..........................................
P..•...........................
•R
W•
•S
V
A.
B.
C.
D.
E.
202
W and S
P and T
P and R
Q and U
V and R
ans: D
Chapter 13:
GRAVITATION
•
•
U
•
T
44. Planet 1 and planet 2 are both in circular orbits around the same central star. The orbit of
planet 2 has a radius that is much larger than the radius of the orbit of planet 1. This means
that:
A. the period of planet 1 is greater than the period of planet 2 and the speed of planet 1 is
greater than the speed of planet 2
B. the period of planet 1 is greater than the period of planet 2 and the speed of planet 1 is
less than the speed of planet 2
C. the period of planet 1 is less than the period of planet 2 and the speed of planet 1 is less
than the speed of planet 2
D. the period of planet 1 is less than the period of planet 2 and the speed of planet 1 is greater
than the speed of planet 2
E. the planets have the same speed and the same period
ans: D
45. For a planet in orbit around a star the perihelion distance is rp ad its speed at perihelion is vp .
The aphelion distance is ra and its speed at aphelion is va . Which of the following is true?
A. va = vp
B. va /ra = vp /rp
C. va ra = vp rp
D. va /ra2 = vp /rp2
E. va ra2 = vp rp2
ans: C
46. A planet is in circular orbit around the Sun. Its distance from the Sun is four times the average
distance of Earth from the Sun. The period of this planet, in Earth years, is:
A. 4
B. 8
C. 16
D. 64
E. 2.52
ans: B
47. Two planets are orbiting a star in a distant galaxy. The first has a semimajor axis of 150 ×
106 km, an eccentricity of 0.20, and a period of 1.0 Earth years. The second has a semimajor
axis of 250 × 106 km, an eccentricity of 0.30, and a period of:
A. 0.46 Earth years
B. 0.57 Earth years
C. 1.4 Earth years
D. 1.8 Earth years
E. 2.2 Earth years
ans: E
Chapter 13:
GRAVITATION
203
48. A small satellite is in elliptical orbit around Earth as shown. If L denotes the magnitude of its
angular momentum and K denotes kinetic energy:
•
•
•
•
•
•
•
..•
.•
.•
...............................
.•
..•
•
....................•
..........
•
..........
........
........
.......
.......
......
......
.....
.
.
.
.
....
...
.
.
...
..
...
.
.
...
...
.
...
....
..
..
....
..
..
•
•
..
•
•
•
•
•
•
•
•
...
•
•
•
•
•
•
..
•
•
•
...
..
...
..
.
.
...
.
.
...
.
..
...
...
....
....
.....
......
.....
......
......
.
.
.
.
.
.......
...
.........
........
.............
..........
....................•
......................
.•
.•
.•
.•
.•
..•
•
•
2•
• Earth
•1
•
•
•
•
•
•
•
•
A.
B.
C.
D.
E.
L2 > L1
L2 > L1
L2 = L 1
L2 < L1
L2 = L 1
ans: E
and
and
and
and
and
K2
K2
K2
K2
K2
> K1
= K1
= K1
= K1
> K1
49. Assume that Earth is in circular orbit around the Sun with kinetic energy K and potential
energy U , taken to be zero for infinite separation. Then, the relationship between K and U :
A. is K = U
B. is K = −U
C. is K = U/2
D. is K = −U/2
E. depends on the radius of the orbit
ans: D
50. An artificial Earth satellite is moved from a circular orbit with radius R to a circular orbit with
radius 2R. During this move:
A. the gravitational force does positive work, the kinetic energy of the satellite increases, and
the potential energy of the Earth-satellite system increases
B. the gravitational force does positive work, the kinetic energy of the satellite increases, and
the potential energy of the Earth-satellite system decreases
C. the gravitational force does positive work, the kinetic energy of the satellite decreases, and
the potential energy of the Earth-satellite system increases
D. the gravitational force does negative work, the kinetic energy of the satellite increases, and
the potential energy of the Earth-satellite system decreases
E. the gravitational force does negative work, the kinetic energy of the satellite decreases, and
the potential energy of the Earth-satellite system increases
ans: E
51. An artificial satellite of Earth nears the end of its life due to air resistance. While still in orbit:
A. it moves faster as the orbit lowers
B. it moves slower as the orbit lowers
C. it slowly spirals away from Earth
D. it moves slower in the same orbit but with a decreasing period
E. it moves faster in the same orbit but with an increasing period
ans: A
204
Chapter 13:
GRAVITATION
52. A spaceship is returning to Earth with its engine turned off. Consider only the gravitational
field of Earth and let M be the mass of Earth, m be the mass of the spaceship, and R be the
distance from the center of Earth. In moving from position 1 to position 2 the kinetic energy
of the spaceship increases by:
]
}
1
1
−
GM m/R2
A. GM m
R22 R12
}
]
1
1
B. GM m
+
R12 R22
R1 − R 2
C. GM m
R12
R1 − R2
D. GM m
R1 R2
R1 − R2
E. GM m 2 2
R1 R2
ans: D
53. Given the perihelion distance, aphelion distance, and speed at perihelion of a planet, which of
the following CANNOT be calculated?
A. The mass of the star
B. The mass of the planet
C. The speed of the planet at aphelion
D. The period of orbit
E. The semimajor axis of the orbit
ans: B
54. The orbit of a certain satellite has a semimajor axis of 1.5 × 107 m and an eccentricity of 0.20.
Its perigee (minimum distance) and apogee (maximum distance) are respectively:
A. 1.2 × 107 m, 1.8 × 107 m
B. 3.0 × 106 m, 1.2 × 107 m
C. 9.6 × 106 m, 1.0 × 107 m
D. 1.0 × 107 m, 1.2 × 107 m
E. 9.6 × 106 m, 1.8 × 107 m
ans: A
55. A planet in another solar system orbits a star with a mass of 4.0 × 1030 kg. At one point in its
orbit it is 250×106 km from the star and is moving at 35 km/s. Take the universal gravitational
2
constant to be 6.67 × 10−11 m2 /s · kg and calculate the semimajor axis of the planet’s orbit.
The result is:
A. 79 × 106 km
B. 160 × 106 km
C. 290 × 106 km
D. 320 × 106 km
E. 590 × 106 km
ans: C
Chapter 13:
GRAVITATION
205
Chapter 14:
1. All
A.
B.
C.
D.
E.
FLUIDS
fluids are:
gases
liquids
gases or liquids
non-metallic
transparent
ans: C
2. Gases may be distinguished from other forms of matter by their:
A. lack of color
B. small atomic weights
C. inability to form free surfaces
D. ability to flow
E. ability to exert a buoyant force
ans: C
3. 1 Pa is:
A. 1 N/m
B. 1 m/N
C. 1 kg/m · s
D. 1 kg/m · s2
E. 1 N/m · s
ans: D
4. Mercury is a convenient liquid to use in a barometer because:
A. it is a metal
B. it has a high boiling point
C. it expands little with temperature
D. it has a high density
E. it looks silvery
ans: D
5. To
A.
B.
C.
D.
E.
206
obtain the absolute pressure from the gauge pressure:
subtract atmospheric pressure
add atmospheric pressure
subtract 273
add 273
convert to N/m2
ans: B
Chapter 14:
FLUIDS
6. Barometers and open-tube manometers are two instruments that are used to measure pressure.
A. Both measure gauge pressure
B. Both measure absolute pressure
C. Barometers measure gauge pressure and manometers measure absolute pressure
D. Barometers measure absolute pressure and manometers measure gauge pressure
E. Both measure an average of the absolute and gauge pressures
ans: D
3
7. To measure moderately low pressures oil with a density of 8.5 × 102 kg/m is used in place of
mercury in a barometer. A change in the height of the oil column of 1.0 mm indicates a change
in pressure of about:
A. 1.2 × 10−7 Pa
B. 1.2 × 10−5 Pa
C. 0.85 Pa
D. 1.2 Pa
E. 8.3 Pa
ans: E
8. The pressure exerted on the ground by a man is greatest when:
A. he stands with both feet flat on the ground
B. he stands flat on one foot
C. he stands on the toes of one foot
D. he lies down on the ground
E. all of the above yield the same pressure
ans: C
9. The vessels shown below all contain water to the same height. Rank them according to the
pressure exerted by the water on the vessel bottoms, least to greatest.
...
...
...
...
..
..
..
..
...
...
...
...
.
.
.
.
...
.
.
...
...
...
...
.
.
.
...
.
.
.
.
...
...
..
...
.
..
.
...
..
.
..
.
...
..
.
..
..
...
...
..
.
.
.
.
.
.
.
.
.
...
...
..
...
..
...
...
..
..
..
...
.
..................................................
..................................................
..................................................
...................................................
1
A.
B.
C.
D.
E.
2
4
3
1, 2, 3, 4
3, 4, 2, 1
4, 3, 2, 1
2, 3, 4, 1
All pressures are the same
ans: E
Chapter 14:
FLUIDS
207
10. In a stationary homogeneous liquid:
A. pressure is the same at all points
B. pressure depends on the direction
C. pressure is independent of any atmospheric pressure on the upper surface of the liquid
D. pressure is the same at all points at the same level
E. none of the above
ans: D
11. Which of the following five statements, concerning the upper surface pressure of a liquid, is
FALSE?
A. It is independent of the surface area
B. It is the same for all points on that surface
C. It would not increase if the liquid depth were increased
D. It would increase if the liquid density were increased
E. It would increase if the atmospheric pressure increased
ans: D
12. Several cans of different sizes and shapes are all filled with the same liquid to the same depth.
Then:
A. the weight of the liquid is the same for all cans
B. the force of the liquid on the bottom of each can is the same
C. the least pressure is at the bottom of the can with the largest bottom area
D. the greatest pressure is at the bottom of the can with the largest bottom area
E. the pressure on the bottom of each can is the same
ans: E
13. An airtight box, having a lid of area 80 cm2 , is partially evacuated. Atmospheric pressure is
1.01 × 105 Pa. A force of 600 N is required to pull the lid off the box. The pressure in the box
was:
A. 2.60 × 104 Pa
B. 6.35 × 104 Pa
C. 7.50 × 104 Pa
D. 1.38 × 105 Pa
E. 1.76 × 105 Pa
ans: A
14. A closed hemispherical shell of radius R is filled with fluid at uniform pressure p. The net force
of the fluid on the curved portion of the shell is given by:
A. 2πR2 p
B. πR2 p
C. 4πR2 p
D. (4/3)πR2 p
E. (4/3)πR3 p
ans: B
208
Chapter 14:
FLUIDS
15. The diagram shows a U-tube with cross-sectional area A and partially filled with oil of density
ρ. A solid cylinder, which fits the tube tightly but can slide without friction, is placed in the
right arm. The system is in equilibrium. The weight of the cylinder is:
...
...
...
↑|
...
...
...
...
...
...
...
...
L
...
...
cylinder
...
...
...
...
↓|
...
...
...
...
...
...
...
↑
...
...
...
...
...
...
|
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
h
oil
...
...
...
...
...
...
...
...
...
...
...
...
...
...
|
...
...
...
...
...
...
↓
...
...
...
............
...
...
...........
...
...
............
...
...........
...
... ............ ...
...
A.
B.
C.
D.
E.
ALρg
L3 ρg
Aρ(L + h)g
Aρ(L − h)g
none of these
ans: A
3
16. The density of water is 1.0 g/cm . The density of the oil in the left column of the U-tube shown
below is:
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
.
...
...
...
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...
...
...
...
...
...
...
...
...
..
...
...
...
............................
...
...
...
...
...
...
...
...
...
...
...
...
.....
.....
...
...
...
...
...
...
...
...
...
...
...
...
....
....
...
...
...........................
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
.....
.....
...
...
...
...
.
.
...
...
....
....
...
...
.
.
.
.
.
.
...
...
.
.
.
.
...
.
...
..
.
.
.
.
...
...
...
...
...
...
....
.....
...
...
.....
......
...
...
......
.........
............................
....
...
.
.
.
.....
....
.....
.....
......
......
.......
..........
.......
.........................................
↓
---------↑|
------2
cm
------------....
---....
↑ ....
oil ---10 cm
---....
---....
---....
---....
---....
---....
---....
|
---....
↓
---....
---....
....
....
water
....
....
....
....
....
....
....
....
....
....
....
....
....
....
....
....
....
....
....
....
....
....
....
....
....
....
....
....
....
....
....
....
....
....
....
....
....
....
....
....
....
....
....
....
....
....
......
......
......
......
.......
.......
........
.........
...
..................
...........................................
. ...............................
....
A.
B.
C.
D.
E.
3
0.20 g/cm
0.80 g/cm3
3
1.0 g/cm
3
1.3 g/cm
3
5.0 g/cm
ans: B
Chapter 14:
FLUIDS
209
3
17. A uniform U-tube is partially filled with water. Oil, of density 0.75 g/cm , is poured into the
right arm until the water level in the left arm rises 3 cm. The length of the oil column is then:
A. 2.25 cm
B. 8 cm
C. 6 cm
D. 4 cm
E. need to know the cross-sectional area of the U-tube
ans: B
18. A long U-tube contains mercury (density = 14 × 103 kg/m3 ). When 10 cm of water (density
3
= 1.0 × 103 kg/m ) is poured into the left arm, the mercury in the right arm rises above its
original level by:
A. 0.36 cm
B. 0.72 cm
C. 14 cm
D. 35 cm
E. 70 cm
ans: A
19. A bucket of water is pushed from left to right with increasing speed across a horizontal surface.
Consider the pressure at two points at the same level in the water.
A. It is the same
B. It is higher at the point on the left
C. It is higher at the point on the right
D. At first it is higher at the point on the left but as the bucket speeds up it is lower there
E. At first it is higher at the point on the right but as the bucket speeds up it is lower there
ans: B
20. A bucket resting on the floor of an elevator contains an incompressible fluid of density ρ. When
the elevator has an upward acceleration of magnitude a the pressure difference between two
points in a fluid separated by a vertical distance ∆h, is given by:
A. ρa∆h
B. ρg∆h
C. ρ(g + a)∆h
D. ρ(g − a)∆h
E. ρga∆h
ans: C
21. A bucket resting on the floor of an elevator contains an incompressible fluid of density ρ. When
the elevator has a downward acceleration of magnitude a the pressure difference between two
points in a fluid, separated by a vertical distance ∆h, is given by:
A. ρa∆h
B. ρg∆h
C. ρ(g + a)∆h
D. ρ(g − a)∆h
E. ρga∆h
ans: D
210
Chapter 14:
FLUIDS
22. “An object completely submerged in a fluid displaces its own volume of fluid”. This is:
A. Pascal’s paradox
B. Archimedes’ principle
C. Pascal’s principle
D. true, but none of the above
E. false
ans: D
23. A certain object floats in fluids of density
1. 0.9ρ0
2. ρ0
3. 1.1ρ0
Which of the following statements is true?
A. the buoyant force of fluid i is greater than the buoyant forces of the other two fluids
B. the buoyant force of fluid 3 is greater than the buoyant forces of the other two fluids
C. the three fluids exert the same buoyant force
D. the object displace the same volume of all three fluids
E. none of these are true
ans: C
24. A certain object floats in fluids of density
1. 0.9ρ0
2. ρ0
3. 1.1ρ0
Rank these fluids according to the volume displaced by the object, least to greatest.
A. 1, 2, 3
B. 3, 2, 1
C. 2, 3, 1
D. 3, 1, 2
E. All are the same
ans: B
Chapter 14:
FLUIDS
211
25. Two identical blocks of ice float in water as shown. Then:
A
B
A. block A displaces a greater volume of water since the pressure acts on a smaller bottom
area
B. block B displaces a greater volume of water since the pressure is less on its bottom
C. the two blocks displace equal volumes of water since they have the same weight
D. block A displaces a greater volume of water since its submerged end is lower in the water
E. block B displaces a greater volume of water since its submerged end has a greater area
ans: C
26. A block of ice at 0◦ C is floating on the surface of ice water in a beaker. The surface of the
water just comes to the top of the beaker. When the ice melts the water level will:
A. rise and overflow will occur
B. remain the same
C. fall
D. depend on the initial ratio of water to ice
E. depend on the shape of the block of ice
ans: B
27. A block of ice at 0◦ C containing a piece of cork is floating on the surface of ice water in a
beaker. When the ice has melted the water level:
A. is higher
B. is lower
C. is the same
D. depends on the initial ratio of water to ice
E. depends on the shape of the ice block
ans: C
28. A pirate chest rests at the bottom of an ocean. If the water is still, the net force it exerts on
the chest:
A. is upward
B. is downward
C. is zero
D. depends on the mass of the chest
E. depends on the contents of the chest
ans: B
212
Chapter 14:
FLUIDS
29. A small steel ball floats in a half-full container of mercury. When water is added:
A. the ball will float on the water
B. the ball will rise slightly
C. the mercury will float on the water
D. the ball will sink to the bottom of the container
E. the ball will lower slightly more into the mercury
ans: B
30. A cork floats on the surface of an incompressible liquid in a container exposed to atmospheric
pressure. The container is then sealed and the air above the liquid is evacuated. The cork:
A. sinks slightly
B. rises slightly
C. floats at the same height
D. bobs up and down about its old position
E. behaves erratically
ans: C
31. An object hangs from a spring balance. The balance indicates 30 N in air and 20 N when the
object is submerged in water. What does the balance indicate when the object is submersed
in a liquid with a density that is half that of water?
A. 20 N
B. 25 N
C. 30 N
D. 35 N
E. 40 N
ans: B
32. A fir wood board floats in fresh water with 60% of its volume under water. The density of the
wood in g/cm3 is:
A. 0.4
B. 0.5
C. 0.6
D. less than 0.4
E. more than 0.6
ans: C
33. A boat floating in fresh water displaces 16, 000 N of water. How many newtons of saltwater
would it displace if it floats in saltwater of specific gravity 1.17?
A. 14, 500
B. 17, 600
C. 16, 000
D. 284
E. 234
ans: C
Chapter 14:
FLUIDS
213
34. A rock, which weighs 1400 N in air, has an apparent weight of 900 N when submerged in fresh
3
water (998 kg/m ). The volume of the rock is:
A. 0.14 m3
B. 0.60 m3
C. 0.90 m3
D. 5.1 × 10−2 m3
E. 9.2 × 10−2 m3
ans: D
35. A loaded ship passes from a lake (fresh water) to the ocean (saltwater). Saltwater is more
dense than fresh water and as a result the ship will:
A. ride higher in the water
B. settle lower in the water
C. ride at the same level in the water
D. experience an increase in buoyant force
E. experience a decrease in buoyant force
ans: A
3
36. The dimensions of a wooden raft (density = 150 kg/m ) are 3.0 m × 3.0 m × 1.0 m. What
3
maximum load can it carry in seawater (density = 1020 kg/m )?
A. 1350 kg
B. 7800 kg
C. 9200 kg
D. 19, 500 kg
E. 24, 300 kg
ans: B
37. A tin can has a volume of 1000 cm3 and a mass of 100 g. Approximately what mass of lead
shot can it carry without sinking in water?
A. 900 g
B. 100 g
C. 1000 g
D. 1100 g
E. 980 g
ans: A
38. A block of wood weighs 160 N and has a specific gravity of 0.60. To sink it in fresh water
requires an additional downward force of:
A. 54 N
B. 64 N
C. 96 N
D. 110 N
E. 240 N
ans: D
214
Chapter 14:
FLUIDS
39. A student standardizes the concentration of a saltwater solution by slowly adding salt until an
egg will just float. The procedure is based on the assumption that:
A. all eggs have the same volume
B. all eggs have the same weight
C. all eggs have the same density
D. all eggs have the same shape
E. the salt tends to neutralize the cholesterol in the egg
ans: C
40. A solid has a volume of 8 cm3 . When weighed on a spring scale calibrated in grams, the scale
indicates 20 g. What does the scale indicate if the object is weighed while immersed in a liquid
3
of density 2 g/cm ?
A. 4 g
B. 10 g
C. 12 g
D. 16 g
E. Zero, since the object will float
ans: A
3
41. A 210-g object apparently loses 30 g when suspended in a liquid of density 2.0 g/cm . The
density of the object is:
A. 7.0 g/cm3
3
B. 3.5 g/cm
3
C. 1.4 g/cm
3
D. 14 g/cm
E. none of these
ans: D
42. A steel ax and an aluminum piston have the same apparent weight in water. When they are
weighed in air:
A. they weigh the same
B. the ax is heavier
C. the piston is heavier
D. both weigh less than they did in water
E. depends on their shapes
ans: C
43. The apparent weight of a steel sphere immersed in various liquids is measured using a spring
scale. The greatest reading is obtained for that liquid:
A. having the smallest density
B. having the largest density
C. subject to the greatest atmospheric pressure
D. having the greatest volume
E. in which the sphere was submerged deepest
ans: A
Chapter 14:
FLUIDS
215
44. A 0.50-N metal sinker appears (as measured using a spring scale) to have a weight of 0.45 N
when submerged in water. The specific gravity of the metal is:
A. 6
B. 8
C. 9
D. 10
E. 12
ans: D
45. An object floats on the surface of a fluid. For purposes of calculating the torque on it, the
buoyant force is taken to act at:
A. the center of the bottom surface of the object
B. the center of gravity of the object
C. the center of gravity of the fluid that the object replaced
D. the geometric center of the object
E. none of the above
ans: C
46. A blast of wind tips a sailboat in the clockwise direction when viewed from the stern. When
the wind ceases the boat rotates back toward the upright position if, when it is tilted, the
center of buoyancy:
A. is above the center of gravity
B. is below the center of gravity
C. is to the right of the center of gravity
D. is to the left of the center of gravity
E. coincides with the center of gravity
ans: C
47. A cork floats in water in a bucket resting on the floor of an elevator. The elevator then
accelerates upward. During the acceleration:
A. the cork is immersed more
B. the cork is immersed less
C. the cork is immersed the same amount
D. at first the cork is immersed less but as the elevator speeds up it is immersed more
E. at first the cork is immersed more but as the elevator speeds up it is immersed less
ans: C
48. Two balls have the same shape and size but one is denser than the other. If frictional forces
are negligible when they are dropped in air, which has the greater acceleration?
A. The heavier ball
B. The lighter ball
C. They have the same acceleration
D. The heavier ball if atmospheric pressure is high, they lighter ball if it is low
E. The lighter ball if atmospheric pressure is high, the heavier ball if it is low
ans: A
216
Chapter 14:
FLUIDS
49. The principle of fluid pressure that is used in hydraulic brakes or lifts is that:
A. pressure is the same at all levels in a fluid
B. increases of pressure are transmitted equally to all parts of a fluid
C. the pressure at a point in a fluid is due to the weight of the fluid above it
D. increases of pressure can only be transmitted through fluids
E. the pressure at a given depth is proportional to the depth in the fluid
ans: B
50. Which of the following statements about Pascal’s principle is true?
A. It is valid only for incompressible fluids
B. It explains why light objects float
C. It explains why the pressure is greater at the bottom of a lake than at the surface
D. It is valid only for objects that are less dense than water
E. None of the above are true
ans: E
51. The hydraulic automobile jack illustrates:
A. Archimedes’ principle
B. Pascal’s principle
C. Hooke’s law
D. Newton’s third law
E. Newton’s second law
ans: B
52. One piston in a hydraulic lift has an area that is twice the area of the other. When the pressure
at the smaller piston is increased by ∆p the pressure at the larger piston:
A. increases by 2∆p
B. increases by ∆p/2
C. increases by ∆p
D. increases by 4∆p
E. does not change
ans: C
53. A hydraulic press has one piston of diameter 2.0 cm and the other piston of diameter 8.0 cm.
What force must be applied to the smaller piston to obtain a force of 1600 N at the larger
piston?
A. 6.25 N
B. 25 N
C. 100 N
D. 400 N
E. 1600 N
ans: C
Chapter 14:
FLUIDS
217
54. The two arms of a U-tube are not identical, one having twice the diameter of the other. A
cork in the narrow arm requires a force of 16 N to remove it. The tube is filled with water and
the wide arm is fitted with a piston. The minimum force that must be applied to the piston
to push the cork out is:
A. 4 N
B. 8 N
C. 16 N
D. 32 N
E. 64 N
ans: E
55. A U-tube has dissimilar arms, one having twice the diameter of the other. It contains an
incompressible fluid and is fitted with a sliding piston in each arm, with each piston in contact
with the fluid. When the piston in the narrow arm is pushed down a distance d, the piston in
the wide arm rises a distance:
A. d
B. 2d
C. d/2
D. 4d
E. d/4
ans: E
56. A U-tube has dissimilar arms, one having twice the diameter of the other. It contains an
incompressible fluid and is fitted with a sliding piston in each arm, with each piston in contact
with the fluid. When an applied force does work W in pushing the piston in the narrow arm
on the piston in the wide arm.
down, the fluid does work
A. W
B. 2W
C. W/2
D. 4W
E. W/4
ans: A
57. A fluid is undergoing “incompressible” flow. This means that:
A. the pressure at a given point cannot change with time
B. the velocity at a given point cannot change with time
C. the velocity must be the same everywhere
D. the pressure must be the same everywhere
E. the density cannot change with time or location
ans: E
58. A fluid is undergoing steady flow. Therefore:
A. the velocity of any given molecule of fluid does not change
B. the pressure does not vary from point to point
C. the velocity at any given point does not vary with time
D. the density does not vary from point to point
E. the flow is not uphill or downhill
ans: C
218
Chapter 14:
FLUIDS
59. If p
A.
B.
C.
D.
E.
is a pressure and ρ is a density then p/ρ has units of:
m2
m2 /s2
N/m2
kg/m2
m3 /kg
ans: B
3
60. One end of a cylindrical pipe has a radius of 1.5 cm. Water (density = 1.0×103 kg/m ) streams
steadily out at 7.0 m/s. The rate at which mass is leaving the pipe is:
A. 2.5 kg/s
B. 4.9 kg/s
C. 7.0 kg/s
D. 48 kg/s
E. 7.0 × 103 kg/s
ans: B
3
61. One end of a cylindrical pipe has a radius of 1.5 cm. Water (density = 1.0×103 kg/m ) streams
steadily out at 7.0 m/s. The volume flow rate is:
A. 4.9 × 10−3 m3 /s
B. 2.5 m3 /s
C. 4.9 m3 /s
D. 7.0 m3 /s
E. 48 m3 /s
ans: A
62. The equation of continuity for fluid flow can be derived from the conservation of:
A. energy
B. mass
C. angular momentum
D. volume
E. pressure
ans: B
Chapter 14:
FLUIDS
219
63. The diagram shows a pipe of uniform cross section in which water is flowing. The directions
of flow and the volume flow rates (in cm3 /s) are shown for various portions of the pipe. The
direction of flow and the volume flow rate in the portion marked A are:
6→
3
↓
5
↓
↑
4
A
A.
B.
C.
D.
E.
3→
↓ and 3 cm3 /s
↑ and 7 cm3 /s
↓ and 9 cm3 /s
↑ and 11 cm3 /s
↓ and 15 cm3 /s
ans: E
64. An incompressible liquid flows along the pipe as shown. The ratio of the speeds v2 /v1 is:
................................................................................
...
..
...
...
..
...
..
.....
.
.. A ....
1
..........................................................................
..
...
..
..
v1.....
...................................
..
.
..
.
..
...
..
...
..
...
.
...
.
..
...
...
..
..
..
...
.
..
...
...
..
..
..
... .
.. ....
.
..
..
..
..
.....
2....
...
..
..
..
...
.. ...
..
...
...
A
v2
..
......................................
..
......................................................................
...
.
.
..
...................................................................
A.
B.
C.
D.
E.
A1 /A2
A2 /A1
0
0A1 /A2
A2 /A1
v1 /v2
ans: A
65. Water flows through a cylindrical pipe of varying cross section. The velocity is 3.0 m/s at a
point where the pipe diameter is 1.0 cm. At a point where the pipe diameter is 3.0 cm, the
velocity is:
A. 9 m/s
B. 3 m/s
C. 1 m/s
D. 0.33 m/s
E. 0.11 m/s
ans: D
220
Chapter 14:
FLUIDS
66. A constriction in a pipe reduces its diameter from 4.0 cm to 2.0 cm. Where the pipe is narrow
the water speed is 8.0 m/s. Where it is wide the water speed is:
A. 2.0 m/s
B. 4.0 m/s
C. 8.0 m/s
D. 16 m/s
E. 32 m/s
ans: C
67. Water flows from a 6.0-cm diameter pipe into an 8.0-cm diameter pipe. The speed in the 6.0-cm
pipe is 5.0 m/s. The speed in the 8.0-cm pipe is:
A. 2.8 m/s
B. 3.7 m/s
C. 6.6 m/s
D. 8.8 m/s
E. 9.9 m/s
ans: A
68. A lawn sprinkler is made of a 1.0-cm diameter garden hose with one end closed and 25 holes,
each with a diameter of 0.050 cm, cut near the closed end. If water flows at 2.0 m/s in the hose,
the speed of the water leaving a hole is:
A. 2.0 m/s
B. 32 m/s
C. 40 m/s
D. 600 m/s
E. 800 m/s
ans: B
69. Bernoulli’s equation can be derived from the conservation of:
A. energy
B. mass
C. angular momentum
D. volume
E. pressure
ans: A
70. Which of the following assumptions is NOT made in the derivation of Bernoulli’s equation?
A. Assume streamline flow
B. Neglect viscosity
C. Neglect friction
D. Neglect gravity
E. Neglect turbulence
ans: D
Chapter 14:
FLUIDS
221
71. The quantity y appearing in Bernoulli’s equation MUST be measured:
A. upward from the center of Earth
B. upward from the surface of Earth
C. upward from the lowest point in the flow
D. downward from the highest point in the flow
E. upward from any convenient level
ans: E
72. Water flows through a constriction in a horizontal pipe. As it enters the constriction, the
water’s:
A. speed increases and pressure decreases
B. speed increases and pressure remains constant
C. speed increases and pressure increases
D. speed decreases and pressure increases
E. speed decreases and pressure decreases
ans: A
73. Water is pumped through the hose shown below, from a lower level to an upper level. Compared
to the water at point 1, the water at point 2:
upper level
←2
...................................................................................................................
......
.....
...
................................................................................................................
...
.....
..
...
... .....
..
..
..
.
..
...
...
...
...
...
...
...
...
...
....
.....
.
...
...
...
.
...
....
...
...
..
...
...
...
.
.
....
....
..
..
.
...
....
...
...
...
...
...
.....
...
.................................................................................
...
...
...
....
......
.......
...........
..............................................................................
1←
lower level
A.
B.
C.
D.
E.
222
has greater speed and greater pressure
has greater speed and less pressure
has less speed and less pressure
has less speed and greater pressure
has greater speed and the same pressure
ans: B
Chapter 14:
FLUIDS
74. A non-viscous incompressible liquid is flowing through a horizontal pipe of constant cross
section. Bernoulli’s equation and the equation of continuity predict that the drop in pressure
along the pipe:
A. is zero
B. depends on the length of the pipe
C. depends on the fluid velocity
D. depends on the cross-sectional area of the pipe
E. depends on the height of the pipe
ans: A
75. A non-viscous incompressible fluid is pumped steadily into the narrow end of a long tapered
pipe and emerges from the wide end. The pressure at the input is greater than at the output.
A possible explanation is:
A. the fluid speed increases from input to output
B. the fluid speed is the same at the two ends
C. the fluid is flowing uphill
D. the fluid is flowing downhill
E. the fluid is flowing horizontally
ans: C
76. Water is pumped into one end of a long pipe at the rate of 40 L/min. It emerges at the other
end at 24 L/min. A possible reason for this decrease in flow is:
A. the water is being pumped uphill
B. the water is being pumped downhill
C. the diameter of the pipe is not the same at the two ends
D. friction in the pipe
E. a leak in the pipe
ans: E
77. Consider a pipe containing a fluid, with the fluid being at rest. To apply Bernoulli’s equation
to this situation:
A. set v equal to zero because there is no motion
B. set g equal to zero because there is no acceleration
C. set v and g both equal to zero
D. set p equal to the atmospheric pressure
E. cannot be done, Bernoulli’s equation applies only to fluids in motion
ans: A
3
78. Water (density = 1.0 × 103 kg/m ) flows through a horizontal tapered pipe. At the wide end
its speed is 4.0 m/s. The difference in pressure between the two ends is 4.5 × 103 Pa. The speed
of the water at the narrow end is:
A. 2.6 m/s
B. 3.4 m/s
C. 4.0 m/s
D. 4.5 m/s
E. 5.0 m/s
ans: E
Chapter 14:
FLUIDS
223
79. Water is streaming downward from a faucet opening with an area of 3.0 × 10−5 m2 . It leaves
the faucet with a speed of 5.0 m/s. The cross-sectional area of the stream 0.50 m below the
faucet is:
A. 1.5 × 10−5 m2
B. 2.0 × 10−5 m2
C. 2.5 × 10−5 m2
D. 3.0 × 10−5 m2
E. 3.5 × 10−5 m2
ans: C
80. A large water tank, open at the top, has a small hole in the bottom. When the water level is
30 m above the bottom of the tank, the speed of the water leaking from the hole:
A. is 2.5 m/s
B. is 24 m/s
C. is 44 m/s
D. cannot be calculated unless the area of the hole is given
E. cannot be calculated unless the areas of the hole and tank are given
ans: B
81. A large tank filled with water has two holes in the bottom, one with twice the radius of the
the speed of the water
other. In steady flow the speed of water leaving the larger hole is
leaving the smaller.
A. twice
B. four times
C. half
D. one-fourth
E. the same as
ans: E
82. A non-viscous incompressible fluid is pumped steadily up a vertical pipe with uniform cross
section. The difference in pressure between points at the top and bottom:
A. is the same as it would be if the fluid were motionless
B. is greater at higher flow rates than at lower flow rates
C. is less at higher flow rates than at lower flow rates
D. does not depend on the density of the fluid
E. is zero
ans: A
224
Chapter 14:
FLUIDS
83. A water line enters a house 2.0 m below ground. A smaller diameter pipe carries water to a
faucet 5.0 m above ground, on the second floor. Water flows at 2.0 m/s in the main line and at
3
7.0 m/s on the second floor. Take the density of water to be 1.0 × 103 kg/m . The difference
in pressure between the main line and the second floor is:
A. 7.15 × 104 Pa with the main line at the higher pressure
B. 2.65 × 104 Pa with the main line at the higher pressure
C. 7.15 × 104 Pa with the main line at the lower pressure
D. 2.65 × 104 Pa with the main line at the lower pressure
E. 9.4 × 104 Pa with the main line at the higher pressure
ans: A
84. A person blows across the top of one arm of a U-tube partially filled with water. The water in
that arm:
A. rises slightly
B. drops slightly
C. remains at the same height
D. rises if the blowing is soft but drops if it is hard
E. rises if the blowing is hard but drops if it is soft
ans: A
Chapter 14:
FLUIDS
225
Chapter 15:
OSCILLATIONS
1. In simple harmonic motion, the restoring force must be proportional to the:
A. amplitude
B. frequency
C. velocity
D. displacement
E. displacement squared
ans: D
2. An
A.
B.
C.
D.
E.
oscillatory motion must be simple harmonic if:
the amplitude is small
the potential energy is equal to the kinetic energy
the motion is along the arc of a circle
the acceleration varies sinusoidally with time
the derivative, dU/dx, of the potential energy is negative
ans: D
3. In simple harmonic motion, the magnitude of the acceleration is:
A. constant
B. proportional to the displacement
C. inversely proportional to the displacement
D. greatest when the velocity is greatest
E. never greater than g
ans: B
4. A particle is in simple harmonic motion with period T . At time t = 0 it is at the equilibrium
point. Of the following times, at which time is it furthest from the equilibrium point?
A. 0.5T
B. 0.7T
C. T
D. 1.4T
E. 1.5T
ans: B
5. A particle moves back and forth along the x axis from x = −xm to x = +xm , in simple
harmonic motion with period T . At time t = 0 it is at x = +xm . When t = 0.75T :
A. it is at x = 0 and is traveling toward x = +xm
B. it is at x = 0 and is traveling toward x = −xm
C. it at x = +xm and is at rest
D. it is between x = 0 and x = +xm and is traveling toward x = −xm
E. it is between x = 0 and x = −xm and is traveling toward x = −xm
ans: A
226
Chapter 15:
OSCILLATIONS
6. A particle oscillating in simple harmonic motion is:
A. never in equilibrium because it is in motion
B. never in equilibrium because there is always a force
C. in equilibrium at the ends of its path because its velocity is zero there
D. in equilibrium at the center of its path because the acceleration is zero there
E. in equilibrium at the ends of its path because the acceleration is zero there
ans: D
7. An
A.
B.
C.
D.
E.
object is undergoing simple harmonic motion. Throughout a complete cycle it:
has constant speed
has varying amplitude
has varying period
has varying acceleration
has varying mass
ans: D
8. When a body executes simple harmonic motion, its acceleration at the ends of its path must
be:
A. zero
B. less than g
C. more than g
D. suddenly changing in sign
E. none of these
ans: E
9. A particle is in simple harmonic motion with period T . At time t = 0 it is halfway between
the equilibrium point and an end point of its motion, traveling toward the end point. The next
time it is at the same place is:
A. t = T
B. t = T /2
C. t = T /4
D. t = T /8
E. none of the above
ans: E
10. An
A.
B.
C.
D.
E.
object attached to one end of a spring makes 20 complete oscillations in 10 s. Its period is:
2 Hz
10 s
0.5 Hz
2s
0.50 s
ans: E
Chapter 15:
OSCILLATIONS
227
11. An
A.
B.
C.
D.
E.
object attached to one end of a spring makes 20 vibrations in 10 s. Its frequency is:
2 Hz
10 s
0.05 Hz
2s
0.50 s
ans: A
12. An
is:
A.
B.
C.
D.
E.
object attached to one end of a spring makes 20 vibrations in 10 s. Its angular frequency
0.79 rad/s
1.57 rad/s
2.0 rad/s
6.3 rad/s
12.6 rad/s
ans: E
13. Frequency f and angular frequency ω are related by
A. f = πω
B. f = 2πω
C. f = ω/π
D. f = ω/2π
E. f = 2ω/π
ans: D
14. A block attached to a spring oscillates in simple harmonic motion along the x axis. The limits
of its motion are x = 10 cm and x = 50 cm and it goes from one of these extremes to the other
in 0.25 s. Its amplitude and frequency are:
A. 40 cm, 2 Hz
B. 20 cm, 4 Hz
C. 40 cm, 2 Hz
D. 25 cm, 4 Hz
E. 20 cm, 2 Hz
ans: B
15. A weight suspended from an ideal spring oscillates up and down with a period T . If the
amplitude of the oscillation is doubled, the period will be:
A. T
D. 1.5T
B. 2T
C. T /2
E. 4T
ans: A
228
Chapter 15:
OSCILLATIONS
16. In simple harmonic motion, the magnitude of the acceleration is greatest when:
A. the displacement is zero
B. the displacement is maximum
C. the speed is maximum
D. the force is zero
E. the speed is between zero and its maximum
ans: B
17. In simple harmonic motion, the displacement is maximum when the:
A. acceleration is zero
B. velocity is maximum
C. velocity is zero
D. kinetic energy is maximum
E. momentum is maximum
ans: C
18. In simple harmonic motion:
A. the acceleration is greatest at the maximum displacement
B. the velocity is greatest at the maximum displacement
C. the period depends on the amplitude
D. the acceleration is constant
E. the acceleration is greatest at zero displacement
ans: A
19. The amplitude and phase constant of an oscillator are determined by:
A. the frequency
B. the angular frequency
C. the initial displacement alone
D. the initial velocity alone
E. both the initial displacement and velocity
ans: E
20. Two identical undamped oscillators have the same amplitude of oscillation only if:
A. they are started with the same displacement x0
B. they are started with the same velocity v0
C. they are started with the same phase
D. they are started so the combination ω2 x20 + v02 is the same
E. they are started so the combination x20 + ω 2 v02 is the same
ans: D
21. The amplitude of any oscillator can be doubled by:
A. doubling only the initial displacement
B. doubling only the initial speed
C. doubling the initial displacement and halving the initial speed
D. doubling the initial speed and halving the initial displacement
E. doubling both the initial displacement and the initial speed
ans: E
Chapter 15:
OSCILLATIONS
229
22. It is impossible for two particles, each executing simple harmonic motion, to remain in phase
with each other if they have different:
A. masses
B. periods
C. amplitudes
D. spring constants
E. kinetic energies
ans: B
23. The acceleration of a body executing simple harmonic motion leads the velocity by what phase?
A. 0
B. π/8 rad
C. π/4 rad
D. π/2 rad
E. π rad
ans: D
24. The displacement of an object oscillating on a spring is given by x(t) = xm cos(ωt + φ). If the
initial displacement is zero and the initial velocity is in the negative x direction, then the phase
constant φ is:
A. 0
B. π/2 rad
C. π rad
D. 3π/2 rad
E. 2π rad
ans: B
25. The displacement of an object oscillating on a spring is given by x(t) = xm cos(ωt + φ). If
the object is initially displaced in the negative x direction and given a negative initial velocity,
then the phase constant φ is between:
A. 0 and π/2 rad
B. π/2 and π rad
C. π and 3π/2 rad
D. 3π/2 and 2π rad
E. none of the above (φ is exactly 0, π/2, π, or 3π/2 rad)
ans: B
26. A certain spring elongates 9.0 mm when it is suspended vertically and a block of mass M is
hung on it. The natural angular frequency of this block-spring system:
A. is 0.088 rad/s
B. is 33 rad/s
C. is 200 rad/s
D. is 1140 rad/s
E. cannot be computed unless the value of M is given
ans: B
230
Chapter 15:
OSCILLATIONS
27. An object of mass m, oscillating on the end of a spring with spring constant k, has amplitude
A. Its maximum speed is:
0
A. A k/m
2
B. A0
k/m
C. A m/k
D. Am/k
E. A2 m/k
ans: A
28. A 0.20-kg object attached to a spring whose spring constant is 500 N/m executes simple harmonic motion. If its maximum speed is 5.0 m/s, the amplitude of its oscillation is:
A. 0.0020 m
B. 0.10 m
C. 0.20 m
D. 25 m
E. 250 m
ans: B
29. A simple harmonic oscillator consists of an particle of mass m and an ideal spring with spring
constant k. Particle oscillates as shown in (i) with period T . If the spring is cut in half and
used with the same particle, as shown in (ii), the period will be:
. . . . . . . . . . . . .
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m
m
2T
√
2T
√
T/ 2
T
T /2
ans: C
30. A particle moves in simple harmonic motion according to x = 2 cos(50t), where x is in meters
and t is in seconds. Its maximum velocity in m/s is:
A. 100 sin(50t)
B. 100 cos(50t)
C. 100
D. 200
E. none of these
ans: C
Chapter 15:
OSCILLATIONS
231
31. A 3-kg block, attached to a spring, executes simple harmonic motion according to x = 2 cos(50t)
where x is in meters and t is in seconds. The spring constant of the spring is:
A. 1 N/m
B. 100 N/m
C. 150 N/m
D. 7500 N/m
E. none of these
ans: D
32. Let U be the potential energy (with the zero at zero displacement) and K be the kinetic energy
of a simple harmonic oscillator. Uavg and Kavg are the average values over a cycle. Then:
A. Kavg > Uavg
B. Kavg < Uavg
C. Kavg = Uavg
D. K = 0 when U = 0
E. K + U = 0
ans: C
33. A particle is in simple harmonic motion along the x axis. The amplitude of the motion is xm .
At one point in its motion its kinetic energy is K = 5 J and its potential energy (measured
with U = 0 at x = 0) is U = 3 J. When it is at x = xm , the kinetic and potential energies are:
A. K = 5 J and U = 3 J
B. K = 5 J and U = −3 J
C. K = 8 J and U = 0
D. K = 0 and U = 8 J
E. K = 0 and U = −8 J
ans: D
34. A particle is in simple harmonic motion along the x axis. The amplitude of the motion is xm .
When it is at x = x1 , its kinetic energy is K = 5 J and its potential energy (measured with
U = 0 at x = 0) is U = 3 J. When it is at x = − 12 x1 , the kinetic and potential energies are:
A. K = 5 J and U = 3 J
B. K = 5 J and U = −3 J
C. K = 8 J and U = 0
D. K = 0 and U = 8 J
E. K = 0 and U = −8 J
ans: A
35. A 0.25-kg block oscillates on the end of the spring with a spring constant of 200 N/m. If the
system has an energy of 6.0 J, then the amplitude of the oscillation is:
A. 0.06 m
B. 0.17 m
C. 0.24 m
D. 4.9 m
E. 6.9 m
ans: C
232
Chapter 15:
OSCILLATIONS
36. A 0.25-kg block oscillates on the end of the spring with a spring constant of 200 N/m. If the
system has an energy of 6.0 J, then the maximum speed of the block is:
A. 0.06 m/s
B. 0.17 m/s
C. 0.24 m/s
D. 4.9 m/s
E. 6.9 m/s
ans: E
37. A 0.25-kg block oscillates on the end of the spring with a spring constant of 200 N/m. If the
oscillation is started by elongating the spring 0.15 m and giving the block a speed of 3.0 m/s,
then the maximum speed of the block is:
A. 0.13 m/s
B. 0.18 m/s
C. 3.7 m/s
D. 5.2 m/s
E. 13 m/s
ans: D
38. A 0.25-kg block oscillates on the end of the spring with a spring constant of 200 N/m. If the
oscillation is started by elongating the spring 0.15 m and giving the block a speed of 3.0 m/s,
then the amplitude of the oscillation is:
A. 0.13 m
B. 0.18 m
C. 3.7 m
D. 5.2 m
E. 13 m
ans: B
39. An object on the end of a spring is set into oscillation by giving it an initial velocity while it
is at its equilibrium position. In the first trial the initial velocity is v0 and in the second it is
4v0 . In the second trial:
A. the amplitude is half as great and the maximum acceleration is twice as great
B. the amplitude is twice as great and the maximum acceleration is half as great
C. both the amplitude and the maximum acceleration are twice as great
D. both the amplitude and the maximum acceleration are four times as great
E. the amplitude is four times as great and the maximum acceleration is twice as great
ans: C
40. A block attached to a spring undergoes simple harmonic motion on a horizontal frictionless
surface. Its total energy is 50 J. When the displacement is half the amplitude, the kinetic
energy is:
A. zero
B. 12.5 J
C. 25 J
D. 37.5 J
E. 50 J
ans: D
Chapter 15:
OSCILLATIONS
233
41. A mass-spring system is oscillating with amplitude A. The kinetic energy will equal the potential energy only when the displacement is:
A. zero
B. ±A/4
√
C. ±A/ 2
D. ±A/2
E. anywhere between −A and +A
ans: C
42. If the length of a simple pendulum is doubled, its period will:
A. halve
√
B. be greater by a factor√of 2
C. be less by a factor of 2
D. double
E. remain the same
ans: B
43. The period of a simple pendulum is 1 s on Earth. When brought to a planet where g is one-tenth
that on Earth, its period becomes:
A. 1 s√
B. 1/ 10 s
C. 1/10
√ s
10 s
D.
E. 10 s
ans: D
44. The amplitude of oscillation of a simple pendulum is increased from 1◦ to 4◦ . Its maximum
acceleration changes by a factor of:
A. 1/4
B. 1/2
C. 2
D. 4
E. 16
ans: D
45. A simple pendulum of length L and mass M has frequency f . To increase its frequency to 2f :
A. increase its length to 4L
B. increase its length to 2L
C. decrease its length to L/2
D. decrease its length to L/4
E. decrease its mass to < M/4
ans: D
234
Chapter 15:
OSCILLATIONS
46. A simple pendulum consists of a small ball tied to a string and set in oscillation. As the
pendulum swings the tension force of the string is:
A. constant
B. a sinusoidal function of time
C. the square of a sinusoidal function of time
D. the reciprocal of a sinusoidal function of time
E. none of the above
ans: E
47. A simple pendulum has length L and period T . As it passes through its equilibrium position,
the string is suddenly clamped at its midpoint. The period then becomes:
A. 2T
B. T
C. T /2
D. T /4
E. none of these
ans: E
48. A simple pendulum is suspended from the ceiling of an elevator. The elevator is accelerating
upwards with acceleration a. The period of this pendulum, in terms of its length L, g, and a
is:
0
A. 2π0L/g
B. 2π0L/(g + a)
C. 2π 0L/(g − a)
D. 2π L/a
0
E. (1/2π) g/L
ans: B
49. Three physical pendulums, with masses m 1 , m2 = 2m1 , and m3 = 3m1 , have the same shape
and size and are suspended at the same point. Rank them according to their periods, from
shortest to longest.
A. 1, 2, 3
B. 3, 2, 1
C. 2, 3, 1
D. 2, 1, 3
E. All the same
ans: E
Chapter 15:
OSCILLATIONS
235
50. Five hoops are each pivoted at a point on the rim and allowed to swing as physical pendulums.
The masses and radii are
hoop 1: M = 150 g and R = 50 cm
hoop 2: M = 200 g and R = 40 cm
hoop 3: M = 250 g and R = 30 cm
hoop 4: M = 300 g and R = 20 cm
hoop 5: M = 350 g and R = 10 cm
Order the hoops according to the periods of their motions, smallest to largest.
A. 1, 2, 3, 4, 5
B. 5, 4, 3, 2, 1
C. 1, 2, 3, 5, 4
D. 1, 2, 5, 4, 3
E. 5, 4, 1, 2, 3
ans: B
51. A meter stick is pivoted at a point a distance a from its center and swings as a physical
pendulum. Of the following values for a, which results in the shortest period of oscillation?
A. a = 0.1 m
B. a = 0.2 m
C. a = 0.3 m
D. a = 0.4 m
E. a = 0.5 m
ans: C
52. The rotational inertia of a uniform thin rod about its end is M L2 /3, where M is the mass
and L is the length. Such a rod is hung vertically from one end and set into small amplitude
oscillation. If L = 1.0 m this rod will have the same period as a simple pendulum of length:
A. 33 cm
B. 50 cm
C. 67 cm
D. 100 cm
E. 150 cm
ans: C
53. Two uniform spheres are pivoted on horizontal axes that are tangent to their surfaces. The
one with the longer period of oscillation is the one with:
A. the larger mass
B. the smaller mass
C. the larger rotational inertia
D. the smaller rotational inertia
E. the larger radius
ans: E
236
Chapter 15:
OSCILLATIONS
54. The x and y coordinates of a point each execute simple harmonic motion. The result might be
a circular orbit if:
A. the amplitudes are the same but the frequencies are different
B. the amplitudes and frequencies are both the same
C. the amplitudes and frequencies are both different
D. the phase constants are the same but the amplitudes are different
E. the amplitudes and the phase constants are both different
ans: B
55. The x and y coordinates of a point each execute simple harmonic motion. The frequencies are
the same but the amplitudes are different. The resulting orbit might be:
A. an ellipse
B. a circle
C. a parabola
D. a hyperbola
E. a square
ans: A
56. For
A.
B.
C.
D.
E.
an oscillator subjected to a damping force proportional to its velocity:
the displacement is a sinusoidal function of time.
the velocity is a sinusoidal function of time.
the frequency is a decreasing function of time.
the mechanical energy is constant.
none of the above is true.
ans: E
57. Five particles undergo damped harmonic motion. Values for the spring constant k, the damping
constant b, and the mass m are given below. Which leads to the smallest rate of loss of
mechanical energy?
A. k = 100 N/m, m = 50 g, b = 8 g/s
B. k = 150 N/m, m = 50 g, b = 5 g/s
C. k = 150 N/m, m = 10 g, b = 8 g/s
D. k = 200 N/m, m = 8 g, b = 6 g/s
E. k = 100 N/m, m = 2 g, b = 4 g/s
ans: B
58. A sinusoidal force with a given amplitude is applied to an oscillator. To maintain the largest
amplitude oscillation the frequency of the applied force should be:
A. half the natural frequency of the oscillator
B. the same as the natural frequency of the oscillator
C. twice the natural frequency of the oscillator
D. unrelated to the natural frequency of the oscillator
E. determined from the maximum speed desired
ans: B
Chapter 15:
OSCILLATIONS
237
59. A sinusoidal force with a given amplitude is applied to an oscillator. At resonance the amplitude
of the oscillation is limited by:
A. the damping force
B. the initial amplitude
C. the initial velocity
D. the force of gravity
E. none of the above
ans: A
60. An oscillator is subjected to a damping force that is proportional to its velocity. A sinusoidal
force is applied to it. After a long time:
A. its amplitude is an increasing function of time
B. its amplitude is a decreasing function of time
C. its amplitude is constant
D. its amplitude is a decreasing function of time only if the damping constant is large
E. its amplitude increases over some portions of a cycle and decreases over other portions
ans: C
61. A block on a spring is subjected to a damping force that is proportional to its velocity and to
an applied sinusoidal force. The energy dissipated by damping is supplied by:
A. the potential energy of the spring
B. the kinetic energy of the mass
C. gravity
D. friction
E. the applied force
ans: E
62. The table below gives the values of the spring constant k, damping constant b, and mass m for
a particle in damped harmonic motion. Which of these takes the longest time for its mechanical
energy to decrease to one-fourth of its initial value?
A
B
C
D
E
ans: E
238
Chapter 15:
OSCILLATIONS
k
b
m
k0
3k0
k0 /2
4k0
k0
b0
2b0
6b0
b0
b0
m0
m0
2m0
2m0
10m0
Chapter 16:
WAVES – I
1. For a transverse wave on a string the string displacement is described by y(x, t) = f (x − at),
where f is a given function and a is a positive constant. Which of the following does NOT
necessarily follow from this statement?
A. The shape of the string at time t = 0 is given by f (x).
B. The shape of the waveform does not change as it moves along the string.
C. The waveform moves in the positive x direction.
D. The speed of the waveform is a.
E. The speed of the waveform is x/t.
ans: E
2. A sinusoidal wave is traveling toward the right as shown. Which letter correctly labels the
amplitude of the wave?
←−−−−−−− A −−−−−−−→
←−− E −−→
v ..
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
......................................................
...........................
... ↑| .........
.
.
..
.
.
.
.
.
.
.....
.....
..
...
.
.
.
.
.
.
.
....
....
.....
.
..
..
B
.....
.....
..... ↑ .......
....
....
.
.
.
.
.
.
.
.
.
.
.
...D
.
.
.
.
.
.
.
.
.
.
...................
...................
.........↓..........
↓|
←−− C −−→
ans: D
3. A sinusoidal wave is traveling toward the right as shown. Which letter correctly labels the
wavelength of the wave?
←−−−−−−− A −−−−−−−→
←−− E −−→
v ..
..................
.
.
......................................................
.
.
...........................
.
.
..
.
↑
.
.
.
|
.
.
.
.
.
.
.....
.
.....
....
....
....
.
.
.
.....
.
.
.
.
.
.
..
.....
.....
B
..... ↑ ........
.....
.....
......
......
.
.
.
.
.
...D
.
.
.
.
.
.
.........↓..........
....................
....................
↓|
←−− C −−→
ans: A
Chapter 16:
WAVES – I
239
4. In the diagram below, the interval PQ represents:
displacement
.......................
.........
......
......
.....
.
.
.
.
.
.
.
.....
...
..
.....
....
....
.
.
.
.
.
.
.
.
.
.
...... Q ......
P
...
..............
...........
A.
B.
C.
D.
E.
time
wavelength/2
wavelength
2 × amplitude
period/2
period
ans: D
5. Let f be the frequency, v the speed, and T the period of a sinusoidal traveling wave. The
correct relationship is:
A. f = 1/T
B. f = v + T
C. f = vT
D. f = v/T
E. f = T /v
ans: A
6. Let f be the frequency, v the speed, and T the period of a sinusoidal traveling wave. The
angular frequency is given by:
A. 1/T
B. 2π/T
C. vT
D. f /T
E. T /f
ans: B
7. The displacement of a string is given by
y(x, t) = ym sin(kx + ωt) .
The wavelength of the wave is:
A. 2πk/ω
B. k/ω
C. ωk
D. 2π/k
E. k/2π
ans: D
240
Chapter 16:
WAVES – I
8. Three traveling sinusoidal waves are on identical strings, with the same tension. The mathematical forms of the waves are y1 (x, t) = ym sin(3x − 6t), y2 (x, t) = ym sin(4x − 8t), and
y3 (x, t) = ym sin(6x − 12t), where x is in meters and t is in seconds. Match each mathematical
form to the appropriate graph below.
y
......
..
.... .......
...
...
.. .
.
.
...
.
.. x
...
.
.... ....
.........
y
...
...
...
.. ....
.. ....
.. .
... .... ... .... ...
. .... .. .... ..
... ..
x
... ..
... .
... ..
.
...
...
ii
i
A.
B.
C.
D.
E.
y
.....
.....
... ....
.. ....
... .....
... ....
...
...
.
.
.. x
... ...
... .
.
......
iii
y1 : i, y2 : ii, y3 : iii
y1 : iii, y2 : ii, y3 : i
y1 : i, y2 : iii, y3 : ii
y1 : ii, y2 : i, y3 : iii
y1 : iii, y2 : i, y3 : ii
ans: A
9. The displacement of a string is given by
y(x, t) = ym sin(kx + ωt) .
The speed of the wave is:
A. 2πk/ω
B. ω/k
C. ωk
D. 2π/k
E. k/2π
ans: B
10. A wave is described by y(x, t) = 0.1 sin(3x + 10t), where x is in meters, y is in centimeters, and
t is in seconds. The angular wave number is:
A. 0.10 rad/m
B. 3π rad/m
C. 10) rad/m
D. 10π) rad/m
E. 3.0 rad/cm
ans: E
11. A wave is described by y(x, t) = 0.1 sin(3x − 10t), where x is in meters, y is in centimeters, and
t is in seconds. The angular frequency is:
A. 0.10 rad/s
B. 3.0π rad/s
C. 10π rad/s
D. 20π rad/s
E. (10 rad/s
ans: E
Chapter 16:
WAVES – I
241
12. Water waves in the sea are observed to have a wavelength of 300 m and a frequency of 0.07 Hz.
The speed of these waves is:
A. 0.00021 m/s
B. 2.1 m/s
C. 21 m/s
D. 210 m/s
E. none of these
ans: C
13. Sinusoidal water waves are generated in a large ripple tank. The waves travel at 20 cm/s
and their adjacent crests are 5.0 cm apart. The time required for each new whole cycle to be
generated is:
A. 100 s
B. 4.0 s
C. 2.0 s
D. 0.5 s
E. 0.25 s
ans: E
14. A traveling sinusoidal wave is shown below. At which point is the motion 180◦ out of phase
with the motion at point P?
displacement
..
.....................................................
..
v
A
D
.........•................
..........•...............
.
.
.
.
.
.
.
.
.....
.....
...
....
..•..
..•
....
.•...
.....
.
.
.
.
.
.
.
.
P ......
E
........•............. C
B
x
ans: C
15. The displacement of a string carrying a traveling sinusoidal wave is given by
y(x, t) = ym sin(kx − ωt − φ) .
At time t = 0 the point at x = 0 has a displacement of 0 and is moving in the positive y
direction. The phase constant φ is:
A. 45◦
B. 90◦
C. 135◦
D. 180◦
E. 270◦
ans: D
242
Chapter 16:
WAVES – I
16. The displacement of a string carrying a traveling sinusoidal wave is given by
y(x, t) = ym sin(kx − ωt − φ) .
At time t = 0 the point at x = 0 has a velocity of 0 and a positive displacement. The phase
constant φ is:
A. 45◦
B. 90◦
C. 135◦
D. 180◦
E. 270◦
ans: E
17. The displacement of a string carrying a traveling sinusoidal wave is given by
y(x, t) = ym sin(kx − ωt − φ) .
At time t = 0 the point at x = 0 has velocity v0 and displacement y0 . The phase constant φ is
given by tan φ =:
A. v0 /ωy0
B. ωy0 /v0
C. ωv0 /y0
D. y0 /ωv0
E. ωv0 y0
ans: B
18. A sinusoidal transverse wave is traveling on a string. Any point on the string:
A. moves in the same direction as the wave
B. moves in simple harmonic motion with a different frequency than that of the wave
C. moves in simple harmonic motion with the same angular frequency as the wave
D. moves in uniform circular motion with a different angular speed than the wave
E. moves in uniform circular motion with the same angular speed as the wave
ans: C
19. Here are the equations for three waves traveling on separate strings. Rank them according to
the maximum transverse speed, least to greatest.
wave 1: y(x, t) = (2.0 mm) sin[(4.0 m−1 )x − (3.0 s−1 )t]
wave 2: y(x, t) = (1.0 mm) sin[(8.0 m−1 )x − (4.0 s−1 )t]
wave 3: y(x, t) = (1.0 mm) sin[(4.0 m−1 )x − (8.0 s−1 )t]
A. 1, 2, 3
B. 1, 3, 2
C. 2, 1, 3
D. 2, 3, 1
E. 3, 1, 2
ans: C
Chapter 16:
WAVES – I
243
20. The transverse wave shown is traveling from left to right in a medium. The direction of the
instantaneous velocity of the medium at point P is:
.......................
.........
.....
......
......
.
.
.
.
.
.
....
..
...
•.....
.....
....
.
.
.
.
.
.
.
P ......
...
.......................
............
A.
B.
C.
D.
E.
..
......................................................
..
v
↑
↓
→
no direction since v = 0
ans: A
21. A wave traveling to the right on a stretched string is shown below. The direction of the
instantaneous velocity of the point P on the string is:
.....
P ............................. ..................................................... v
.........................
.
.
.
.
.
....
.....
...•
...
....
....
....
....
.
.
.....
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.....
.
.
.
......
...
...
.
.
.......
.
.
.
.
.
.
.
.
.
.
...............
.....
.......
A.
B.
C.
D.
E.
↑
↓
→
no direction since v = 0
ans: B
22. Sinusoidal waves travel on five different strings, all with the same tension. Four of the strings
have the same linear mass density, but the fifth has a different linear mass density. Use the
mathematical forms of the waves, given below, to identify the string with the different linear
mass density. In the expressions x and y are in centimeters and t is in seconds.
A. y(x, t) = (2 cm) sin(2x − 4t)
B. y(x, t) = (2 cm) sin(4x − 10t)
C. y(x, t) = (2 cm) sin(6x − 12t)
D. y(x, t) = (2 cm) sin(8x − 16t)
E. y(x, t) = (2 cm) sin(10x − 20t)
ans: B
23. Any point on a string carrying a sinusoidal wave is moving with its maximum speed when:
A. the magnitude of its acceleration is a maximum
B. the magnitude of its displacement is a maximum
C. the magnitude of its displacement is a minimum
D. the magnitude of its displacement is half the amplitude
E. the magnitude of its displacement is one-fourth the amplitude
ans: C
244
Chapter 16:
WAVES – I
24. The mathematical forms for three sinusoidal traveling waves are given by
wave 1: y(x, t) = (2 cm) sin(3x − 6t)
wave 2: y(x, t) = (3 cm) sin(4x − 12t)
wave 3: y(x, t) = (4 cm) sin(5x − 11t)
where x is in meters and t is in seconds. Of these waves:
A. wave 1 has the greatest wave speed and the greatest maximum transverse string speed
B. wave 2 has the greatest wave speed and wave 1 has the greatest maximum transverse string
speed
C. wave 3 has the greatest wave speed and the greatest maximum transverse string speed
D. wave 2 has the greatest wave speed and wave 3 has the greatest maximum transverse string
speed
E. wave 3 has the greatest wave speed and wave 2 has the greatest maximum transverse string
speed
ans: D
25. Suppose the maximum speed of a string carrying a sinusoidal wave is vs . When the displacement
of a point on the string is half its maximum, the speed of the point is:
A. vs /2
B. 2vs
C. vs /4
D. √
3vs /4
3vs /2
E.
ans: E
26. A string carries a sinusoidal wave with an amplitude of 2.0 cm and a frequency of 100 Hz. The
maximum speed of any point on the string is:
A. 2.0 m/s
B. 4.0 m/s
C. 6.3 m/s
D. 13 m/s
E. unknown (not enough information is given)
ans: D
27. A transverse traveling sinusoidal wave on a string has a frequency of 100 Hz, a wavelength of
0.040 m, and an amplitude of 2.0 mm. The maximum velocity in m/s of any point on the string
is:
A. 0.2
B. 1.3
C. 4
D. 15
E. 25
ans: B
Chapter 16:
WAVES – I
245
28. A transverse traveling sinusoidal wave on a string has a frequency of 100 Hz, a wavelength of
0.040 m, and an amplitude of 2.0 mm. The maximum acceleration in m/s2 of any point on the
string is:
A. 0
B. 130
C. 395
D. 790
E. 1600
ans: D
29. The speed of a sinusoidal wave on a string depends on:
A. the frequency of the wave
B. the wavelength of the wave
C. the length of the string
D. the tension in the string
E. the amplitude of the wave
ans: D
30. The time required for a small pulse to travel from A to B on a stretched cord shown is NOT
altered by changing:
A. the linear mass density of the cord
B. the length between A and B
C. the shape of the pulse
D. the tension in the cord
E. none of the above (changes in all alter the time)
ans: C
31. The diagrams show three identical strings that have been put under tension by suspending
blocks of 5 kg each. For which is the wave speed the greatest?
...
....
..
....
..
....
..
....
..
....
.
....
..
....
..
....
..
....
..
...
........
.... ...
........
•
1
A.
B.
C.
D.
E.
246
........
.... ....
........
WAVES – I
....
• .......•.............
2
1
2
3
1 and 3 tie
2 and 3 tie
ans: D
Chapter 16:
...
... .
..
....
..
....
..
... .
..
....
.
....
..
....
..
....
..
... .
..
...
...
... .
..
....
..
....
..
... .
..
....
.
....
..
....
..
....
..
... .
..
...
......
..... ....
........
......
..... ....
........
•
•
3
32. For
A.
B.
C.
D.
E.
a given medium, the frequency of a wave is:
independent of wavelength
proportional to wavelength
inversely proportional to wavelength
proportional to the amplitude
inversely proportional to the amplitude
ans: C
33. The tension in a string with a linear mass density of 0.0010 kg/m is 0.40 N. A sinusoidal wave
with a wavelength of 20 cm on this string has a frequency of:
A. 0.0125 Hz
B. 0.25 Hz
C. 100 Hz
D. 630 Hz
E. 2000 Hz
ans: C
34. When a 100-Hz oscillator is used to generate a sinusoidal wave on a certain string the wavelength
is 10 cm. When the tension in the string is doubled the generator produces a wave with a
frequency and wavelength of:
A. 200 Hz and 20 cm
B. 141 Hz and 10 cm
C. 100 Hz and 20 cm
D. 100 Hz and 14 cm
E. 50 Hz and 14 cm
ans: D
35. A source of frequency f sends waves of wavelength λ traveling with speed v in some medium.
If the frequency is changed from f to 2f , then the new wavelength and new speed are (respectively):
A. 2λ, v
B. λ/2, v
C. λ, 2v
D. λ, v/2
E. λ/2, 2v
ans: B
36. A long string is constructed by joining the ends of two shorter strings. The tension in the strings
is the same but string I has 4 times the linear mass density of string II. When a sinusoidal
wave passes from string I to string II:
A. the frequency decreases by a factor of 4
B. the frequency decreases by a factor of 2
C. the wavelength decreases by a factor of 4
D. the wavelength decreases by a factor of 2
E. the wavelength increases by a factor of 2
ans: D
Chapter 16:
WAVES – I
247
37. Three separate strings are made of the same material. String 1 has length L and tension τ ,
string 2 has length 2L and tension 2τ , and string 3 has length 3L and tension 3τ . A pulse is
started at one end of each string. If the pulses start at the same time, the order in which they
reach the other end is:
A. 1, 2, 3
B. 3, 2, 1
C. 2, 3, 1
D. 3, 1, 2
E. they all take the same time
ans: A
38. A long string is constructed by joining the ends of two shorter strings. The tension in the strings
is the same but string I has 4 times the linear mass density of string II. When a sinusoidal
wave passes from string I to string II:
A. the frequency decreases by a factor of 4
B. the frequency decreases by a factor of 2
C. the wave speed decreases by a factor of 4
D. the wave speed decreases by a factor of 2
E. the wave speed increases by a factor of 2
ans: E
39. Two identical but separate strings, with the same tension, carry sinusoidal waves with the same
frequency. Wave A has a amplitude that is twice that of wave B and transmits energy at a
that of wave B.
rate that is
A. half
B. twice
C. one-fourth
D. four times
E. eight times
ans: D
40. Two identical but separate strings, with the same tension, carry sinusoidal waves with the same
frequency. Wave A has an amplitude that is twice that of wave B and transmits energy at a
that of wave B.
rate that is
A. half
B. twice
C. one-fourth
D. four times
E. eight times
ans: D
248
Chapter 16:
WAVES – I
41. A sinusoidal wave is generated by moving the end of a string up and down periodically. The
generator must supply the greatest power when the end of the string
A. has its greatest acceleration
B. has its greatest displacement
C. has half its greatest displacement
D. has one-fourth its greatest displacement
E. has its least displacement
ans: E
42. A sinusoidal wave is generated by moving the end of a string up and down periodically. The
generator does not supply any power when the end of the string
A. has its least acceleration
B. has its greatest displacement
C. has half its greatest displacement
D. has one-fourth its greatest displacement
E. has its least displacement
ans: B
43. The sum of two sinusoidal traveling waves is a sinusoidal traveling wave only if:
A. their amplitudes are the same and they travel in the same direction.
B. their amplitudes are the same and they travel in opposite directions.
C. their frequencies are the same and they travel in the same direction.
D. their frequencies are the same and they travel in opposite directions.
E. their frequencies are the same and their amplitudes are the same.
ans: C
44. Two traveling sinusoidal waves interfere to produce a wave with the mathematical form
y(x, t) = ym sin(kx + ωt + α) .
If the value of φ is appropriately chosen, the two waves might be:
A. y1 (x, t) = (ym /3) sin(kx + ωt) and y2 (x, t) = (ym /3) sin(kx + ωt + φ)
B. y1 (x, t) = 0.7ym sin(kx − ωt) and y2 (x, t) = 0.7ym sin(kx − ωt + φ)
C. y1 (x, t) = 0.7ym sin(kx − ωt) and y2 (x, t) = 0.7ym sin(kx + ωt + φ)
D. y1 (x, t) = 0.7ym sin[(kx/2) − (ωt/2)] and y2 (x, t) = 0.7ym sin[(kx/2) − (ωt/2) + φ]
E. y1 (x, t) = 0.7ym sin(kx + ωt) and y2 (x, t) = 0.7ym sin(kx + ωt + φ)
ans: E
45. Fully constructive interference between two sinusoidal waves of the same frequency occurs only
if they:
A. travel in opposite directions and are in phase
B. travel in opposite directions and are 180◦ out of phase
C. travel in the same direction and are in phase
D. travel in the same direction and are 180◦ out of phase
E. travel in the same direction and are 90◦ out of phase
ans: C
Chapter 16:
WAVES – I
249
46. Fully destructive interference between two sinusoidal waves of the same frequency and amplitude occurs only if they:
A. travel in opposite directions and are in phase
B. travel in opposite directions and are 180◦ out of phase
C. travel in the same direction and are in phase
D. travel in the same direction and are 180◦ out of phase
E. travel in the same direction and are 90◦ out of phase
ans: D
47. Two sinusoidal waves travel in the same direction and have the same frequency. Their amplitudes are y1m and y2m . The smallest possible amplitude of the resultant wave is:
A. y1m + y2m and occurs if they are 180◦ out of phase
B. |y1m − y2m | and occurs if they are 180◦ out of phase
C. y1m + y2m and occurs if they are in phase
D. |y1m − y2m | and occurs if they are in phase
E. |y1m − y2m | and occurs if they are 90◦ out of phase
ans: B
48. Two sinusoidal waves have the same angular frequency, the same amplitude ym , and travel in
the same direction in the same medium. If they differ in phase by 50◦ , the amplitude of the
resultant wave is given by:
A. 0.64ym
B. 1.3ym
C. 0.91ym
D. 1.8ym
E. 0.35ym
ans: D
49. Two separated sources emit sinusoidal traveling waves that have the same wavelength λ and
are in phase at their respective sources. One travels a distance 1 to get to the observation
point while the other travels a distance 2 . The amplitude is a minimum at the observation
point if 1 − 2 is:
A. an odd multiple of λ/2
B. an odd multiple of λ/4
C. a multiple of λ
D. an odd multiple of π/2
E. a multiple of π
ans: A
250
Chapter 16:
WAVES – I
50. Two separated sources emit sinusoidal traveling waves that have the same wavelength λ and
are in phase at their respective sources. One travels a distance 1 to get to the observation
point while the other travels a distance 2 . The amplitude is a maximum at the observation
point if 1 − 2 is:
A. an odd multiple of λ/2
B. an odd multiple of λ/4
C. a multiple of λ
D. an odd multiple of π/2
E. a multiple of π
ans: C
51. Two sources, S1 and S2 , each emit waves of wavelength λ in the same medium. The phase
difference between the two waves, at the point P shown, is (2π/λ)( 2 − 1 ) + . The quantity
is:
.
.
S1 .....•.........................................................................................................................................................................................................................................................................................................................• P
...
..
.........
1
.........
.........
........
.
.
.
.
.
.
.
...
.........
........
........
.........
........
.
.
.
.
.
.
.
...
.........
........
........
.........
2
........
.
.
.
.
.
.
.
..
.........
........
.
.
.
.
.
.
.
.
. ..........
...........
.................
S2 •
A.
B.
C.
D.
E.
the distance S1 S2
the angle S1 PS2
π/2
the phase difference between the two sources
zero for transverse waves, π for longitudinal waves
ans: D
52. A wave on a stretched string is reflected from a fixed end P of the string. The phase difference,
at P, between the incident and reflected waves is:
A. zero
B. π rad
C. π/2 rad
D. depends on the velocity of the wave
E. depends on the frequency of the wave
ans: B
53. The sinusoidal wave
y(x, t) = ym sin(kx − ωt)
is incident on the fixed end of a string at x = L. The reflected wave is given by:
A. ym sin(kx + ωt)
B. −ym sin(kx + ωt)
C. ym sin(kx + ωt − kL)
D. ym sin(kx + ωt − 2kL)
E. −ym sin(kx + ωt + 2kL)
ans: D
Chapter 16:
WAVES – I
251
54. A wave on a string is reflected from a fixed end. The reflected wave:
A. is in phase with the original wave at the end
B. is 180◦ out of phase with the original wave at the end
C. has a larger amplitude than the original wave
D. has a larger speed than the original wave
E. cannot be transverse
ans: B
55. A standing wave:
A. can be constructed from two similar waves traveling in opposite directions
B. must be transverse
C. must be longitudinal
D. has motionless points that are closer than half a wavelength
E. has a wave velocity that differs by a factor of two from what it would be for a traveling
wave
ans: A
56. Which of the following represents a standing wave?
A. y = (6.0 mm) sin[(3.0 m−1 )x + (2.0 s−1 )t] − (6.0 mm) cos[(3.0 m−1 )x + 2.0]
B. y = (6.0 mm) cos[(3.0 m−1 )x − (2.0 s−1 )t] + (6.0 mm) cos[(2.0 s−1 )t + 3.0 m−1 )x]
C. y = (6.0 mm) cos[(3.0 m−1 )x − (2.0 s−1 )t] − (6.0 mm) sin[(2.0 s−1 )t − 3.0]
D. y = (6.0 mm) sin[(3.0 m−1 )x − (2.0 s−1 )t] − (6.0 mm) cos[(2.0 s−1 )t + 3.0 m−1 )x]
E. y = (6.0 mm) sin[(3.0 m−1 )x] + (6.0 mm) cos[(2.0 s−1 )t]
ans: B
57. When a certain string is clamped at both ends, the lowest four resonant frequencies are 50,
100, 150, and 200 Hz. When the string is also clamped at its midpoint, the lowest four resonant
frequencies are:
A. 50, 100, 150, and 200 Hz
B. 50, 150, 250, and 300 Hz
C. 100, 200, 300, and 400 Hz
D. 25, 50, 75, and 100 Hz
E. 75, 150, 225, and 300 Hz
ans: C
58. When a certain string is clamped at both ends, the lowest four resonant frequencies are measured to be 100, 150, 200, and 250 Hz. One of the resonant frequencies (below 200 Hz) is
missing. What is it?
A. 25 Hz
B. 50 Hz
C. 75 Hz
D. 125 Hz
E. 225 Hz
ans: B
252
Chapter 16:
WAVES – I
59. Two traveling waves y1 = A sin[k(x − vt)] and y2 = A sin[k(x + vt)] are superposed on the same
string. The distance between the adjacent nodes is:
A. vt/π
B. vt/2π
C. π/2k
D. π/k
E. 2π/k
ans: D
60. If λ is the wavelength of each of the component sinusoidal traveling waves that form a standing
wave, the distance between adjacent nodes in the standing wave is:
A. λ/4
B. λ/2
C. 3λ/4
D. λ
E. 2λ
ans: B
61. A standing wave pattern is established in a string as shown. The wavelength of one of the
component traveling waves is:
...
.....
..
.....
..
....
..
....
.
....
..
.....
..
.....
..
....
..
....
.
....
..
...
...
..
.....
..
.....
...
... .
..
.....
..
.....
..
.....
..
.....
...
... .
..
.....
..
.....
...
.
....
...
...
....... ........
........ ............
........ ............
.... ......
.... ↑| ........ ......
....
.
.
......
..
•....... 0.5 m .............
.
.
. .....
..•.
.
.
....
.
.
.
.
.
.
.
.
.....
.....
...... ↓| ......
.....................
.....................
............
←−−−−−−−−−− 6 m −−−−−−−−−−→
A.
B.
C.
D.
E.
0.25 m
0.5 m
1m
2m
4m
ans: E
62. Standing waves are produced by the interference of two traveling sinusoidal waves, each of
frequency 100 Hz. The distance from the second node to the fifth node is 60 cm. The wavelength
of each of the two original waves is:
A. 50 cm
B. 40 cm
C. 30 cm
D. 20 cm
E. 15 cm
ans: B
Chapter 16:
WAVES – I
253
63. A string of length 100 cm is held fixed at both ends and vibrates in a standing wave pattern.
The wavelengths of the constituent traveling waves CANNOT be:
A. 400 cm
B. 200 cm
C. 100 cm
D. 66.7 cm
E. 50 cm
ans: A
64. A string of length L is clamped at each end and vibrates in a standing wave pattern. The
wavelengths of the constituent traveling waves CANNOT be:
A. L
B. 2L
C. L/2
D. 2L/3
E. 4L
ans: E
65. Two sinusoidal waves, each of wavelength 5 m and amplitude 10 cm, travel in opposite directions
on a 20-m long stretched string that is clamped at each end. Excluding the nodes at the ends
of the string, how many nodes appear in the resulting standing wave?
A. 3
B. 4
C. 5
D. 7
E. 8
ans: D
66. A string, clamped at its ends, vibrates in three segments. The string is 100 cm long. The
wavelength is:
A. 33.3 cm
B. 66.7 cm
C. 150 cm
D. 300 cm
E. need to know the frequency
ans: B
67. A stretched string, clamped at its ends, vibrates in its fundamental frequency. To double the
fundamental frequency, one can change the string tension by a factor of:
A. 2
B. √
4
2
C.
D. 1/2
√
E. 1/ 2
ans: B
254
Chapter 16:
WAVES – I
68. When a string is vibrating in a standing wave pattern the power transmitted across an antinode,
compared to the power transmitted across a node, is:
A. more
B. less
C. the same (zero)
D. the same (non-zero)
E. sometimes more, sometimes less, and sometimes the same
ans: C
69. A 40-cm long string, with one end clamped and the other free to move transversely, is vibrating
in its fundamental standing wave mode. The wavelength of the constituent traveling waves is:
A. 10 cm
B. 20 cm
C. 40 cm
D. 80 cm
E. 160 cm
ans: E
70. A 30-cm long string, with one end clamped and the other free to move transversely, is vibrating
in its second harmonic. The wavelength of the constituent traveling waves is:
A. 10 cm
B. 30 cm
C. 40 cm
D. 60 cm
E. 120 cm
ans: C
71. A 40-cm long string, with one end clamped and the other free to move transversely, is vibrating
in its fundamental standing wave mode. If the wave speed is 320 cm/s the frequency is:
A. 32 Hz
B. 16 Hz
C. 8 Hz
D. 4 Hz
E. 2 Hz
ans: E
Chapter 16:
WAVES – I
255
Chapter 17:
WAVES – II
1. The speed of a sound wave is determined by:
A. its amplitude
B. its intensity
C. its pitch
D. number of harmonics present
E. the transmitting medium
ans: E
2. Take the speed of sound to be 340 m/s. A thunder clap is heard about 3 s after the lightning
is seen. The source of both light and sound is:
A. moving overhead faster than the speed of sound
B. emitting a much higher frequency than is heard
C. emitting a much lower frequency than is heard
D. about 1000 m away
E. much more than 1000 m away
ans: D
3. A sound wave has a wavelength of 3.0 m. The distance from a compression center to the
adjacent rarefaction center is:
A. 0.75 m
B. 1.5 m
C. 3.0 m
D. need to know wave speed
E. need to know frequency
ans: B
4. A fire whistle emits a tone of 170 Hz. Take the speed of sound in air to be 340 m/s. The
wavelength of this sound is about:
A. 0.5 m
B. 1.0 m
C. 2.0 m
D. 3.0 m
E. 340 m
ans: C
5. During a time interval of exactly one period of vibration of a tuning fork, the emitted sound
travels a distance:
A. equal to the length of the tuning fork
B. equal to twice the length of the tuning fork
C. of about 330 m
D. which decreases with time
E. of one wavelength in air
ans: E
256
Chapter 17:
WAVES – II
6. At
A.
B.
C.
D.
E.
points in a sound wave where the gas is maximally compressed, the pressure
is a maximum
is a minimum
is equal to the ambient value
is greater than the ambient value but less than the maximum
is less than the ambient value but greater than the minimum
ans: A
7. You are listening to an “A” note played on a violin string. Let the subscript “s” refer to the
violin string and “a” refer to the air. Then:
A. fs = fa but λs = λa
B. fs = fa and λs = λa
C. λs = λa but fs = fa
D. λs = λa and fs = fa
E. linear density of string = volume density of air
ans: A
8. “Beats” in sound refer to:
A. interference of two waves of the same frequency
B. combination of two waves of slightly different frequency
C. reversal of phase of reflected wave relative to incident wave
D. two media having slightly different sound velocities
E. effect of relative motion of source and observer
ans: B
9. To
A.
B.
C.
D.
E.
produce beats it is necessary to use two waves:
traveling in opposite directions
of slightly different frequencies
of equal wavelengths
of equal amplitudes
whose ratio of frequencies is an integer
ans: B
10. In order for two sound waves to produce audible beats, it is essential that the two waves have:
A. the same amplitude
B. the same frequency
C. the same number of harmonics
D. slightly different amplitudes
E. slightly different frequencies
ans: E
Chapter 17:
WAVES – II
257
11. The largest number of beats per second will be heard from which pair of tuning forks?
A. 200 and 201 Hz
B. 256 and 260 Hz
C. 534 and 540 Hz
D. 763 and 774 Hz
E. 8420 and 8422 Hz
ans: D
12. Two stationary tuning forks (350 and 352 Hz) are struck simultaneously. The resulting sound
is observed to:
A. beat with a frequency of 2 beats/s
B. beat with a frequency of 351 beats/s
C. be loud but not beat
D. be Doppler shifted by 2 Hz
E. have a frequency of 702 Hz
ans: A
13. When listening to tuning forks of frequency 256 Hz and 260 Hz, one hears the following number
of beats per second:
A. zero
B. 2
C. 4
D. 8
E. 258
ans: C
14. Two identical tuning forks vibrate at 256 Hz. One of them is then loaded with a drop of wax,
after which 6 beats/s are heard. The period of the loaded tuning fork is:
A. 0.006 s
B. 0.005 s
C. 0.004 s
D. 0.003 s
E. none of these
ans: C
15. Which of the following properties of a sound wave determine its “pitch”?
A. Amplitude
B. Distance from source to detector
C. Frequency
D. Phase
E. Speed
ans: C
258
Chapter 17:
WAVES – II
16. Two notes are an “octave” apart. The ratio of their frequencies is:
A. 8
B. √
10
8
C.
D. √
2
2
E.
ans: D
17. Consider two imaginary spherical surfaces with different radii, each centered on a point sound
source emitting spherical waves. The power transmitted across the larger sphere is
the
power transmitted across the smaller and the intensity at a point on the larger sphere is
the intensity at a point on the smaller.
A. greater than, the same as
B. greater than, greater than
C. greater than, less than
D. the same as, less than
E. the same as, the same as
ans: D
2
18. The sound intensity 5.0 m from a point source is 0.50 W/m . The power output of the source
is:
A. 39 W
B. 160 W
C. 266 W
D. 320 W
E. 390 W
ans: B
19. The standard reference sound level is about:
A. the threshold of human hearing at 1000 Hz
B. the threshold of pain for human hearing at 1000 Hz
C. the level of sound produced when the 1 kg standard mass is dropped 1 m onto a concrete
floor
D. the level of normal conversation
E. the level of sound emitted by a standard 60 Hz tuning fork
ans: A
20. The intensity of sound wave A is 100 times that of sound wave B. Relative to wave B the sound
level of wave A is:
A. −2 db
B. +2 db
C. +10 db
D. +20 db
E. +100 db
ans: D
Chapter 17:
WAVES – II
259
2
21. The intensity of a certain sound wave is 6 µW/cm . If its intensity is raised by 10 db, the new
intensity (in µW/cm2 ) is:
A. 60
B. 6.6
C. 6.06
D. 600
E. 12
ans: A
22. If the sound level is increased by 10 db the intensity increases by a factor of:
A. 2
B. 5
C. 10
D. 20
E. 100
ans: C
23. The sound level at a point P is 14 db below the sound level at a point 1.0 m from a point source.
The distance from the source to point P is:
A. 4.0 cm
B. 20 2m
C. 2.0 m
D. 5.0 m
E. 25 m
ans: D
24. To
A.
B.
C.
D.
E.
raise the pitch of a certain piano string, the piano tuner:
loosens the string
tightens the string
shortens the string
lengthens the string
removes some mass
ans: B
25. A piano wire has length L and mass M . If its fundamental frequency is f , its tension is:
A. 2Lf /m
B. 4M Lf
C. 2M f 2 /L
D. 4f 2 L3 /M
E. 4LM f 2
ans: E
260
Chapter 17:
WAVES – II
26. If the length of a piano wire (of given density) is increased by 5%, what approximate change
in tension is necessary to keep its fundamental frequency unchanged?
A. Decrease of 10%
B. Decrease of 5%
C. Increase of 5%
D. Increase of 10%
E. Increase of 20%
ans: C
27. A piano wire has a length of 81 cm and a mass of 2.0 g. If its fundamental frequency is to be
394 Hz, its tension must be:
A. 0.32 N
B. 63 N
C. 130 N
D. 250 N
E. none of these
ans: B
28. A stretched wire of length 1.0 m is clamped at both ends. It is plucked at its center as shown.
The three longest wavelengths in the wire are (in meters):
...
....
..
.....
..
.. ..
..
.....
.
....
..
....
..
.....
..
.. ..
..
.....
.
....
..
...
...
..
.....
..
.....
...
... .
..
.....
..
.....
..
.....
..
.....
...
... .
..
.....
..
.....
...
.
.................................................
...................
...................
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
..................
..
.•.................
•.
A.
B.
C.
D.
E.
4, 2, 1
2, 1, 0.5
2, 0.67, 0.4
1, 0.5, 0.33
1, 0.67, 0.5
ans: C
29. Two identical strings, A and B, have nearly the same tension. When they both vibrate in their
fundamental resonant modes, there is a beat frequency of 3 Hz. When string B is tightened
slightly, to increase the tension, the beat frequency becomes 6 Hz. This means:
A. that before tightening A had a higher frequency than B, but after tightening, B has a
higher frequency than A
B. that before tightening B had a higher frequency than A, but after tightening, A has a
higher frequency than B
C. that before and after tightening A has a higher frequency than B
D. that before and after tightening B has a higher frequency than A
E. none of the above
ans: D
Chapter 17:
WAVES – II
261
30. Two pipes are each open at one end and closed at the other. Pipe A has length L and pipe B
has length 2L. Which harmonic of pipe B matches in frequency the fundamental of pipe A?
A. The fundamental
B. The second
C. The third
D. The fourth
E. There are none
ans: E
31. A column of argon is open at one end and closed at the other. The shortest length of such a
column that will resonate with a 200 Hz tuning fork is 42.5 cm. The speed of sound in argon
must be:
A. 85.0 m/s
B. 170 m/s
C. 340 m/s
D. 470 m/s
E. 940 m/s
ans: C
32. A tuning fork produces sound waves of wavelength λ in air. This sound is used to cause
resonance in an air column, closed at one end and open at the other. The length of this column
CANNOT be:
A. λ/4
B. 2λ/4
C. 3λ/4
D. 5λ/4
E. 7λ/4
ans: B
33. A 1024 Hz tuning fork is used to obtain a series of resonance levels in a gas column of variable
length, with one end closed and the other open. The length of the column changes by 20 cm
from resonance to resonance. From this data, the speed of sound in this gas is:
A. 20 cm/s
B. 51 cm/s
C. 102 cm/s
D. 205 m/s
E. 410 m/s
ans: E
34. A vibrating tuning fork is held over a water column with one end closed and the other open.
As the water level is allowed to fall, a loud sound is heard for water levels separated by 17 cm.
If the speed of sound in air is 340 m/s, the frequency of the tuning fork is:
A. 500 Hz
B. 1000 Hz
C. 2000 Hz
D. 5780 Hz
E. 578, 000 Hz
ans: B
262
Chapter 17:
WAVES – II
35. An organ pipe with one end open and the other closed is operating at one of its resonant
frequencies. The open and closed ends are respectively:
A. pressure node, pressure node
B. pressure node, displacement node
C. displacement antinode, pressure node
D. displacement node, displacement node
E. pressure antinode, pressure node
ans: B
36. An organ pipe with one end closed and the other open has length L. Its fundamental frequency
is proportional to:
A. L
B. 1/L
C. 1/L2
D. √
L2
E.
L
ans: B
37. Five organ pipes are described below. Which one has the highest frequency fundamental?
A. A 2.3-m pipe with one end open and the other closed
B. A 3.3-m pipe with one end open and the other closed
C. A 1.6-m pipe with both ends open
D. A 3.0-m pipe with both ends open
E. A pipe in which the displacement nodes are 5 m apart
ans: C
38. If the speed of sound is 340 m/s, the length of the shortest closed pipe that resonates at 218 Hz
is:
A. 23 cm
B. 17 cm
C. 39 cm
D. 78 cm
E. 1.56 cm
ans: C
39. The lowest tone produced by a certain organ comes from a 3.0-m pipe with both ends open. If
the speed of sound is 340 m/s, the frequency of this tone is approximately:
A. 7 Hz
B. 14 Hz
C. 28 Hz
D. 57 Hz
E. 70 Hz
ans: D
Chapter 17:
WAVES – II
263
40. The speed of sound in air is 340 m/s. The length of the shortest pipe, closed at one end, that
will respond to a 512 Hz tuning fork is approximately:
A. 4.2 cm
B. 9.4 cm
C. 17 cm
D. 33 cm
E. 66 cm
ans: C
41. If the speed of sound is 340 m/s, the two lowest frequencies of an 0.5-m organ pipe, closed at
one end, are approximately:
A. 170 and 340 Hz
B. 170 and 510 Hz
C. 340 and 680 Hz
D. 340 and 1020 Hz
E. 57 and 170 Hz
ans: B
42. Organ pipe Y (open at both ends) is half as long as organ pipe X (open at one end) as shown.
The ratio of their fundamental frequencies fX :fY is:
X
Y
A.
B.
C.
D.
E.
1:1
1:2
2:1
1:4
4:1
ans: A
43. A 200-cm organ pipe with one end open is in resonance with a sound wave of wavelength
270 cm. The pipe is operating in its:
A. fundamental frequency
B. second harmonic
C. third harmonic
D. fourth harmonic
E. fifth harmonic
ans: B
264
Chapter 17:
WAVES – II
44. An organ pipe with both ends open is 0.85 m long. Assuming that the speed of sound is 340 m/s,
the frequency of the third harmonic of this pipe is:
A. 200 Hz
B. 300 Hz
C. 400 Hz
D. 600 Hz
E. none of these
ans: D
45. The “A” on a trumpet and a clarinet have the same pitch, but the two are clearly distinguishable. Which property is most important in enabling one to distinguish between these two
instruments?
A. Intensity
B. Fundamental frequency
C. Displacement amplitude
D. Pressure amplitude
E. Harmonic content
ans: E
46. The valves of a trumpet and the slide of a trombone are for the purpose of:
A. playing short (staccato) notes
B. tuning the instruments
C. changing the harmonic content
D. changing the length of the air column
E. producing gradations in loudness
ans: D
47. Two small identical speakers are connected (in phase) to the same source. The speakers are
3 m apart and at ear level. An observer stands at X, 4 m in front of one speaker as shown. If
the amplitudes are not changed, the sound he hears will be most intense if the wavelength is:
↑
|
|
3m
|
|
↓
...
...
..................
....
...
....
................................
...
...
....
.............
.........
... ... ......................... ....
...
... ....
...
... .
... .......................
..
.............. ...
. .
.
...
.............
speakers
...
...
..................
....
...
....
................................
...
...
....
.............
.........
... ... ......................... ....
...
... ....
...
... .
... .......................
..
.............. ...
. .
.
...
.............
•X
←−−−−−−−−−−− 4 m −−−−−−−−−−−→
A.
B.
C.
D.
E.
1m
2m
3m
4m
5m
ans: A
Chapter 17:
WAVES – II
265
48. Two small identical speakers are connected (in phase) to the same source. The speakers are
3 m apart and at ear level. An observer stands at X, 4 m in front of one speaker as shown. The
sound she hears will be most intense if the wavelength is:
↑
|
|
3m
|
|
↓
... ........
...
...
....
..................................
....
...
... ...............
.............
...........
... ............................. ....
...
... ..
...
... ...
..
... ... .....................
.................
.
.
.
.............
speakers
... ........
...
...
....
..................................
....
...
... ...............
.............
...........
... ............................. ....
...
... ..
..
... ...
... ... .....................
...
.................
.
.
.
.............
•X
←−−−−−−−−−−− 4 m −−−−−−−−−−−→
A.
B.
C.
D.
E.
5m
4m
3m
2m
1m
ans: E
49. The rise in pitch of an approaching siren is an apparent increase in its:
A. speed
B. amplitude
C. frequency
D. wavelength
E. number of harmonics
ans: C
50. The diagram shows four situations in which a source of sound S with variable frequency and a
detector D are either moving or stationary. The arrows indicate the directions of motion. The
speeds are all the same. Detector 3 is stationary. The frequency detected is the same. Rank
the situations according to the frequency of the source, lowest to highest.
.............................
•...........................
D
•
S
.............................
1
A.
B.
C.
D.
E.
266
.............................
•
D
2
1, 2, 3, 4
4, 3, 2, 1
1, 3, 4, 2
2, 1, 2, 3
None of the above
ans: B
Chapter 17:
•
S
WAVES – II
•........................... •
S
D
3
•........................... ...........................•..
S
D
4
51. A stationary source generates 5.0 Hz water waves whose speed is 2.0 m/s. A boat is approaching
the source at 10 m/s. The frequency of these waves, as observed by a person in the boat, is:
A. 5.0 Hz
B. 15 Hz
C. 20 Hz
D. 25 Hz
E. 30 Hz
ans: E
52. A stationary source S generates circular outgoing waves on a lake. The wave speed is 5.0 m/s
and the crest-to-crest distance is 2.0 m. A person in a motor boat heads directly toward S at
3.0 m/s. To this person, the frequency of these waves is:
A. 1.0 Hz
B. 1.5 Hz
C. 2.0 Hz
D. 4.0 Hz
E. 8.0 Hz
ans: D
53. A stationary source emits a sound wave of frequency f . If it were possible for a man to
travel toward the source at the speed of sound, he would observe the emitted sound to have a
frequency of:
A. zero
B. f /2
C. 2f /3
D. 2f
E. infinity
ans: D
54. A source emits sound with a frequency of 1000 Hz. It and an observer are moving in the same
direction with the same speed, 100 m/s. If the speed of sound is 340 m/s, the observer hears
sound with a frequency of:
A. 294 Hz
B. 545 Hz
C. 1000 Hz
D. 1830 Hz
E. 3400 Hz
ans: C
55. A source emits sound with a frequency of 1000 Hz. It and an observer are moving toward each
other, each with a speed of 100 m/s. If the speed of sound is 340 m/s, the observer hears sound
with a frequency of:
A. 294 Hz
B. 545 Hz
C. 1000 Hz
D. 1830 Hz
E. 3400 Hz
ans: D
Chapter 17:
WAVES – II
267
56. A source emits sound with a frequency of 1000 Hz. It is moving at 20 m/s toward a stationary
reflecting wall. If the speed of sound is 340 m/s an observer at rest directly behind the source
hears a beat frequency of:
A. 11 Hz
B. 86 Hz
C. 97 Hz
D. 118 Hz
E. 183 Hz
ans: D
57. In each of the following two situations a source emits sound with a frequency of 1000 Hz. In
situation I the source is moving at 100 m/s toward an observer at rest. In situation II the
observer is moving at 100 m/s toward the source, which is stationary. The speed of sound is
340 m/s. The frequencies heard by the observers in the two situations are:
A. I: 1417 Hz; II: 1294 Hz
B. I: 1417 Hz; II: 1417 Hz
C. I: 1294 Hz; II: 1294 Hz
D. I: 773 Hz; II: 706 Hz
E. I: 773 Hz; II: 773 Hz
ans: A
58. The Doppler shift formula for the frequency detected is
f =f
v ± vD
,
v ∓ vS
where f is the frequency emitted, v is the speed of sound, vD is the speed of the detector, and
vS is the speed of the source. Suppose the source is traveling at 5 m/s away from the detector,
the detector is traveling at 7 m/s toward the source, and there is a 3-m/s wind blowing from
the source toward the detector. The values that should be substituted into the Doppler shift
equation are:
A. vD = 7 m/s and vS = 5 m/s
B. vD = 10 m/s and vS = 8 m/s
C. vD = 4 m/s and vS = 2 m/s
D. vD = 10 m/s and vS = 2 m/s
E. vD = 4 m/s and vS = 8 m/s
ans: B
59. A plane produces a sonic boom only when:
A. it emits sound waves of very long wavelength
B. it emits sound waves of high frequency
C. it flys at high altitudes
D. it flys on a curved path
E. it flys faster than the speed of sound
ans: E
268
Chapter 17:
WAVES – II
60. If the speed of sound is 340 m/s a plane flying at 400 m/s creates a conical shock wave with an
apex half angle of:
A. 0 (no shock wave)
B. 32◦
C. 40◦
D. 50◦
E. 58◦
ans: E
61. The speed of sound is 340 m/s. A plane flys horizontally at an altitude of 10, 000 m and a speed
of 400 m/s. When an observer on the ground hears the sonic boom the horizontal distance
from the point on its path directly above the observer to the plane is:
A. 5800 m
B. 6200 m
C. 8400 m
D. 12, 000 m
E. 16, 000 m
ans: B
Chapter 17:
WAVES – II
269
Chapter 19: TEMPERATURE, HEAT,
AND THE FIRST LAW OF THERMODYNAMICS
1. If two objects are in thermal equilibrium with each other:
A. they cannot be moving
B. they cannot be undergoing an elastic collision
C. they cannot have different pressures
D. they cannot be at different temperatures
E. they cannot be falling in Earth’s gravitational field
ans: D
2. When two gases separated by a diathermal wall are in thermal equilibrium with each other:
A. only their pressures must be the same
B. only their volumes must be the same
C. they must have the same number of particles
D. they must have the same pressure and the same volume
E. only their temperatures must be the same
ans: E
3. A balloon is filled with cold air and placed in a warm room. It is NOT in thermal equilibrium
with the air of the room until:
A. it rises to the ceiling
B. it sinks to the floor
C. it stops expanding
D. it starts to contract
E. none of the above
ans: C
4. Suppose object C is in thermal equilibrium with object A and with object B. The zeroth law
of thermodynamics states:
A. that C will always be in thermal equilibrium with both A and B
B. that C must transfer energy to both A and B
C. that A is in thermal equilibrium with B
D. that A cannot be in thermal equilibrium with B
E. nothing about the relationship between A and B
ans: C
5. The zeroth law of thermodynamics allows us to define:
A. work
B. pressure
C. temperature
D. thermal equilibrium
E. internal energy
ans: C
270
Chapter 18: TEMPERATURE, HEAT, AND THE FIRST LAW OF THERMODYNAMICS
6. If the zeroth law of thermodynamics were not valid, which of the following could not be considered a property of an object?
A. Pressure
B. Center of mass energy
C. Internal energy
D. Momentum
E. Temperature
ans: E
7. The international standard thermometer is kept:
A. near Washington, D.C.
B. near Paris, France
C. near the north pole
D. near Rome, Italy
E. nowhere (there is none)
ans: E
8. In constructing a thermometer it is NECESSARY to use a substance that:
A. expands with rising temperature
B. expands linearly with rising temperature
C. will not freeze
D. will not boil
E. undergoes some change when heated or cooled
ans: E
9. The “triple point” of a substance is that point for which the temperature and pressure are such
that:
A. only solid and liquid are in equilibrium
B. only liquid and vapor are in equilibrium
C. only solid and vapor are in equilibrium
D. solid, liquid, and vapor are all in equilibrium
E. the temperature, pressure and density are all numerically equal
ans: D
10. Constant-volume gas thermometers using different gases all indicate nearly the same temperature when in contact with the same object if:
A. the volumes are all extremely large
B. the volumes are all the same
D. the pressures are all extremely large
C. the pressures are the same
E. the particle concentrations are all extremely small
ans: E
Chapter 18: TEMPERATURE, HEAT, AND THE FIRST LAW OF THERMODYNAMICS
271
11. A constant-volume gas thermometer is used to measure the temperature of an object. When
the thermometer is in contact with water at its triple point (273.16 K) the pressure in the
thermometer is 8.500 × 104 Pa. When it is in contact with the object the pressure is 9.650 ×
104 Pa. The temperature of the object is:
A. 37.0 K
B. 241 K
C. 310 K
D. 314 K
E. 2020 K
ans: C
12. When a certain constant-volume gas thermometer is in thermal contact with water at its triple
point (273.16 K) the pressure is 6.30 × 104 Pa. For this thermometer a kelvin corresponds to a
change in pressure of about:
A. 4.34 × 102 Pa
B. 2.31 × 102 Pa
C. 1.72 × 103 Pa
D. 2.31 × 103 Pa
E. 1.72 × 107 Pa
ans: B
13. The diagram shows four thermometers, labeled W, X, Y, and Z. The freezing and boiling points
of water are indicated. Rank the thermometers according to the size of a degree on their scales,
smallest to largest.
A.
B.
C.
D.
E.
100◦
125◦
175◦
75◦
0◦
45◦
55◦
35◦
W
X
Y
Z
boiling point
freezing point
W, X, Y, Z
Z, Y, X, W
Z, Y, W, X
Z, X, W, Y
W, Y, Z, X
ans: D
14. There is a temperature at which the reading on the Kelvin scale is numerically:
A. equal to that on the Celsius scale
B. lower than that on the Celsius scale
C. equal to that on the Fahrenheit scale
D. less than zero
E. none of the above
ans: C
272
Chapter 18: TEMPERATURE, HEAT, AND THE FIRST LAW OF THERMODYNAMICS
15. Fahrenheit and Kelvin scales agree numerically at a reading of:
A. -40
B. 0
C. 273
D. 301
E. 574
ans: E
16. Which one of the following statements is true?
A. Temperatures differing by 25◦ on the Fahrenheit scale must differ by 45◦ on the Celsius
scale
B. 40 K corresponds to −40◦ C
C. Temperatures which differ by 10◦ on the Celsius scale must differ by 18◦ on the Fahrenheit
scale
D. Water at 90◦ C is warmer than water at 202◦ F
E. 0◦ F corresponds to −32◦ C
ans: C
17. A Kelvin thermometer and a Fahrenheit thermometer both give the same reading for a certain
sample. The corresponding Celsius temperature is:
A. 574◦ C
B. 232◦ C
C. 301◦ C
D. 614◦ C
E. 276◦ C
ans: C
18. Room temperature is about 20 degrees on the:
A. Kelvin scale
B. Celsius scale
C. Fahrenheit scale
D. absolute scale
E. C major scale
ans: B
19. A thermometer indicates 98.6◦ C. It may be:
A. outdoors on a cold day
B. in a comfortable room
C. in a cup of hot tea
D. in a normal person’s mouth
E. in liquid air
ans: C
Chapter 18: TEMPERATURE, HEAT, AND THE FIRST LAW OF THERMODYNAMICS
273
20. The air temperature on a summer day might be about:
A. 0◦ C
B. 10◦ C
C. 25◦ C
D. 80◦ C
E. 125◦ C
ans: C
21. The two metallic strips that constitute some thermostats must differ in:
A. length
B. thickness
C. mass
D. rate at which they conduct heat
E. coefficient of linear expansion
ans: E
22. Thin strips of iron and zinc are riveted together to form a bimetallic strip that bends when
heated. The iron is on the inside of the bend because:
A. it has a higher coefficient of linear expansion
B. it has a lower coefficient of linear expansion
C. it has a higher specific heat
D. it has a lower specific heat
E. it conducts heat better
ans: B
23. It is more difficult to measure the coefficient of volume expansion of a liquid than that of a
solid because:
A. no relation exists between linear and volume expansion coefficients
B. a liquid tends to evaporate
C. a liquid expands too much when heated
D. a liquid expands too little when heated
E. the containing vessel also expands
ans: E
24. A surveyor’s 30-m steel tape is correct at 68◦ F. On a hot day the tape has expanded to 30.01 m.
On that day, the tape indicates a distance of 15.52 m between two points. The true distance
between these points is:
A. 15.50 m
B. 15.51 m
C. 15.52 m
D. 15.53 m
E. 15.54 m
ans: B
274
Chapter 18: TEMPERATURE, HEAT, AND THE FIRST LAW OF THERMODYNAMICS
25. The figure shows a rectangular brass plate at 0◦ C in which there is cut a rectangular hole of
dimensions indicated. If the temperature of the plate is raised to 150◦ C:
..............................................................................................................................
....
....
....
.... . . . . . . . . . . . . . . . . . . . . . . . . . ....
....
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
....................................................................................................................................
...............................
←−−−−−− x −−−−−−→
A.
B.
C.
D.
E.
↓
z
↑
|
y
|
↓
x will increase and y will decrease
both x and y will decrease
x will decrease and y will increase
both x and y will increase
the changes in x and y depend on the dimension z
ans: D
26. The Stanford linear accelerator contains hundreds of brass disks tightly fitted into a steel tube
(see figure). The coefficient of linear expansion of the brass is 2.00 × 10−5 per C◦ . The system
was assembled by cooling the disks in dry ice (−57◦ C) to enable them to just slide into the
close-fitting tube. If the diameter of a disk is 80.00 mm at 43◦ C, what is its diameter in the
dry ice?
...............................
...
brass disk
...
.
...................................................................................................................................................................................................
.. ...
..
..
...
...
.
.
...
...
...
..
.
.....
.
.
...
.
..
..
..
...
.
..
..
.
.
... ..
..
.
.
.
.....................................................................................................................................................................................
.........
. ..
steel tube
A.
B.
C.
D.
E.
......
......
......
.
..........................................
78.40 mm
79.68 mm
80.16 mm
79.84 mm
None of these
ans: D
27. When the temperature of a copper penny is increased by 100◦ C, its diameter increases by
0.17%. The area of one of its faces increases by:
A. 0.17%
B. 0.34%
C. 0.51%
D. 0.13%
E. 0.27%
ans: B
Chapter 18: TEMPERATURE, HEAT, AND THE FIRST LAW OF THERMODYNAMICS
275
28. An annular ring of aluminum is cut from an aluminum sheet as shown. When this ring is
heated:
.......
.............
.........
......
............ .
.............
...................................................................
...... . ...
.............
................. .............
.
.
.
.............................
.....
......
.
.
.
.
.
.
.
.
.
. . ......
........
....
.....
...
..
.....
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.....
.....
...
...
.....
..
.
...
.
....
...
.
...
..
.....
.
.
.
..
.
.....
..
.......
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..
.
..
....
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......
.
..
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...
.....
.
.
..
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..
.
.....
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.
..
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.
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.
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... .
.
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.
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................................................ ...................................
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.................. . . . ...
...................
........ . . . ...........
..
..........
................................................
.......
.......
A.
B.
C.
D.
E.
the aluminum expands outward and the hole remains the same in size
the hole decreases in diameter
the area of the hole expands the same percent as any area of the aluminum
the area of the hole expands a greater percent than any area of the aluminum
linear expansion forces the shape of the hole to be slightly elliptical
ans: C
29. Possible units for the coefficient of volume expansion are:
A. mm/C◦
B. mm3 /C◦
C. (C◦ )3
D. 1/(C◦ )3
E. 1/C◦
ans: E
30. The mercury column in an ordinary medical thermometer doubles in length when its temperature changes from 95◦ F to 105◦ F. Choose the correct statement:
A. the coefficient of volume expansion of mercury is 0.1 per F◦
B. the coefficient of volume expansion of mercury is 0.3 per F◦
C. the coefficient of volume expansion of mercury is (0.1/3) per F◦
D. the vacuum above the column helps to “pull up” the mercury this large amount
E. none of the above is true
ans: E
31. The coefficient of linear expansion of iron is 1.0 × 10−5 per C◦ . The surface area of an iron
cube, with an edge length of 5.0 cm, will increase by what amount if it is heated from 10◦ C to
60◦ C?
A. 0.0125 cm2
B. 0.025 cm2
C. 0.075 cm2
D. 0.15 cm2
E. 0.30 cm2
ans: D
276
Chapter 18: TEMPERATURE, HEAT, AND THE FIRST LAW OF THERMODYNAMICS
32. The diagram shows four rectangular plates and their dimensions. All are made of the same
material. The temperature now increases. Of these plates:
L
2L
L
L
1
A. the vertical
most
B. the vertical
most
C. the vertical
most
D. the vertical
most
E. the vertical
most
ans: D
3L
2L
2L
L
2
3
4
dimension of plate 1 increases the most and the area of plate 1 increases the
dimension of plate 2 increases the most and the area of plate 4 increases the
dimension of plate 3 increases the most and the area of plate 1 increases the
dimension of plate 4 increases the most and the area of plate 3 increases the
dimension of plate 4 increases the most and the area of plate 4 increases the
33. The coefficient of linear expansion of steel is 11 × 10−6 per C◦ . A steel ball has a volume of
exactly 100 cm3 at 0◦ C. When heated to 100◦ C, its volume becomes:
A. 100.33 cm3
B. 100.0011 cm3
C. 100.0033 cm3
D. 100.000011 cm3
E. none of these
ans: A
34. The coefficient of linear expansion of a certain steel is 0.000012 per C◦ . The coefficient of
volume expansion, in (C◦ )−1 , is:
A. (0.000012)3
B. (4π/3)(0.000012)3
C. 3 × 0.000012
D. 0.000012
E. depends on the shape of the volume to which it will be applied
ans: C
35. Metal pipes, used to carry water, sometimes burst in the winter because:
A. metal contracts more than water
B. outside of the pipe contracts more than the inside
C. metal becomes brittle when cold
D. ice expands when it melts
E. water expands when it freezes
ans: E
Chapter 18: TEMPERATURE, HEAT, AND THE FIRST LAW OF THERMODYNAMICS
277
36. A gram of distilled water at 4◦ C:
A. will increase slightly in weight when heated to 6◦ C
B. will decrease slightly in weight when heated to 6◦ C
C. will increase slightly in volume when heated to 6◦ C
D. will decrease slightly in volume when heated to 6◦ C
E. will not change in either volume or weight
ans: D
37. Heat is:
A. energy transferred by virtue of a temperature difference
B. energy transferred by macroscopic work
C. energy content of an object
D. a temperature difference
E. a property objects have by virtue of their temperatures
ans: A
38. Heat has the same units as:
A. temperature
B. work
C. energy/time
D. heat capacity
E. energy/volume
ans: B
39. A calorie is about:
A. 0.24 J
B. 8.3 J
C. 250 J
D. 4.2 J
E. 4200 J
ans: D
40. The heat capacity of an object is:
A. the amount of heat energy that raises its temperature by 1◦ C
B. the amount of heat energy that changes its state without changing its temperature
C. the amount of heat energy per kilogram that raises its temperature by 1◦ C
D. the ratio of its specific heat to that of water
E. the change in its temperature caused by adding 1 J of heat
ans: A
278
Chapter 18: TEMPERATURE, HEAT, AND THE FIRST LAW OF THERMODYNAMICS
41. The specific heat of a substance is:
A. the amount of heat energy to change the state of one gram of the substance
B. the amount of heat energy per unit mass emitted by oxidizing the substance
C. the amount of heat energy per unit mass to raise the substance from its freezing to its
boiling point
D. the amount of heat energy per unit mass to raise the temperature of the substance by 1◦ C
E. the temperature of the object divided by its mass
ans: D
42. Two different samples have the same mass and temperature. Equal quantities of energy are
absorbed as heat by each. Their final temperatures may be different because the samples have
different:
A. thermal conductivities
B. coefficients of expansion
C. densities
D. volumes
E. heat capacities
ans: E
43. The same energy Q enters five different substances as heat.
The temperature of 3 g of substance A increases by 10 K
The temperature of 4 g of substance B increases by 4 K
The temperature of 6 g of substance C increases by 15 K
The temperature of 8 g of substance D increases by 6 K
The temperature of 10 g of substance E increases by 10 K
Which substance has the greatest specific heat?
ans: B
44. For constant-volume processes the heat capacity of gas A is greater than the heat capacity of
gas B. We conclude that when they both absorb the same energy as heat at constant volume:
A. the temperature of A increases more than the temperature of B
B. the temperature of B increases more than the temperature of A
C. the internal energy of A increases more than the internal energy of B
D. the internal energy of B increases more than the internal energy of A
E. A does more positive work than B
ans: B
45. The heat capacity at constant volume and the heat capacity at constant pressure have different
values because:
A. heat increases the temperature at constant volume but not at constant pressure
B. heat increases the temperature at constant pressure but not at constant volume
C. the system does work at constant volume but not at constant pressure
D. the system does work at constant pressure but not at constant volume
E. the system does more work at constant volume than at constant pressure
ans: D
Chapter 18: TEMPERATURE, HEAT, AND THE FIRST LAW OF THERMODYNAMICS
279
46. A cube of aluminum has an edge length of 20 cm. Aluminum has a density 2.7 times that of
3
water (1 g/cm ) and a specific heat 0.217 times that of water (1 cal/g · C◦ ). When the internal
energy of the cube increases by 47000 cal its temperature increases by:
A. 5 C◦
B. 10 C◦
C. 20 C◦
D. 100 C◦
E. 200 C◦
ans: B
47. An insulated container, filled with water, contains a thermometer and a paddle wheel. The
paddle wheel can be rotated by an external source. This apparatus can be used to determine:
A. specific heat of water
B. relation between kinetic energy and absolute temperature
C. thermal conductivity of water
D. efficiency of changing work into heat
E. mechanical equivalent of heat
ans: E
48. Take the mechanical equivalent of heat as 4 J/cal. A 10-g bullet moving at 2000 m/s plunges
into 1 kg of paraffin wax (specific heat 0.7 cal/g · C◦ ). The wax was initially at 20◦ C. Assuming
that all the bullet’s energy heats the wax, its final temperature (in ◦ C) is:
A. 20.14
B. 23.5
C. 20.006
D. 27.1
E. 30.23
ans: D
49. The energy given off as heat by 300 g of an alloy as it cools through 50 C◦ raises the temperature
of 300 g of water from 30◦ C to 40◦ C. The specific heat of the alloy (in cal/g · C◦ ) is:
A. 0.015
B. 0.10
C. 0.15
D. 0.20
E. 0.50
ans: D
50. The specific heat of lead is 0.030 cal/g · C◦ . 300 g of lead shot at 100◦ C is mixed with 100 g of
water at 70◦ C in an insulated container. The final temperature of the mixture is:
A. 100◦ C
B. 85.5◦ C
C. 79.5◦ C
D. 74.5◦ C
E. 72.5◦ C
ans: E
280
Chapter 18: TEMPERATURE, HEAT, AND THE FIRST LAW OF THERMODYNAMICS
51. Object A, with heat capacity CA and initially at temperature TA , is placed in thermal contact
with object B, with heat capacity CB and initially at temperature TB . The combination is
thermally isolated. If the heat capacities are independent of the temperature and no phase
changes occur, the final temperature of both objects is:
A. (CA TA − CB TB )/(CA + CB )
B. (CA TA + CB TB )/(CA + CB )
C. (CA TA − CB TB )/(CA − CB )
D. (CA − CB )|TA − TB |
E. (CA + CB )|TA − TB |
ans: B
52. The heat capacity of object B is twice that of object A. Initially A is at 300 K and B is at 450 K.
They are placed in thermal contact and the combination is isolated. The final temperature of
both objects is:
A. 200 K
B. 300 K
C. 400 K
D. 450 K
E. 600 K
ans: C
53. A heat of transformation of a substance is:
A. the energy absorbed as heat during a phase transformation
B. the energy per unit mass absorbed as heat during a phase transformation
C. the same as the heat capacity
D. the same as the specific heat
E. the same as the molar specific heat
ans: B
54. The heat of fusion of water is cal/g. This means 80 cal of energy are required to:
A. raise the temperature of 1 g of water by 1 K
B. turn 1 g of water to steam
C. raise the temperature of 1 g of ice by 1 K
D. melt 1 g of ice
E. increase the internal energy of 80 g of water by 1 cal
ans: D
55. Solid A, with mass M , is at its melting point TA . It is placed in thermal contact with solid
B, with heat capacity CB and initially at temperature TB (TB > TA ). The combination is
thermally isolated. A has latent heat of fusion L and when it has melted has heat capacity CA .
If A completely melts the final temperature of both A and B is:
A. (CA TA + CB TB − M L)/(CA + CB )
B. (CA TA − CB TB + M L)/(CA + CB )
C. (CA TA − CB TB − M L)/(CA + CB )
D. (CA TA + CB TB + M L)/(CA − CB )
E. (CA TA + CB TB + M L)/(CA − CB )
ans: A
Chapter 18: TEMPERATURE, HEAT, AND THE FIRST LAW OF THERMODYNAMICS
281
56. During the time that latent heat is involved in a change of state:
A. the temperature does not change
B. the substance always expands
C. a chemical reaction takes place
D. molecular activity remains constant
E. kinetic energy changes into potential energy
ans: A
57. The formation of ice from water is accompanied by:
A. absorption of energy as heat
B. temperature increase
C. decrease in volume
D. an evolution of heat
E. temperature decrease
ans: A
58. How many calories are required to change one gram of 0◦ C ice to 100◦ C steam? The latent
heat of fusion is 80 cal/g and the latent heat of vaporization is 540 cal/g. The specific heat of
water is 1.00 cal/g · K.
A. 100
B. 540
C. 620
D. 720
E. 900
ans: D
59. Ten grams of ice at −20◦ C is to be changed to steam at 130◦ C. The specific heat of both
ice and steam is 0.5 cal/g · C◦ . The heat of fusion is 80 cal/g and the heat of vaporization is
540 cal/g. The entire process requires:
A. 750 cal
B. 1250 cal
C. 6950 cal
D. 7450 cal
E. 7700 cal
ans: D
60. Steam at 1 atm and 100◦ C enters a radiator and leaves as water at 1 atm and 80◦ C. Take the
heat of vaporization to be 540 cal/g. Of the total energy given off as heat, what percent arises
from the cooling of the water?
A. 100
B. 54
C. 26
D. 14
E. 3.6
ans: E
282
Chapter 18: TEMPERATURE, HEAT, AND THE FIRST LAW OF THERMODYNAMICS
61. A certain humidifier operates by raising water to the boiling point and then evaporating it.
Every minute 30 g of water at 20◦ C are added to replace the 30 g that are evaporated. The
heat of fusion of water is 333 kJ/kg, the heat of vaporization is 2256 kJ/kg, and the specific
heat is 4190 J/kg · K. How many joules of energy per minute does this humidifier require?
A. 3.0 × 104
B. 8.8 × 104
C. 7.8 × 104
D. 1.1 × 105
E. 2.0 × 104
ans: B
62. A metal sample of mass M requires a power input P to just remain molten. When the heater
is turned off, the metal solidifies in a time T . The specific latent heat of fusion of this metal is:
A. P/M T
B. T /P M
C. P M/T
D. P M T
E. P T /M
ans: E
63. Fifty grams of ice at 0◦ C is placed in a thermos bottle containing one hundred grams of water
at 6◦ C. How many grams of ice will melt? The heat of fusion of water is 333 kJ/kg and the
specific heat is 4190 J/kg · K.
A. 7.5
B. 2.0
C. 8.3
D. 17
E. 50
ans: A
64. According to the first law of thermodynamics, applied to a gas, the increase in the internal
energy during any process:
A. equals the heat input minus the work done on the gas
B. equals the heat input plus the work done on the gas
C. equals the work done on the gas minus the heat input
D. is independent of the heat input
E. is independent of the work done on the gas
ans: B
Chapter 18: TEMPERATURE, HEAT, AND THE FIRST LAW OF THERMODYNAMICS
283
65. Pressure versus volume graphs for a certain gas undergoing five different cyclic processes are
shown below. During which cycle does the gas do the greatest positive work?
p
p
..................................
..........................
..
.. . .... ...
............................................................
.....
V
A
p
..................
.. ................................................
..
..
..
..
..
.
.
.............................................................
...
V
.................................
.. ...............................
..
..
.............................................................
......
V
B
D
p
..........
.. .........................................
.... ......
..
..
..
..
.. .
..............................................................
.....
C
V
p
....................................................................
..
...
..
..
..................................................................
....
E
V
ans: D
66. During an adiabatic process an object does 100 J of work and its temperature decreases by 5 K.
During another process it does 25 J of work and its temperature decreases by 5 K. Its heat
capacity for the second process is:
A. 20 J/K
B. 24 J/K
C. 5 J/K
D. 15 J/K
E. 100 J/K
ans: D
67. A system undergoes an adiabatic process in which its internal energy increases by 20 J. Which
of the following statements is true?
A. 20 J of work was done on the system
B. 20 J of work was done by the system
C. the system received 20 J of energy as heat
D. the system lost 20 J of energy as heat
E. none of the above are true
ans: A
68. In an adiabatic process:
A. the energy absorbed as heat equals the work done by the system on its environment
B. the energy absorbed as heat equals the work done by the environment on the system
C. the absorbed as heat equals the change in internal energy
D. the work done by the environment on the system equals the change in internal energy
E. the work done by the system on its environment equals to the change in internal energy
ans: D
284
Chapter 18: TEMPERATURE, HEAT, AND THE FIRST LAW OF THERMODYNAMICS
69. In a certain process a gas ends in its original thermodynamic state. Of the following, which is
possible as the net result of the process?
A. It is adiabatic and the gas does 50 J of work
B. The gas does no work but absorbs 50 J of energy as heat
C. The gas does no work but loses 50 J of energy as heat
D. The gas loses 50 J of energy as heat and does 50 J of work
E. The gas absorbs 50 J of energy as heat and does 50 J of work
ans: E
70. Of
A.
B.
C.
D.
E.
the following which might NOT vanish over one cycle of a cyclic process?
the change in the internal energy of the substance
the change in pressure of the substance
the work done by the substance
the change in the volume of the substance
the change in the temperature of the substance
ans: C
71. Of
A.
B.
C.
D.
E.
the following which might NOT vanish over one cycle of a cyclic process?
the work done by the substance minus the energy absorbed by the substance as heat
the change in the pressure of the substance
the energy absorbed by the substance as heat
the change in the volume of the substance
the change in the temperature of the substance
ans: C
72. The unit of thermal conductivity might be:
A. cal · cm/(s · C◦ )
B. cal/(cm · s · C◦ )
C. cal · s/(cm · C◦ )
D. cm · s · C◦ C/cal
E. C◦ /(cal · cm · s)
ans: B
73. A slab of material has area A, thickness L, and thermal conductivity k. One of its surfaces (P)
is maintained at temperature T1 and the other surface (Q) is maintained at a lower temperature
T2 . The rate of heat flow by conduction from P to Q is:
A. kA(T1 − T2 )/L2
B. kL(T1 − T2 )/A
C. kA(T1 − T2 )/L
D. k(T1 − T2 )/(LA)
E. LA(T1 − T2 )/k
ans: C
Chapter 18: TEMPERATURE, HEAT, AND THE FIRST LAW OF THERMODYNAMICS
285
74. The rate of heat flow by conduction through a slab does NOT depend upon the:
A. temperature difference between opposite faces of the slab
B. thermal conductivity of the slab
C. slab thickness
D. cross-sectional area of the slab
E. specific heat of the slab
ans: E
75. The rate of heat flow by conduction through a slab is Pcond . If the slab thickness is doubled,
its cross-sectional area is halved, and the temperature difference across it is doubled, then the
rate of heat flow becomes:
A. 2Pcond
B. Pcond /2
C. Pcond
D. Pcond /8
E. 8Pcond
ans: B
76. The diagram shows four slabs of different materials with equal thickness, placed side by side.
Heat flows from left to right and the steady-state temperatures of the interfaces are given.
Rank the materials according to their thermal conductivities, smallest to largest.
←
− d−
→←
− d−
→←
− d−
→←
− d−
→
1
35◦ C
A.
B.
C.
D.
E.
1, 2, 3,
2, 1, 3,
3, 4, 1,
3, 4, 2,
4, 3, 2,
ans: D
2
30◦ C
3
20◦ C
4
0◦ C
−15◦ C
4
4
2
1
1
77. Inside a room at a uniform comfortable temperature, metallic objects generally feel cooler to
the touch than wooden objects do. This is because:
A. a given mass of wood contains more heat than the same mass of metal
B. metal conducts heat better than wood
C. heat tends to flow from metal to wood
D. the equilibrium temperature of metal in the room is lower than that of wood
E. the human body, being organic, resembles wood more closely than it resembles metal
ans: B
286
Chapter 18: TEMPERATURE, HEAT, AND THE FIRST LAW OF THERMODYNAMICS
78. On a very cold day, a child puts his tongue against a fence post. It is much more likely that
his tongue will stick to a steel post than to a wooden post. This is because:
A. steel has a higher specific heat
B. steel is a better radiator of heat
C. steel has a higher specific gravity
D. steel is a better heat conductor
E. steel is a highly magnetic material
ans: D
79. An
A.
B.
C.
D.
E.
iron stove, used for heating a room by radiation, is more efficient if:
its inner surface is highly polished
its inner surface is covered with aluminum paint
its outer surface is covered with aluminum paint
its outer surface is rough and black
its outer surface is highly polished
ans: D
80. To help keep buildings cool in the summer, dark colored window shades have been replaced by
light colored shades. This is because light colored shades:
A. are more pleasing to the eye
B. absorb more sunlight
C. reflect more sunlight
D. transmit more sunlight
E. have a lower thermal conductivity
ans: C
81. Which of the following statements pertaining to a vacuum flask (thermos) is NOT correct?
A. Silvering reduces radiation loss
B. Vacuum reduces conduction loss
C. Vacuum reduces convection loss
D. Vacuum reduces radiation loss
E. Glass walls reduce conduction loss
ans: D
82. A thermos bottle works well because:
A. its glass walls are thin
B. silvering reduces convection
C. vacuum reduces heat radiation
D. silver coating is a poor heat conductor
E. none of the above
ans: E
Chapter 18: TEMPERATURE, HEAT, AND THE FIRST LAW OF THERMODYNAMICS
287
Chapter 19:
THE KINETIC THEORY OF GASES
1. Evidence that a gas consists mostly of empty space is the fact that:
A. the density of a gas becomes much greater when it is liquefied
B. gases exert pressure on the walls of their containers
C. gases are transparent
D. heating a gas increases the molecular motion
E. nature abhors a vacuum
ans: A
2. Air enters a hot-air furnace at 7◦ C and leaves at 77◦ C. If the pressure does not change each
entering cubic meter of air expands to:
A. 0.80 m3
B. 1.25 m3
C. 1.9 m3
D. 7.0 m3
E. 11 m3
ans: B
3. 273 cm3 of an ideal gas is at 0◦ C. It is heated at constant pressure to 10◦ C. It will now occupy:
A. 263 cm3
B. 273 cm3
C. 283 cm3
D. 278 cm3
E. 293 cm3
ans: C
4. Two identical rooms in a house are connected by an open doorway. The temperatures in the
two rooms are maintained at different values. Which room contains more air?
A. the room with higher temperature
B. the room with lower temperature
C. the room with higher pressure
D. neither because both have the same pressure
E. neither because both have the same volume
ans: B
5. It is known that 28 g of a certain ideal gas occupy 22.4 liters at standard conditions (0◦ C,
1 atm). The volume occupied by 42 g of this gas at standard conditions is:
A. 14.9 liters
B. 22.4 liters
C. 33.6 liters
D. 42 liters
E. more data are needed
ans: C
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6. An automobile tire is pumped up to a gauge pressure of 2.0 × 105 Pa when the temperature is
27◦ C. What is its gauge pressure after the car has been running on a hot day so that the tire
temperature is 77◦ C? Assume that the volume remains fixed and take atmospheric pressure
to be 1.013 × 105 Pa.
A. 1.6 × 105 Pa
B. 2.6 × 105 Pa
C. 3.6 × 105 Pa
D. 5.9 × 105 Pa
E. 7.9 × 105 Pa
ans: A
7. A sample of an ideal gas is compressed by a piston from 10 m3 to 5 m3 and simultaneously
cooled from 273◦ C to 0◦ C. As a result there is:
A. an increase in pressure
B. a decrease in pressure
C. a decrease in density
D. no change in density
E. an increase in density
ans: E
8. A 2-m3 weather balloon is loosely filled with helium at 1 atm (76 cm Hg) and at 27◦ C. At
an elevation of 20, 000 ft, the atmospheric pressure is down to 38 cm Hg and the helium has
expanded, being under no constraint from the confining bag. If the temperature at this elevation
is -48◦ C, the gas volume (in m3 ) is:
A. 3
B. 4
C. 2
D. 2.5
E. 5.3
ans: A
9. Oxygen (molar mass = 32 g) occupies a volume of 12 liters when its temperature is 20◦ C and
its pressure is 1 atm. Using R = 0.082 liter · atm/mol · K, calculate the mass of the oxygen:
A. 6.4 g
B. 10. g7
C. 16 g
D. 32 g
E. 64 g
ans: C
10. An ideal gas occupies 12 liters at 293 K and 1 atm (76 cm Hg). Its temperature is now raised
to 373 K and its pressure increased to 215 cm Hg. The new volume is:
A. 0.2 liters
B. 5.4 liters
C. 13.6 liters
D. 20.8 liters
E. none of these
ans: B
Chapter 19:
THE KINETIC THEORY OF GASES
289
11. Use R = 8.2 × 10−5 m3 · atm/mol · K and NA = 6.02 × 1023 mol−1 . The approximate number
of air molecules in a 1 m3 volume at room temperature (300 K and atmospheric pressure is:
A. 41
B. 450
C. 2.5 × 1025
D. 2.7 × 1026
E. 5.4 × 1026
ans: C
3
12. An air bubble doubles in volume as it rises from the bottom of a lake (1000 kg/m ). Ignoring
any temperature changes, the depth of the lake is:
A. 21 m
B. 0.76 m
C. 4.9 m
D. 10 m
E. 0.99 m
ans: D
13. An
A.
B.
C.
D.
E.
isothermal process for an ideal gas is represented on a p-V diagram by:
a horizontal line
a vertical line
a portion of an ellipse
a portion of a parabola
a portion of a hyperbola
ans: E
14. An ideal gas undergoes an isothermal process starting with a pressure of 2 × 105 Pa and a
volume of 6 cm3 . Which of the following might be the pressure and volume of the final state?
A. 1 × 105 Pa and 10 cm3
B. 3 × 105 Pa and 6 cm3
C. 4 × 105 Pa and 4 cm3
D. 6 × 105 Pa and 2 cm3
E. 8 × 105 Pa and 2 cm3
ans: D
15. The pressures p and volumes V of five ideal gases, with the same number of molecules, are
given below. Which has the highest temperature?
A. p = 1 × 105 Pa and V = 10 cm3
B. p = 3 × 105 Pa and V = 6 cm3
C. p = 4 × 105 Pa and V = 4 cm3
D. p = 6 × 105 Pa and V = 2 cm3
E. p = 8 × 105 Pa and V = 2 cm3
ans: B
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THE KINETIC THEORY OF GASES
16. During a slow adiabatic expansion of a gas:
A. the pressure remains constant
B. energy is added as heat
C. work is done on the gas
D. no energy enters or leaves as heat
E. the temperature is constant
ans: D
17. An
A.
B.
C.
D.
E.
adiabatic process for an ideal gas is represented on a p-V diagram by:
a horizontal line
a vertical line
a hyperbola
a circle
none of these
ans: E
18. A real gas undergoes a process that can be represented as a curve on a p-V diagram. The work
done by the gas during this process is:
A. pV
B. p(V2 − V1 )
C. (p
$ 2 − p1 )V
D.
p dV
E. V dp
ans: D
19. A real gas is changed slowly from state 1 to state 2. During this process no work is done on or
by the gas. This process must be:
A. isothermal
B. adiabatic
C. isovolumic
D. isobaric
E. a closed cycle with state 1 coinciding with state 2
ans: C
20. A given mass of gas is enclosed in a suitable container so that it may be maintained at constant
volume. Under these conditions, there can be no change in what property of the gas?
A. Pressure
B. Density
C. Molecular kinetic energy
D. Internal energy
E. Temperature
ans: B
Chapter 19:
THE KINETIC THEORY OF GASES
291
21. A quantity of an ideal gas is compressed to half its initial volume. The process may be adiabatic,
isothermal, or isobaric. Rank those three processes in order of the work required of an external
agent, least to greatest.
A. adiabatic, isothermal, isobaric
B. adiabatic, isobaric, isothermal
C. isothermal, adiabatic, isobaric
D. isobaric, adiabatic, isothermal
E. isobaric, isothermal, adiabatic
ans: E
22. During a reversible adiabatic expansion of an ideal gas, which of the following is NOT true?
A. pV γ = constant
B. pV = nRT
C. T V γ−1$= constant
D. |W | = p dV
E. pV = constant
ans: E
23. In order that a single process be both isothermal and isobaric:
A. one must use an ideal gas
B. such a process is impossible
C. a change of phase is essential
D. one may use any real gas such as N2
E. one must use a solid
ans: C
24. Over 1 cycle of a cyclic process in which a system does net work on its environment:
A. the change in the pressure of the system cannot be zero
B. the change in the volume of the system cannot be zero
C. the change in the temperature of the system cannot be zero
D. the change in the internal energy of the system cannot be zero
E. none of the above
ans: E
25. Evidence that molecules of a gas are in constant motion is:
A. winds exert pressure
B. two gases interdiffuse quickly
C. warm air rises
D. energy as heat is needed to vaporize a liquid
E. gases are easily compressed
ans: B
292
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THE KINETIC THEORY OF GASES
26. According to the kinetic theory of gases, the pressure of a gas is due to:
A. change of kinetic energy of molecules as they strike the wall
B. change of momentum of molecules as the strike the wall
C. average kinetic energy of the molecules
D. force of repulsion between the molecules
E. rms speed of the molecules
ans: B
27. The force on the walls of a vessel of a contained gas is due to:
A. the repulsive force between gas molecules
B. a slight loss in the speed of a gas molecule during a collision with the wall
C. a change in momentum of a gas molecule during a collision with the wall
D. elastic collisions between gas molecules
E. inelastic collisions between gas molecules
ans: C
28. A gas is confined to a cylindrical container of radius 1 cm and length 1 m. The pressure exerted
on an end face, compared with the pressure exerted on the long curved face, is:
A. smaller because its area is smaller
B. smaller because most molecules cannot traverse the length of the cylinder without undergoing collisions
C. larger because the face is flat
D. larger because the molecules have a greater distance in which to accelerate before they
strike the face
E. none of these
ans: E
29. Air
A.
B.
C.
D.
E.
is pumped into a bicycle tire at constant temperature. The pressure increases because:
more molecules strike the tire wall per second
the molecules are larger
the molecules are farther apart
each molecule is moving faster
each molecule has more kinetic energy
ans: A
30. The temperature of a gas is most closely related to:
A. the kinetic energy of translation of its molecules
B. its total molecular kinetic energy
C. the sizes of its molecules
D. the potential energy of its molecules
E. the total energy of its molecules
ans: A
Chapter 19:
THE KINETIC THEORY OF GASES
293
31. The temperature of low pressure hydrogen is reduced from 100◦ C to 20◦ C. The rms speed of
its molecules decreases by approximately:
A. 80%
B. 89%
C. 46%
D. 21%
E. 11%
ans: E
32. The mass of an oxygen molecule is 16 times that of a hydrogen molecule. At room temperature,
the ratio of the rms speed of an oxygen molecule to that of a hydrogen molecule is:
A. 16
B. 4
C. 1
D. 1/4
E. 1/16
ans: D
33. The rms speed of an oxygen molecule at 0◦ C is 460 m/s. If the molar mass of oxygen is 32 g
and that of helium is 4 g, then the rms speed of a helium molecule at 0◦ C is:
A. 230 m/s
B. 326 m/s
C. 650 m/s
D. 920 m/s
E. 1300 m/s
ans: E
34. A sample of argon gas (molar mass 40 g) is at four times the absolute temperature of a sample
of hydrogen gas (molar mass 2 g). The ratio of the rms speed of the argon molecules to that of
the hydrogen is:
A. 1
B. 5
C. 1/5
√
5√
D.
E. 1/ 5
ans: D
35. If the molecules in a tank of hydrogen have the same rms speed as the molecules in a tank of
oxygen, we may be sure that:
A. the pressures are the same
B. the hydrogen is at the higher temperature
C. the hydrogen is at the greater pressure
D. the temperatures are the same
E. the oxygen is at the higher temperature
ans: E
294
Chapter 19:
THE KINETIC THEORY OF GASES
36. The principle of equipartition of energy states that the internal energy of a gas is shared equally:
A. among the molecules
B. between kinetic and potential energy
C. among the relevant degrees of freedom
D. between translational and vibrational kinetic energy
E. between temperature and pressure
ans: C
37. The number of degrees of freedom of a rigid diatomic molecule is:
A. 2
B. 3
C. 4
D. 5
E. 6
ans: D
38. The number of degrees of freedom of a triatomic molecule is:
A. 1
B. 3
C. 6
D. 8
E. 9
ans: E
39. Five molecules have speeds of 2.8, 3.2, 5.8, 7.3, and 7.4 m/s. Their root-mean-square speed is
closest to:
A. 5.3 m/s
B. 5.7 m/s
C. 7.3 m/s
D. 28 m/s
E. 32 m/s
ans: B
40. The speeds of 25 molecules are distributed as follows: 5 in the range from 2 to 3 m/s, 10 in the
range from 3 to 4 m/s, 5 in the range from 4 to 5 m/s, 3 in the range from 5 to 6 m/s, 1 in the
range from 6 to 7 m/s, and 1 in the range from 7 to 8 m/s. Their average speed is about:
A. 2 m/s
B. 3 m/s
C. 4 m/s
D. 5 m/s
E. 6 m/s
ans: C
Chapter 19:
THE KINETIC THEORY OF GASES
295
41. In a system of N gas molecules, the individual speeds are v1 , v2 , . . ., vN . The rms speed of
these molecules is:
1√
v1 + v 2 + . . . + vN
A.
N
1
2
B.
v12 + v22 + . . . + vN
N
C.
2 )/N
(v12 + v22 + . . . + vN
2
[(v1 + v2 + . . . + vN )/N ]
0
E.
(v1 + v2 + . . . + vN )2 /N
ans: C
D.
42. A system consists of N gas molecules, each with mass m. Their rms speed is vrms . Their total
translational kinetic energy is:
A. (1/2)m(N vrms )2
B. (1/2)N (mvrms )2
2
C. (1/2)mvrms
2
D. (1/2)N mvrms
2
E. N [(1/2)mvrms ]
ans: D
43. The average speeds v and molecular diameters d of five ideal gases are given below. The number
of molecules per unit volume is the same for all of them. For which is the collision rate the
greatest?
A. v = v0 and d = d0
B. v = 2v0 and d = d0 /2
C. v = 3v0 and d = d0
D. v = v0 and d = 2d0
E. v = 4v0 and d = d0 /2
ans: D
44. The internal energy of an ideal gas depends on:
A. the temperature only
B. the pressure only
C. the volume only
D. the temperature and pressure only
E. temperature, pressure, and volume
ans: A
296
Chapter 19:
THE KINETIC THEORY OF GASES
45. The diagram shows three isotherms for an ideal gas, with T3 − T2 the same as T2 − T1 . It also
shows five thermodynamic processes carried out on the gas. Rank the processes in order of the
change in the internal energy of th gas, least to greatest.
p
......
......
......
......
.......
.......
.......
.......
........
........
.........
.........
..........
..........
........
...........
........
...........
........
.............
.........
.............
..........
...............
..........
................
............
.................
............
....................
..............
......................
................
........................
.................
.....
.....................
......................
..........................
...............
...............................
.................
................................
...................
................
......................
.............................
......................................
..............................................
...............................................................
...........................
...
........
.. .. II
....... ...
..
I ..
..
..
.
........
III
............... .........................................
.
.
.
.
.
.
.
.
.
.
.
... .......................................
....
IV
......................................V
.................................................
T3
T2
T1
V
A.
B.
C.
D.
E.
I, II, III, IV, V
V, then I, III, and IV tied, then II
V, I, then III and IV tied, then II
IV, V, III, I, II
II, I, then III, IV, and V tied
ans: B
46. An ideal gas of N monatomic molecules is in thermal equilibrium with an ideal gas of the same
number of diatomic molecules and equilibrium is maintained as the temperature is increased.
The ratio of the changes in the internal energies ∆Edia /∆Emon is:
A. 1/2
B. 3/5
C. 1
D. 5/3
E. 2
ans: D
47. Two ideal gases, each consisting of N monatomic molecules, are in thermal equilibrium with
each other and equilibrium is maintained as the temperature is increased. A molecule of the
first gas has mass m and a molecule of the second has mass 4m. The ratio of the changes in
the internal energies ∆E4m /∆Em is:
A. 1/4
B. 1/2
C. 1
D. 2
E. 4
ans: C
Chapter 19:
THE KINETIC THEORY OF GASES
297
48. Three gases, one consisting of monatomic molecules, one consisting of diatomic molecules, and
one consisting of polyatomic molecules, are in thermal equilibrium with each other and remain
in thermal equilibrium as the temperature is raised. All have the same number of molecules.
The gases with the least and greatest change in internal energy are respectively:
A. polyatomic, monatomic
B. monatomic, polyatomic
C. diatomic, monatomic
D. polyatomic, diatomic
E. monatomic, diatomic
ans: B
49. An ideal gas of N diatomic molecules has temperature T . If the number of molecules is doubled
without changing the temperature, the internal energy increases by:
A. 0
B. (1/2)N kT
C. (3/2)N kT
D. (5/2)N kT
E. 3N kT
ans: D
50. Both the pressure and volume of an ideal gas of diatomic molecules are doubled. The ratio of
the new internal energy to the old, both measured relative to the internal energy at 0 K, is
A. 1/4
B. 1/2
C. 1
D. 2
E. 4
ans: E
51. The pressure of an ideal gas of diatomic molecules is doubled by halving the volume. The ratio
of the new internal energy to the old, both measured relative to the internal energy at 0 K, is:
A. 1/4
B. 1/2
C. 1
D. 2
E. 4
ans: C
52. When work W is done on an ideal gas of N diatomic molecules in thermal isolation the temperature increases by:
A. W/2N k
B. W/3N k
C. 2W/3N k
D. 2W/5N k
E. W/N k
ans: D
298
Chapter 19:
THE KINETIC THEORY OF GASES
53. When work W is done on an ideal gas of diatomic molecules in thermal isolation the increase
in the total rotational energy of the molecules is:
A. 0
B. W/3
C. 2W/3
D. 2W/5
E. W
ans: D
54. When work W is done on an ideal gas of diatomic molecules in thermal isolation the increase
in the total translational kinetic energy of the molecules is:
A. 0
B. 2W/3
C. 2W/5
D. 3W/5
E. W
ans: D
55. The pressure of an ideal gas is doubled in an isothermal process. The root-mean-square speed
of the molecules:
A. does not change
√
B. increases by a factor of 2√
C. decreases by a factor of 1/ 2
D. increases by a factor of 2
E. decreases by a factor of 1/2
ans: A
56. The Maxwellian speed distribution provides a direct explanation of:
A. thermal expansion
B. the ideal gas law
C. heat
D. evaporation
E. boiling
ans: D
57. For a gas at thermal equilibrium the average speed v, the most probable speed vp , and the
root-mean-square speed vrms are in the order:
A. vp < vrms < v
B. vrms < vp < v
C. v < vrms < vp
D. vp < v < vrms
E. v < vp < vrms
ans: D
Chapter 19:
THE KINETIC THEORY OF GASES
299
58. The average speed of air molecules at room temperature is about:
A. zero
B. 2 m/s (walking speed)
C. 30 m/s (fast car)
D. 500 m/s (supersonic airplane)
E. 3 × 108 m/s (speed of light)
ans: D
59. The root-mean-square sped of molecules in a gas is:
A. the most probable speed
B. that speed such that half the molecules are moving faster than vrms and the other half are
moving slower
C. the average speed of the molecules
D. the square root of the square of the average speed
E. none of the above
ans: E
60. According to the Maxwellian speed distribution, as the temperature increases the number of
molecules with speeds within a small interval near the most probable speed:
A. increases
B. decreases
C. increases at high temperatures and decreases at low
D. decreases at high temperatures and increases at low
E. stays the same
ans: B
61. According to the Maxwellian speed distribution, as the temperature increases the most probable
speed:
A. increases
B. decreases
C. increases at high temperatures and decreases at low
D. decreases at high temperatures and increases at low
E. stays the same
ans: A
62. According to the Maxwellian speed distribution, as the temperature increases the average
speed:
A. increases
B. decreases
C. increases at high temperatures and decreases at low
D. decreases at high temperatures and increases at low
E. stays the same
ans: A
300
Chapter 19:
THE KINETIC THEORY OF GASES
63. As
A.
B.
C.
D.
E.
the pressure in an ideal gas is increased isothermally the average molecular speed:
increases
decreases
increases at high temperature, decreases at low
decreases at high temperature, increases at low
stays the same
ans: E
64. As
A.
B.
C.
D.
E.
the volume of an ideal gas is increased at constant pressure the average molecular speed:
increases
decreases
increases at high temperature, decreases at low
decreases at high temperature, increases at low
stays the same
ans: A
65. Two ideal monatomic gases are in thermal equilibrium with each other. Gas A is composed of
molecules with mass m while gas B is composed of molecules with mass 4m. The ratio of the
average molecular speeds vA /vB is:
A. 1/4
B. 1/2
C. 1
D. 2
E. 4
ans: D
66. Ideal monatomic gas A is composed of molecules with mass m while ideal monatomic gas B is
composed of molecules with mass 4m. The average molecular speeds are the same if the ratio
of the temperatures TA /TB is:
A. 1/4
B. 1/2
C. 1
D. 2
E. 4
ans: A
67. Two monatomic ideal gases are in thermal equilibrium with each other. Gas A is composed of
molecules with mass m while gas B is composed of molecules with mass 4m. The ratio of the
average translational kinetic energies KA /KB is:
A. 1/4
B. 1/2
C. 1
D. 2
E. 4
ans: C
Chapter 19:
THE KINETIC THEORY OF GASES
301
68. Ideal monatomic gas A is composed of molecules with mass m while ideal monatomic gas B is
composed of molecules with mass 4m. The average translational kinetic energies are the same
if the ratio of the temperatures TA /TB is:
A. 1/4
B. 1/2
C. 1
D. 2
E. 4
ans: C
69. Which of the following change when the pressure of an ideal gas is changed isothermally?
A. Mean free path
B. Root-mean-square molecular speed
C. Internal energy
D. Most probable kinetic energy
E. Average speed
ans: A
70. When an ideal gas undergoes a slow isothermal expansion:
A. the work done by the gas is the same as the energy absorbed as heat
B. the work done by the environment is the same as the energy absorbed as heat
C. the increase in internal energy is the same as the energy absorbed as heat
D. the increase in internal energy is the same as the work done by the gas
E. the increase in internal energy is the same as the work done by the environment
ans: A
71. The pressure of an ideal gas is doubled during a process in which the energy given up as heat
by the gas equals the work done on the gas. As a result, the volume is:
A. doubled
B. halved
C. unchanged
D. need more information to answer
E. nonsense; the process is impossible
ans: B
72. The energy absorbed as heat by an ideal gas for an isothermal process equals:
A. the work done by the gas
B. the work done on the gas
C. the change in the internal energy of the gas
D. the negative of the change in internal energy of the gas
E. zero since the process is isothermal
ans: A
302
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THE KINETIC THEORY OF GASES
73. An ideal gas has molar specific heat Cp at constant pressure. When the temperature of n moles
is increased by ∆T the increase in the internal energy is:
A. nCp ∆T
B. n(Cp + R) ∆T
C. n(Cp − R) ∆T
D. n(2Cp + R) ∆T
E. n(2Cp − R) ∆T
ans: C
74. The temperature of n moles of an ideal monatomic gas is increased by ∆T at constant pressure.
The energy Q absorbed as heat, change ∆Eint in internal energy, and work W done by the
environment are given by:
A. Q = (5/2)nR ∆T , ∆Eint = 0, W = −nR ∆T
B. Q = (3/2)nR ∆T , ∆Eint = (5/2)nR ∆T , W = −(3/2)nR ∆T
C. Q = (5/2)nR ∆T , ∆Eint = (5/2)nR ∆T , W = 0
D. Q = (3/2)nR ∆T , ∆Eint = 0, W = −nR ∆T
E. Q = (5/2)nR ∆T , ∆Eint = (3/2)nR ∆T , W = −nR ∆T
ans: E
75. The temperature of n moles of an ideal monatomic gas is increased by ∆T at constant volume.
The energy Q absorbed as heat, change ∆Eint in internal energy, and work W done by the
environment are given by:
A. Q = (5/2)nR ∆T , ∆Eint = 0, W = 0
B. Q = (3/2)nR ∆T , ∆Eint = (3/2)nR ∆T , W = 0
C. Q = (3/2)nR ∆T , ∆Eint = (1/2)nR ∆T , W = −nR ∆t
D. Q = (5/2)nR ∆T , ∆Eint = (3/2)nR ∆T , W = −nR ∆T
E. Q = (3/2)nR ∆T , ∆Eint = 0, W = −(3/2)nR ∆T
ans: B
76. The heat capacity at constant volume of an ideal gas depends on:
A. the temperature
B. the pressure
C. the volume
D. the number of molecules
E. none of the above
ans: D
77. The specific heat at constant volume of an ideal gas depends on:
A. the temperature
B. the pressure
C. the volume
D. the number of molecules
E. none of the above
ans: E
Chapter 19:
THE KINETIC THEORY OF GASES
303
78. The difference between the molar specific heat at constant pressure and the molar specific heat
at constant volume for an ideal gas is:
A. the Boltzmann constant k
B. the universal gas constant R
C. the Avogadro constant NA
D. kT
E. RT
ans: B
79. An
A.
B.
C.
D.
E.
ideal monatomic gas has a molar specific heat Cv at constant volume of:
R
3R/2
5R/2
7R/2
9R/2
ans: B
80. The specific heat Cv at constant volume of a monatomic gas at low pressure is proportional to
T n where the exponent n is:
A. −1
B. 0
C. 1
D. 1/2
E. 2
ans: B
81. An
A.
B.
C.
D.
E.
ideal diatomic gas has a molar specific heat at constant pressure Cp of:
R
3R/2
5R/2
7R/2
9R/2
ans: D
82. The specific heat of a polyatomic gas is greater than the specific heat of a monatomic gas
because:
A. the polyatomic gas does more positive work when energy is absorbed as heat
B. the monatomic gas does more positive work when energy is absorbed as heat
C. the energy absorbed by the polyatomic gas is split among more degrees of freedom
D. the pressure is greater in the polyatomic gas
E. a monatomic gas cannot hold as much heat
ans: C
304
Chapter 19:
THE KINETIC THEORY OF GASES
83. The ratio of the specific heat of a gas at constant volume to its specific heat at constant pressure
is:
A. 1
B. less than 1
C. more than 1
D. has units of pressure/volume
E. has units of volume/pressure
ans: B
84. The ratio of the specific heat of an ideal gas at constant volume to its specific heat at constant
pressure is:
A. R
B. 1/R
C. dependent on the temperature
D. dependent on the pressure
E. different for monatomic, diatomic, and polyatomic gases
ans: E
85. Consider the ratios of the heat capacities γ = Cp /Cv for the three types of ideal gases:
monatomic, diatomic, and polyatomic.
A. γ is the greatest for monatomic gases
B. γ is the greatest for polyatomic gases
C. γ is the same only for diatomic and polyatomic gases
D. γ is the same only for monatomic and diatomic gases
E. γ is the same for all three
ans: A
86. T V γ−1 is constant for an ideal gas undergoing an adiabatic process, where γ is the ratio of
heat capacities Cp /Cv . This is a direct consequence of:
A. the zeroth law of thermodynamics alone
B. the zeroth law and the ideal gas equation of state
C. the first law of thermodynamics alone
D. the ideal gas equation of state alone
E. the first law and the equation of state
ans: E
87. Monatomic, diatomic, and polyatomic ideal gases each undergo slow adiabatic expansions from
the same initial volume and the same initial pressure to the same final volume. The magnitude
of the work done by the environment on the gas:
A. is greatest for the polyatomic gas
B. is greatest for the diatomic gas
C. is greatest for the monatomic gas
D. is the same only for the diatomic and polyatomic gases
E. is the same for all three gases
ans: A
Chapter 19:
THE KINETIC THEORY OF GASES
305
88. The mean free path of a gas molecule is:
A. the shortest dimension of the containing vessel
B. the cube root of the volume of the containing vessel
C. approximately the diameter of a molecule
D. average distance between adjacent molecules
E. average distance a molecule travels between intermolecular collisions
ans: E
89. The mean free path of molecules in a gas is:
A. the average distance a molecule travels before escaping
B. the average distance a molecule travels between collisions
C. the greatest distance a molecule travels between collisions
D. the shortest distance a molecule travels between collisions
E. the average distance a molecule travels before splitting apart
ans: B
90. The mean free path of air molecules at room temperature and atmospheric pressure is about:
A. 10−3 m
B. 10−5 m
C. 10−7 m
D. 10−9 m
E. 10−11 m
ans: C
91. The mean free path of molecules in a gas is proportional to:
A. the molecular cross-sectional area
B. the reciprocal of the molecular cross-sectional area
C. the root-mean-square molecular speed
D. the square of the average molecular speed
E. the molar mass
ans: B
92. The mean free path of molecules in a gas is proportional to:
A. the molecular diameter
B. the reciprocal of the molecular diameter
C. the molecular concentration
D. the reciprocal of the molecular concentration
E. the average molecular speed
ans: D
306
Chapter 19:
THE KINETIC THEORY OF GASES
93. In a certain gas the molecules are 5.0 × 10−9 m apart on average, have a mean free path of
5.0×10−6 m, and have an average speed of 500 m/s. The rate at which a molecule has collisions
with other molecules is about:
A. 10−11 s−1
B. 10−8 s−1
C. 1 s−1
D. 108 s−1
E. 1011 s−1
ans: D
94. If the temperature T of an ideal gas is increased at constant pressure the mean free path:
A. decreases in proportion to 1/T
B. decreases in proportion to 1/T 2
C. increases in proportion to T
D. increases in proportion to T 2
E. does not change
ans: C
95. A certain ideal gas has a temperature 300 K and a pressure 5.0 × 104 Pa. The molecules have
a mean free path of 4.0 × 10−7 m. If the temperature is raised to 350 K and the pressure is
reduced to 1.0 × 104 Pa the mean free path is then:
A. 6.9 × 10−8 m
B. 9.3 × 10−8 m
C. 3.3 × 10−7 m
D. 1.7 × 10−6 m
E. 2.3 × 10−6 m
ans: E
Chapter 19:
THE KINETIC THEORY OF GASES
307
Chapter 20:
ENTROPY AND THE SECOND LAW OF THERMODYNAMICS
1. In a reversible process the system:
A. is always close to equilibrium states
B. is close to equilibrium states only at the beginning and end
C. might never be close to any equilibrium state
D. is close to equilibrium states throughout, except at the beginning and end
E. is none of the above
ans: A
2. A slow (quasi-static) process is NOT reversible if:
A. the temperature changes
B. energy is absorbed or emitted as heat
C. work is done on the system
D. friction is present
E. the pressure changes
ans: D
3. The difference in
$ entropy ∆S = SB − SA for two states A and B of a system can be computed
as the integral dQ/T provided:
A. A and B are on the same adiabat
B. A and B have the same temperature
C. a reversible path is used for the integral
D. the change in internal energy is first computed
E. the energy absorbed as heat by the system is first computed
ans: C
4. Possible units of entropy are:
A. J
B. J/K
C. J−1
D. liter·atm
E. cal/mol
ans: B
5. Which of the following is NOT a state variable?
A. Work
B. Internal energy
C. Entropy
D. Temperature
E. Pressure
ans: A
308
Chapter 20:
ENTROPY AND THE SECOND LAW OF THERMODYNAMICS
6. The change in entropy is zero for:
A. reversible adiabatic processes
B. reversible isothermal processes
C. reversible processes during which no work is done
D. reversible isobaric processes
E. all adiabatic processes
ans: A
7. Which of the following processes leads to a change in entropy of zero for the system undergoing
the process?
A. Non-cyclic isobaric (constant pressure)
B. Non-cyclic isochoric (constant volume)
C. Non-cyclic isothermal (constant temperature)
D. Any closed cycle
E. None of these
ans: D
8. Rank, from smallest to largest, the changes in entropy of a pan of water on a hot plate, as the
temperature of the water
1. goes from 20◦ C to 30◦ C
2. goes from 30◦ C to 40◦ C
3. goes from 40◦ C to 45◦ C
4. goes from 80◦ C to 85◦ C
A. 1, 2, 3, 4
B. 4, 3, 2, 1
C. 1 and 2 tie, then 3 and 4 tie
D. 3 and 4 tie, then 1 and 2 tie
E. 4, 3, 2, 1
ans: E
9. An
A.
D.
B.
E.
C.
ideal gas expands into a vacuum in a rigid vessel. As a result there is:
a change in entropy
an increase of pressure
a change in temperature
a decrease of internal energy
a change in phase
ans: A
10. Consider all possible isothermal contractions of an ideal gas. The change in entropy of the gas:
A. is zero for all of them
B. does not decrease for any of them
C. does not increase for any of them
D. increases for all of them
E. decreases for all of them
ans: E
Chapter 20:
ENTROPY AND THE SECOND LAW OF THERMODYNAMICS
309
11. An ideal gas is to taken reversibly from state i, at temperature T1 , to any of the other states
labeled I, II, III, IV, and V on the p-V diagram below. All are at the same temperature T2 .
Rank the five processes according to the change in entropy of the gas, least to greatest.
p
T2
...
...
...
...
...
...
...
...
...
...
....
....
....
...
....
.....
.....
.....
......
......
......
......
.......
.......
.......
.......
........
.........
.........
..........
...........
...........
.............
..............
...............
.................
....................
.. I
.......
..
..
..
............ II
..
.
.
.. .....
........ III
.. ..... ...............................
.
.
.
.
.
...................... IV
.
.
.
.
.
.
i .................................................................................................................................................................................... V
T1
V
A.
B.
C.
D.
E.
I, II, III, IV, V
V, IV, III, II, I
I, then II, III, IV, and V tied
I, II, III, and IV tied, then V
I and V tied, then II, III, IV
ans: A
12. An ideal gas, consisting of n moles, undergoes a reversible isothermal process during which the
volume changes from Vi to Vf . The change in entropy of the thermal reservoir in contact with
the gas is given by:
A. nR(Vf − Vi )
B. nR ln(Vf − Vi )
C. nR ln(Vi /Vf )
D. nR ln(Vf /Vi )
E. none of the above (entropy can’t be calculated for a reversible process)
ans: C
13. One mole of an ideal gas expands reversibly and isothermally at temperature T until its volume
is doubled. The change of entropy of this gas for this process is:
A. R ln 2
B. (ln 2)/T
C. 0
D. RT ln 2
E. 2R
ans: A
310
Chapter 20:
ENTROPY AND THE SECOND LAW OF THERMODYNAMICS
14. An ideal gas, consisting of n moles, undergoes an irreversible process in which the temperature
has the same value at the beginning and end. If the volume changes from Vi to Vf , the change
in entropy of the gas is given by:
A. nR(Vf − Vi )
B. nR ln(Vf − Vi )
C. nR ln(Vi /Vf )
D. nR ln(Vf /Vi )
E. none of the above (entropy can’t be calculated for an irreversible process)
ans: D
15. The temperature of n moles of a gas is increased from Ti to Tf at constant volume. If the
molar specific heat at constant volume is CV and is independent of temperature, then change
in the entropy of the gas is:
A. nCV ln(Tf /Ti )
B. nCV ln(Ti /Tf )
C. nCV ln(Tf − Ti )
D. nCV ln(1 − Ti /Tf )
E. nCV (Tf − Ti )
ans: A
16. Consider the following processes: The temperature of two identical gases are increased from
the same initial temperature to the same final temperature. Reversible processes are used. For
gas A the process is carried out at constant volume while for gas B it is carried out at constant
pressure. The change in entropy:
A. is the same for A and B
B. is greater for A
C. is greater for B
D. is greater for A only if the initial temperature is low
E. is greater for A only if the initial temperature is high
ans: C
17. A hot object and a cold object are placed in thermal contact and the combination is isolated.
They transfer energy until they reach a common temperature. The change ∆Sh in the entropy
of the hot object, the change ∆Sc in the entropy of the cold object, and the change ∆Stotal in
the entropy of the combination are:
A. ∆Sh > 0, ∆Sc > 0, ∆Stotal > 0
B. ∆Sh < 0, ∆Sc > 0, ∆Stotal > 0
C. ∆Sh < 0, ∆Sc > 0, ∆Stotal < 0
D. ∆Sh > 0, ∆Sc < 0, ∆Stotal > 0
E. ∆Sh > 0, ∆Sc < 0, ∆Stotal < 0
ans: B
Chapter 20:
ENTROPY AND THE SECOND LAW OF THERMODYNAMICS
311
18. Let SI denote the change in entropy of a sample for an irreversible process from state A to
state B. Let SR denote the change in entropy of the same sample for a reversible process from
state A to state B. Then:
A. SI > SR
B. SI = SR
C. SI < SR
D. SI = 0
E. SR = 0
ans: B
19. For
A.
B.
C.
D.
E.
all adiabatic processes:
the entropy of the system
the entropy of the system
the entropy of the system
the entropy of the system
the entropy of the system
ans: E
20. For
A.
B.
C.
D.
E.
all reversible processes involving a system and its environment:
the entropy of the system does not change
the entropy of the system increases
the total entropy of the system and its environment does not change
the total entropy of the system and its environment increases
none of the above
ans: C
21. For
A.
B.
C.
D.
E.
all irreversible processes involving a system and its environment:
the entropy of the system does not change
the entropy of the system increases
the total entropy of the system and its environment does not change
the total entropy of the system and its environment increases
none of the above
ans: D
does not change
increases
decreases
does not increase
does not decrease
22. According to the second law of thermodynamics:
A. heat energy cannot be completely converted to work
B. work cannot be completely converted to heat energy
C. for all cyclic processes we have dQ/T < 0
D. the reason all heat engine efficiencies are less than 100% is friction, which is unavoidable
E. all of the above are true
ans: A
312
Chapter 20:
ENTROPY AND THE SECOND LAW OF THERMODYNAMICS
23. Consider the following processes:
I. Energy flows as heat from a hot object to a colder object
II. Work is done on a system and an equivalent amount of energy is rejected as heat by the
system
III. Energy is absorbed as heat by a system and an equivalent amount of work is done by the
system
Which are never found to occur?
A. Only I
B. Only II
C. Only III
D. Only II and III
E. I, II, and III
ans: C
24. An inventor suggests that a house might be heated by using a refrigerator to draw energy as
heat from the ground and reject energy as heat into the house. He claims that the energy
supplied to the house as heat can exceed the work required to run the refrigerator. This:
A. is impossible by first law
B. is impossible by second law
C. would only work if the ground and the house were at the same temperature
D. is impossible since heat energy flows from the (hot) house to the (cold) ground
E. is possible
ans: E
25. In a thermally insulated kitchen, an ordinary refrigerator is turned on and its door is left open.
The temperature of the room:
A. remains constant according to the first law of thermodynamics
B. increases according to the first law of thermodynamics
C. decreases according to the first law of thermodynamics
D. remains constant according to the second law of thermodynamics
E. increases according to the second law of thermodynamics
ans: B
26. A heat engine:
A. converts heat input to an equivalent amount of work
B. converts work to an equivalent amount of heat
C. takes heat in, does work, and loses energy as heat
D. uses positive work done on the system to transfer heat from a low temperature reservoir
to a high temperature reservoir
E. uses positive work done on the system to transfer heat from a high temperature reservoir
to a low temperature reservoir.
ans: C
Chapter 20:
ENTROPY AND THE SECOND LAW OF THERMODYNAMICS
313
27. A heat engine absorbs energy of magnitude |QH | as heat from a high temperature reservoir, does
work of magnitude |W |, and transfers energy of magnitude |QL | as heat to a low temperature
reservoir. Its efficiency is:
A. |QH |/|W |
B. |QL |/|W |
C. |QH |/|QL |
D. |W |/|QH |
E. |W |/|QL |
ans: D
28. The temperatures TC of the cold reservoirs and the temperatures TH of the hot reservoirs for
four Carnot heat engines are
engine 1: TC = 400 K and TH = 500 K
engine 2: TC = 500 K and TH = 600 K
engine 3: TC = 400 K and TH = 600 K
engine 4: TC = 600 K and TH = 800 K
Rank these engines according to their efficiencies, least to greatest
A. 1, 2, 3, 4
B. 1 and 2 tie, then 3 and 4 tie
C. 2, 1, 3, 4
D. 1, 2, 4, 3
E. 2, 1, 4, 3
ans: E
29. A Carnot heat engine runs between a cold reservoir at temperature TC and a hot reservoir at
temperature TH . You want to increase its efficiency. Of the following, which change results in
the greatest increase in efficiency? The value of ∆T is the same for all changes.
A. Raise the temperature of the hot reservoir by ∆T
B. Raise the temperature of the cold reservoir by ∆T
C. Lower the temperature of the hot reservoir by ∆T
D. Lower the temperature of the cold reservoir by ∆T
E. Lower the temperature of the hot reservoir by 12 ∆T and raise the temperature of the cold
reservoir by 12 ∆T
ans: D
30. 31. A certain heat engine draws 500 cal/s from a water bath at 27◦ C and transfers 400 cal/s to
a reservoir at a lower temperature. The efficiency of this engine is:
A. 80%
B. 75%
C. 55%
D. 25%
E. 20%
ans: E
314
Chapter 20:
ENTROPY AND THE SECOND LAW OF THERMODYNAMICS
32. A heat engine that in each cycle does positive work and loses energy as heat, with no heat
energy input, would violate:
A. the zeroth law of thermodynamics
B. the first law of thermodynamics
C. the second law of thermodynamics
D. the third law of thermodynamics
E. Newton’s second law
ans: B
33. A cyclical process that transfers energy as heat from a high temperature reservoir to a low
temperature reservoir with no other change would violate:
A. the zeroth law of thermodynamics
B. the first law of thermodynamics
C. the second law of thermodynamics
D. the third law of thermodynamics
E. none of the above
ans: E
34. On a warm day a pool of water transfers energy to the air as heat and freezes. This is a direct
violation of:
A. the zeroth law of thermodynamics
B. the first law of thermodynamics
C. the second law of thermodynamics
D. the third law of thermodynamics
E. none of the above
ans: C
35. A heat engine in each cycle absorbs energy of magnitude |QH | as heat from a high temperature
reservoir, does work of magnitude |W |, and then absorbs energy of magnitude |QL | as heat
from a low temperature reservoir. If |W | = |QH | + |QL | this engine violates:
A. the zeroth law of thermodynamics
B. the first law of thermodynamics
C. the second law of thermodynamics
D. the third law of thermodynamics
E. none of the above
ans: C
36. A heat engine in each cycle absorbs energy from a reservoir as heat and does an equivalent
amount of work, with no other changes. This engine violates:
A. the zeroth law of thermodynamics
B. the first law of thermodynamics
C. the second law of thermodynamics
D. the third law of thermodynamics
E. none of the above
ans: C
Chapter 20:
ENTROPY AND THE SECOND LAW OF THERMODYNAMICS
315
37. A Carnot cycle:
A. is bounded by two isotherms and two adiabats on a p-V graph
B. consists of two isothermal and two constant volume processes
C. is any four-sided process on a p-V graph
D. only exists for an ideal gas
E. has an efficiency equal to the enclosed area on a p-V diagram
ans: A
38. According to the second law of thermodynamics:
A. all heat engines have the same efficiency
B. all reversible heat engines have the same efficiency
C. the efficiency of any heat engine is independent of its working substance
D. the efficiency of a Carnot engine depends only on the temperatures of the two reservoirs
E. all Carnot engines theoretically have 100% efficiency
ans: D
39. A Carnot heat engine operates between 400 K and 500 K. Its efficiency is:
A. 20%
B. 25%
C. 44%
D. 79%
E. 100%
ans: A
40. A Carnot heat engine operates between a hot reservoir at absolute temperature TH and a cold
reservoir at absolute temperature TC . Its efficiency is:
A. TH /TC
B. TC /TH
C. 1 − TH /TC
D. 1 − TC /TH
E. 100%
ans: D
41. A heat engine operates between a high temperature reservoir at TH and a low temperature
reservoir at TL . Its efficiency is given by 1 − TL /TH :
A. only if the working substance is an ideal gas
B. only if the engine is reversible
C. only if the engine is quasi-static
D. only if the engine operates on a Stirling cycle
E. no matter what characteristics the engine has
ans: B
316
Chapter 20:
ENTROPY AND THE SECOND LAW OF THERMODYNAMICS
42. The maximum theoretical efficiency of a Carnot heat engine operating between reservoirs at
the steam point and at room temperature is about:
A. 10%
B. 20%
C. 50%
D. 80%
E. 99%
ans: B
43. An inventor claims to have a heat engine that has an efficiency of 40% when it operates between
a high temperature reservoir of 150◦ C and a low temperature reservoir of 30◦ C. This engine:
A. must violate the zeroth law of thermodynamics
B. must violate the first law of thermodynamics
C. must violate the second law of thermodynamics
D. must violate the third law of thermodynamics
E. does not necessarily violate any of the laws of thermodynamics
ans: C
44. A Carnot heat engine and an irreversible heat engine both operate between the same high
temperature and low temperature reservoirs. They absorb the same energy from the high
temperature reservoir as heat. The irreversible engine:
A. does more work
B. transfers more energy to the low temperature reservoir as heat
C. has the greater efficiency
D. has the same efficiency as the reversible engine
E. cannot absorb the same energy from the high temperature reservoir as heat without violating the second law of thermodynamics
ans: B
45. A perfectly reversible heat pump with a coefficient of performance of 14 supplies energy to a
building as heat to maintain its temperature at 27◦ C. If the pump motor does work at the
rate of 1 kW, at what rate does the pump supply energy to the building as heat?
A. 15 kW
B. 3.85 kW
C. 1.35 kW
D. 1.07 kW
E. 1.02 kW
ans: A
46. A heat engine operates between 200 K and 100 K. In each cycle it takes 100 J from the hot
reservoir, loses 25 J to the cold reservoir, and does 75 J of work. This heat engine violates:
A. both the first and second laws of thermodynamics
B. the first law but not the second law of thermodynamics
C. the second law but not the first law of thermodynamics
D. neither the first law nor the second law of thermodynamics
E. cannot answer without knowing the mechanical equivalent of heat
ans: C
Chapter 20:
ENTROPY AND THE SECOND LAW OF THERMODYNAMICS
317
47. A refrigerator absorbs energy of magnitude |QC | as heat from a low temperature reservoir and
transfers energy of magnitude |QH | as heat to a high temperature reservoir. Work W is done
on the working substance. The coefficient of performance is given by:
A. |QC |/W
B. |QH |/W
C. (|QC | + |QH |)/W
D. W/|QC |
E. W/|QH |
ans: A
48. A reversible refrigerator operates between a low temperature reservoir at TC and a high temperature reservoir at TH . Its coefficient of performance is given by:
A. (TH − TC )/TC
B. TC /(TH − TC )
C. (TH − TC )/TH
D. TH /(TH − TC )
E. TH (TH + TC )
ans: B
49. An Carnot refrigerator runs between a cold reservoir at temperature TC and a hot reservoir at
temperature TH . You want to increase its coefficient of performance. Of the following, which
change results in the greatest increase in the coefficient? The value of ∆T is the same for all
changes.
A. Raise the temperature of the hot reservoir by ∆T
B. Raise the temperature of the cold reservoir by ∆T
C. Lower the temperature of the hot reservoir by ∆T
D. Lower the temperature of the cold reservoir by ∆T
E. Lower the temperature of the hot reservoir by 12 ∆T and raise the temperature of the cold
reservoir by 12 ∆T
ans: B
50. For one complete cycle of a reversible heat engine, which of the following quantities is NOT
zero?
A. the change in the entropy of the working gas
B. the change in the pressure of the working gas
C. the change in the internal energy of the working gas
D. the work done by the working gas
E. the change in the temperature of the working gas
ans: D
318
Chapter 20:
ENTROPY AND THE SECOND LAW OF THERMODYNAMICS
51. Twenty-five identical molecules are in a box. Microstates are designated by identifying the
molecules in the left and right halves of the box. The multiplicity of the configuration with 15
molecules in the right half and 10 molecules in the left half is:
A. 1.03 × 1023
B. 3.27 × 106
C. 150
D. 25
E. 5
ans: B
52. Twenty-five identical molecules are in a box. Microstates are designated by identifying the
molecules in the left and right halves of the box. The Boltzmann constant is 1.38 × 10−23 J/K.
The entropy associated with the configuration for which 15 molecules are in the left half and
10 molecules are in the right half is:
A. 2.07 × 10−22 J/K
B. 7.31 × 10−22 J/K
C. 4.44 × 10−23 J/K
D. 6.91 × 10−23 J/K
E. 2.22 × 10−23 J/K
ans: A
53. The thermodynamic state of a gas changes from one with 3.8 × 1018 microstates to one with
7.9 × 1019 microstates. The Boltzmann constant is 1.38 × 10−23 J/K. The change in entropy
is:
A. ∆S = 0
B. ∆S = 1.04 × 10−23 J/K
C. ∆S = −1.04 × 10−23 J/K
D. ∆S = 4.19 × 10−23 J/K
E. ∆S = −4.19 × 10−23 J/K
ans: D
54. Let k be the Boltzmann constant. If the configuration of the molecules in a gas changes so that
the multiplicity is reduced to one-third its previous value, the entropy of the gas changes by:
A. ∆S = 0
B. ∆S = 3k ln 2
C. ∆S = −3k ln 2
D. ∆S = −k ln 3
E. ∆S = k ln 3
ans: D
55. Let k be the Boltzmann constant. If the configuration of molecules in a gas changes from one
with a multiplicity of M1 to one with a multiplicity of M2 , then entropy changes by:
A. ∆S = 0
B. ∆S = k(M2 − M1 )
C. ∆S = kM2 /M1
D. ∆S = k ln(M2 M1 )
E. ∆S = k ln(M2 /M1 )
ans: E
Chapter 20:
ENTROPY AND THE SECOND LAW OF THERMODYNAMICS
319
56. Let k be the Boltzmann constant. If the thermodynamic state of a gas at temperature T
changes isothermally and reversibly to a state with three times the number of microstates as
initially, the energy input to the gas as heat is:
A. Q = 0
B. Q = 3kT
C. Q = −3kT
D. kT ln 3
E. −kT ln 3
ans: D
320
Chapter 20:
ENTROPY AND THE SECOND LAW OF THERMODYNAMICS
Chapter 21:
ELECTRIC CHARGE
1. A coulomb is the same as:
A. an ampere/second
B. half an ampere·second2
C. an ampere/meter2
D. an ampere·second
E. a newton·meter2
ans: D
2. A kiloampere·hour is a unit of:
A. current
B. charge per time
C. power
D. charge
E. energy
ans: D
3. The magnitude of the charge on an electron is approximately:
A. 1023 C
B. 10−23 C
C. 1019 C
D. 10−19 C
E. 109 C
ans: D
4. The total negative charge on the electrons in 1 mol of helium (atomic number 2, molar mass
4) is:
A. 4.8 × 104 C
B. 9.6 × 104 C
C. 1.9 × 105 C
D. 3.8 × 105 C
E. 7.7 × 105 C
ans: C
5. The total negative charge on the electrons in 1 kg of helium (atomic number 2, molar mass 4)
is:
A. 48 C
B. 2.4 × 107 C
C. 4.8 × 107 C
D. 9.6 × 108 C
E. 1.9 × 108 C
ans: C
Chapter 21:
ELECTRIC CHARGE
321
6. A wire carries a steady current of 2 A. The charge that passes a cross section in 2 s is:
A. 3.2 × 10−19 C
B. 6.4 × 10−19 C
C. 1 C
D. 2 C
E. 4 C
ans: E
7. A wire contains a steady current of 2 A. The number of electrons that pass a cross section in
2 s is:
A. 2
B. 4
C. 6.3 × 1018
D. 1.3 × 1019
E. 2.5 × 1019
ans: E
8. The charge on a glass rod that has been rubbed with silk is called positive:
A. by arbitrary convention
B. so that the proton charge will be positive
C. to conform to the conventions adopted for G and m in Newton’s law of gravitation
D. because like charges repel
E. because glass is an insulator
ans: A
9. To
A.
B.
C.
D.
E.
10. To
A.
B.
C.
D.
E.
322
make an uncharged object have a negative charge we must:
add some atoms
remove some atoms
add some electrons
remove some electrons
write down a negative sign
ans: C
make an uncharged object have a positive charge:
remove some neutrons
add some neutrons
add some electrons
remove some electrons
heat it to cause a change of phase
ans: D
Chapter 21:
ELECTRIC CHARGE
11. When a hard rubber rod is given a negative charge by rubbing it with wool:
A. positive charges are transferred from rod to wool
B. negative charges are transferred from rod to wool
C. positive charges are transferred from wool to rod
D. negative charges are transferred from wool to rod
E. negative charges are created and stored on the rod
ans: D
12. An
A.
B.
C.
D.
E.
electrical insulator is a material:
containing no electrons
through which electrons do not flow easily
that has more electrons than protons on its surface
cannot be a pure chemical element
must be a crystal
ans: B
13. A conductor is distinguished from an insulator with the same number of atoms by the number
of:
A. nearly free atoms
B. electrons
C. nearly free electrons
D. protons
E. molecules
ans: C
14. The diagram shows two pairs of heavily charged plastic cubes. Cubes 1 and 2 attract each
other and cubes 1 and 3 repel each other.
↑
1
1
↓
↑
2
3
↓
Which of the following illustrates the forces of cube 2 on cube 3 and cube 3 on cube 2?
↑
2
↑
3
A
↑
2
3
↓
B
2
↓
↑
3
2
↓
3
↓
D
C
↑
2
3
E
ans: C
Chapter 21:
ELECTRIC CHARGE
323
15. The diagram shows a pair of heavily charged plastic cubes that attract each other.
1
↓
↑
2
Cube 3 is a conductor and is uncharged. Which of the following illustrates the forces between
cubes 1 and 3 and between cubes 2 and 3?
↑
1
↑
2
↑
1
3
↓
3
↓
3
↓
A
↑
1
↑
3
D
2
↓
↑
3
1
↓
↑
3
B
2
↓
↑
3
C
2
↓
1
2
3
↓
3
3
E
ans: C
16. A neutral metal ball is suspended by a string. A positively charged insulating rod is placed
near the ball, which is observed to be attracted to the rod. This is because:
A. the ball becomes positively charged by induction
B. the ball becomes negatively charged by induction
C. the number of electrons in the ball is more than the number in the rod
D. the string is not a perfect insulator
E. there is a rearrangement of the electrons in the ball
ans: E
17. A positively charged insulating rod is brought close to an object that is suspended by a string.
If the object is attracted toward the rod we can conclude:
A. the object is positively charged
B. the object is negatively charged
C. the object is an insulator
D. the object is a conductor
E. none of the above
ans: E
324
Chapter 21:
ELECTRIC CHARGE
18. A positively charged insulating rod is brought close to an object that is suspended by a string.
If the object is repelled away from the rod we can conclude:
A. the object is positively charged
B. the object is negatively charged
C. the object is an insulator
D. the object is a conductor
E. none of the above
ans: A
19. Two uncharged metal spheres, L and M, are in contact. A negatively charged rod is brought
close to L, but not touching it, as shown. The two spheres are slightly separated and the rod
is then withdrawn. As a result:
L
M
...........................
................................
......
........
.....
.......
....
......
....
.....
...
... ......
...
.
...
.
... ..
.
...
......
....
...
....
....
..
..
...
...
......
...
...
...
..
.
.
. ...
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
... ...
. ...
.
.
.
...
..
.
.
.
.
.
.
.
....
...
.
......
....
......
....
...
...
........
......
........
......
...
...
..........................
..........................
...
...
..
.
...
.
.
.
.
...
...
...
...
...
...
..
.
...
.
.
.
..
...
..
..
...
...
+
++
++
++
++
insulating supports
A.
B.
C.
D.
E.
both spheres are neutral
both spheres are positive
both spheres are negative
L is negative and M is positive
L is positive and M is negative
ans: D
20. A positively charged metal sphere A is brought into contact with an uncharged metal sphere
B. As a result:
A. both spheres are positively charged
B. A is positively charged and B is neutral
C. A is positively charged and B is negatively charged
D. A is neutral and B is positively charged
E. A is neutral and B is negatively charged
ans: A
21. The leaves of a positively charged electroscope diverge more when an object is brought near
the knob of the electroscope. The object must be:
A. a conductor
B. an insulator
C. positively charged
D. negatively charged
E. uncharged
ans: C
Chapter 21:
ELECTRIC CHARGE
325
22. A negatively charged rubber rod is brought near the knob of a positively charged electroscope.
The result is that:
A. the electroscope leaves will move farther apart
B. the rod will lose its charge
C. the electroscope leaves will tend to collapse
D. the electroscope will become discharged
E. nothing noticeable will happen
ans: C
23. An electroscope is charged by induction using a glass rod that has been made positive by
rubbing it with silk. The electroscope leaves:
A. gain electrons
B. gain protons
C. lose electrons
D. lose protons
E. gain an equal number of protons and electrons
ans: A
24. Consider the following procedural steps:
1. ground an electroscope
2. remove the ground from the electroscope
3. touch a charged rod to the electroscope
4. bring a charged rod near, but not touching, the electroscope
5. remove the charged rod
To charge an electroscope by induction, use the sequence:
A. 1, 4, 5, 2
B. 4, 1, 2, 5
C. 3, 1, 2, 5
D. 4, 1, 5, 2
E. 3, 5
ans: B
25. A charged insulator can be discharged by passing it just above a flame. This is because the
flame:
A. warms it
B. dries it
C. contains carbon dioxide
D. contains ions
E. contains more rapidly moving atoms
ans: D
326
Chapter 21:
ELECTRIC CHARGE
26. A small object has charge Q. Charge q is removed from it and placed on a second small object.
The two objects are placed 1 m apart. For the force that each object exerts on the other to be
a maximum. q should be:
A. 2Q
B. Q
C. Q/2
D. Q/4
E. 0
ans: C
27. Two small charged objects attract each other with a force F when separated by a distance
d. If the charge on each object is reduced to one-fourth of its original value and the distance
between them is reduced to d/2 the force becomes:
A. F/16
B. F/8
C. F/4
D. F/2
E. F
ans: C
28. Two identical conducting spheres A and B carry equal charge. They are separated by a distance
much larger than their diameters. A third identical conducting sphere C is uncharged. Sphere
C is first touched to A, then to B, and finally removed. As a result, the electrostatic force
between A and B, which was originally F , becomes:
A. F/2
B. F/4
C. 3F/8
D. F/16
E. 0
ans: C
29. Two particles, X and Y, are 4 m apart. X has a charge of 2Q and Y has a charge of Q. The
force of X on Y:
A. has twice the magnitude of the force of Y on X
B. has half the magnitude of the force of Y on X
C. has four times the magnitude of the force of Y on X
D. has one-fourth the magnitude of the force of Y on X
E. has the same magnitude as the force of Y on X
ans: E
30. The units of 1/4π
A. N2 C2
B. N · m/C
2
C. N2 · m2 /C
2
D. N · m2 /C
2
E. m2 /C
ans: D
0
are:
Chapter 21:
ELECTRIC CHARGE
327
31. A 5.0-C charge is 10 m from a −2.0-C charge. The electrostatic force on the positive charge is:
A. 9.0 × 108 N toward the negative charge
B. 9.0 × 108 N away from the negative charge
C. 9.0 × 109 N toward the negative charge
D. 9.0 × 109 N away from the negative charge
E. none of these
ans: A
32. Two identical charges, 2.0 m apart, exert forces of magnitude 4.0 N on each other. The value
of either charge is:
A. 1.8 × 10−9 C
B. 2.1 × 10−5 C
C. 4.2 × 10−5 C
D. 1.9 × 105 C
E. 3.8 × 105 C
ans: C
33. Two electrons (e1 and e2 ) and a proton (p) lie on a straight line, as shown. The directions of
the force of e2 on e1 , the force of p on e1 , and the total force on e1 , respectively, are:
•
e1
A.
B.
C.
D.
E.
−→, ←−,
←−, −→,
−→, ←−,
←−, −→,
←−, ←−,
ans: D
•
e2
•
p
−→
−→
←−
←−
←−
34. Two protons (p1 and p2 ) and an electron (e) lie on a straight line, as shown. The directions of
the force of p1 on e, the force of p2 on e, and the total force on e, respectively, are:
•
p1
A.
B.
C.
D.
E.
328
−→, ←−,
←−, −→,
−→, ←−,
←−, −→,
←−, ←−,
ans: D
•
e
−→
−→
←−
←−
←−
Chapter 21:
ELECTRIC CHARGE
•
p2
35. Two particles have charges Q and −Q (equal magnitude and opposite sign). For a net force of
zero to be exerted on a third charge it must be placed:
A. midway between Q and −Q
B. on the perpendicular bisector of the line joining Q and −Q, but not on that line itself
C. on the line joining Q and −Q, to the side of Q opposite −Q
D. on the line joining Q and −Q, to the side of −Q opposite Q
E. at none of these places (there is no place)
ans: E
36. Particles 1, with charge q1 , and 2, with charge q2 , are on the x axis, with particle 1 at x = a
and particle 2 at x = −2a. For the net force on a third charged particle, at the origin, to be
zero, q1 and q2 must be related by q2 =:
A. 2q1
B. 4q1
C. −2q1
D. −4q1
E. −q1 /4
ans: B
37. Two particles A and B have identical charge Q. For a net force of zero to be exerted on a third
charged particle it must be placed:
A. midway between A and B
B. on the perpendicular bisector of the line joining A and B but away from the line
C. on the line joining A and B, not between the particles
D. on the line joining A and B, closer to one of them than the other
E. at none of these places (there is no place)
ans: A
38. A particle with charge 2-µC is placed at the origin, an identical particle, with the same charge,
is placed 2 m from the origin on the x axis, and a third identical particle, with the same charge,
is placed 2 m from the origin on the y axis. The magnitude of the force on the particle at the
origin is:
A. 9.0 × 10−3 N
B. 6.4 × 10−3 N
C. 1.3 × 10−2 N
D. 1.8 × 10−2 N
E. 3.6 × 10−2 N
ans: C
39. Charge Q is spread uniformly along the circumference of a circle of radius R. A point particle
with charge q is placed at the center of this circle. The total force exerted on the particle can
be calculated by Coulomb’s law:
A. just use R for the distance
B. just use 2R for the distance
C. just use 2πR for the distance
D. the result of the calculation is zero
E. none of the above
ans: D
Chapter 21:
ELECTRIC CHARGE
329
40. Two particles, each with charge Q, and a third particle, with charge q, are placed at the vertices
of an equilateral triangle as shown. The total force on the particle with charge q is:
...........
.... ....
.............
..
.
.
.
.
.
.......... ..............
...
...
...
..
.
...
.
...
...
...
..
.
.
...
..
.
...
.
...
...
.
...
..
.
...
.
.
.
...
..
.
...
.
...
...
.
...
.
.
.
..
............
..............
...
.
.........
.........
..... ................................................................................................................ ..... ....
... .... ...
.... .... ....
.
......
.......
+ q
Q +
A.
B.
C.
D.
E.
+ Q
parallel to the left side of the triangle
parallel to the right side of the triangle
parallel to the bottom side of the triangle
perpendicular to the bottom side of the triangle
perpendicular to the left side of the triangle
ans: D
41. A particle with charge Q is on the y axis a distance a from the origin and a particle with charge
q is on the x axis a distance d from the origin. The value of d for which the x component of
the force on the second particle is the greatest is:
A. 0
B. √
a
2a
C.
D. a/2
√
E. a/ 2
ans: E
42. In the Rutherford model of the hydrogen atom, a proton (mass M , charge Q) is the nucleus
and an electron (mass m, charge q) moves around the proton in a circle of radius r. Let k
denote the Coulomb force constant (1/4π 0 ) and G the universal gravitational constant. The
ratio of the electrostatic force to the gravitational force between electron and proton is:
A. kQq/GM mr2
B. GQq/kM m
C. kM m/GQq
D. GM m/kQq
E. kQq/GM m
ans: E
43. A particle with a charge of 5 × 10−6 C and a mass of 20 g moves uniformly with a speed of
7 m/s in a circular orbit around a stationary particle with a charge of −5 × 10−6 C. The radius
of the orbit is:
A. 0
B. 0.23 m
C. 0.62 m
D. 1.6
E. 4.4 m
ans: B
330
Chapter 21:
ELECTRIC CHARGE
44. Charge is distributed uniformly on the surface of a spherical balloon (an insulator). A point
particle with charge q is inside. The electrical force on the particle is greatest when:
A. it is near the inside surface of the balloon
B. it is at the center of the balloon
C. it is halfway between the balloon center and the inside surface
D. it is anywhere inside (the force is same everywhere and is not zero)
E. it is anywhere inside (the force is zero everywhere)
ans: E
45. Charge is distributed on the surface of a spherical conducting shell. A point particle with
charge q is inside. If polarization effects are negligible the electrical force on the particle is
greatest when:
A. it is near the inside surface of the balloon
B. it is at the center of the balloon
C. it is halfway between the balloon center and the inside surface
D. it is anywhere inside (the force is same everywhere and is not zero)
E. it is anywhere inside (the force is zero everywhere)
ans: A
Chapter 21:
ELECTRIC CHARGE
331
Chapter 22:
ELECTRIC FIELDS
1. An
A.
B.
C.
D.
E.
electric field is most directly related to:
the momentum of a test charge
the kinetic energy of a test charge
the potential energy of a test charge
the force acting on a test charge
the charge carried by a test charge
ans: D
2. As
A.
B.
C.
D.
E.
used in the definition of electric field, a “test charge”:
has zero charge
has charge of magnitude 1 C
has charge of magnitude 1.6 × 10−19 C
must be an electron
none of the above
ans: E
3. Experimenter A uses a test charge q0 and experimenter B uses a test charge −2q0 to measure
an electric field produced by stationary charges. A finds a field that is:
A. the same in both magnitude and direction as the field found by B
B. greater in magnitude than the field found by B
C. less in magnitude than the field found by B
D. opposite in direction to the field found by B
E. either greater or less than the field found by B, depending on the accelerations of the test
charges
ans: A
4. The units of the electric field are:
A. N · C2
B. C/N
C. N
D. N/C
2
E. C/m
ans: D
5. The units of the electric field are:
A. J/(C·m)
B. J/C
C. J·C
D. J/m
E. none of these
ans: A
332
Chapter 22:
ELECTRIC FIELDS
6. Electric field lines:
A. are trajectories of a test charge
B. are vectors in the direction of the electric field
C. form closed loops
D. cross each other in the region between two point charges
E. are none of the above
ans: E
7. Two thin spherical shells, one with radius R and the other with radius 2R, surround an isolated
charged point particle. The ratio of the number of field lines through the larger sphere to the
number through the smaller is:
A. 1
B. 2
C. 4
D. 1/2
E. 1/4
ans: A
8. A certain physics textbook shows a region of space in which two electric field lines cross each
other. We conclude that:
A. at least two point charges are present
B. an electrical conductor is present
C. an insulator is present
D. the field points in two directions at the same place
E. the author made a mistake
ans: E
9. Choose the correct statement concerning electric field lines:
A. field lines may cross
B. field lines are close together where the field is large
C. field lines point away from a negatively charged particle
D. a charged point particle released from rest moves along a field line
E. none of these are correct
ans: B
10. The diagram shows the electric field lines due to two charged parallel metal plates. We conclude
that:
.. .. .. .. ... .... ................
.. ..
... .. .........
.. Y .. .. Z ..
... ...
... ... .......
.. • .. .. • ..
... ....
. . ................... metal
.
.
.
.
.
.
.
.
...... ...... ..... ..... ..... • ..... ....... ....... ............................ plates
... ...
.. .. .. X ..
. .. .........
.. ..
. . . . .. .. ..............
A.
B.
C.
D.
E.
the upper plate is positive and the lower plate is negative
a proton at X would experience the same force if it were placed at Y
a proton at X experiences a greater force than if it were placed at Z
a proton at X experiences less force than if it were placed at Z
an electron at X could have its weight balanced by the electrical force
ans: B
Chapter 22:
ELECTRIC FIELDS
333
11. Let k denote 1/4π 0 . The magnitude of the electric field at a distance r from an isolated point
particle with charge q is:
A. kq/r
B. kr/q
C. kq/r 3
D. kq/r2
E. kq 2 /r2
ans: D
12. The diagram shows the electric field lines in a region of space containing two small charged
spheres (Y and Z). Then:
...
..
...
...
...
...
...
...
........
...
...
...
....... ...
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
...
.
.
.
.
.
....
.
.. ....
.
.
.
.......
.........
..... ....
.
.
.
.
.
.
...
.
.
.
.
.
.
.
.
.
.
.
.
.....
..
..
...
.....
.......
....
..
......... ............. ......
..
....
.
. .
......
... ... ....
........
....... . .. . ...
.........
......
.
..
............. .. ... . ...
..............
.................................................
.
.
.
.
.
..........
......
.
.
.......
......
.. .
.......
..
..
..
...................................................................
........................................
..................................
..
..
..
.
........
......
..
.
.
.
..............
.
.
.
.
.
.
.
.................
.
.......
....... . .. . ...
........................................
..
...............
..
....... . . ..
......
.........
....
... .... ....
..... .. . . ....
......
...
....
.
...
...... ............
.........
.....
..
....
.
...
.
..
.
.
.
.
.
.
.
.
...... .
........
...
...
.....
.
.
.
..
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.........................
...
...
..... ..
...
...
.....
...
...
...
...
...
..
..
...
..
..............
.... Y ....
...........
A.
B.
C.
D.
E.
..............
.... Z ....
...........
X
•
Y is negative and Z is positive
the magnitude of the electric field is the same everywhere
the electric field is strongest midway between Y and Z
the electric field is not zero anywhere (except infinitely far from the spheres)
Y and Z must have the same sign
ans: D
13. The diagram shows the electric field lines in a region of space containing two small charged
spheres (Y and Z). Then:
...
..
...
...
...
...
...
...
..
...
........
...
..
....... ...
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
...
....
.
.
.
........
........
........
...........
.
.
.
.
...
.
.
.
...
.
.
.
.
......
....
.
..
...
..
.....
....
..
.......
......... ............. ......
....
.
..
.
......
... ... ....
.....
.........
........ .. . ..
......
..
..............
.
............ .. .. . ...
...............................................
.
.
.
.
.
.
.
.
.........
.......
.
.
........
.......
.. ..
........
..
..
..
...................................................................
........................................
..................................
.
.
..
........
.......
.
.
.
.
.
.
.
.
.
.
.
.
.
.
......
.......... ......
.
.
..............
................ . . ...
......................................
.. .. ....
......
.... .. . ...
......
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
...
..
...
.. .. .
. ...
..
...
....
....... ...........
.....
..
.....
....
....
...........
...
....
......
......
.
.
..
.
.
.
.
..
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.............................
...
...
..... ...
...
...
...
.......
...
...
...
...
...
...
.
...
.
..
.............
..... Y ....
............
A.
B.
C.
D.
E.
334
.............
..... Z ....
............
Y is negative and Z is positive
the magnitude of the electric field is the same everywhere
the electric field is strongest midway between Y and Z
Y is positive and Z is negative
Y and Z must have the same sign
ans: D
Chapter 22:
ELECTRIC FIELDS
14. The electric field at a distance of 10 cm from an isolated point particle with a charge of 2×10−9 C
is:
A. 1.8 N/C
B. 180 N/C
C. 18 N/C
D. 1800 N/C
E. none of these
ans: D
15. An isolated charged point particle produces an electric field with magnitude E at a point 2 m
away from the charge. A point at which the field magnitude is E/4 is:
A. 1 m away from the particle
B. 0.5 m away from the particle
C. 2 m away from the particle
D. 4 m away from the particle
E. 8 m away from the particle
ans: D
16. An isolated charged point particle produces an electric field with magnitude E at a point 2 m
away. At a point 1 m from the particle the magnitude of the field is:
A. E
B. 2E
C. 4E
D. E/2
E. E/4
ans: C
17. Two protons (p1 and p2 ) are on the x axis, as shown below. The directions of the electric field
at points 1, 2, and 3, respectively, are:
1
×
A.
B.
C.
D.
E.
−→, ←−,
←−, −→,
←−, −→,
←−, ←−,
←−, ←−,
ans: E
•
p1
2
×
•
p2
3
×
−→
←−
−→
←−
−→
Chapter 22:
ELECTRIC FIELDS
335
18. Two point particles, with a charges of q1 and q2 , are placed a distance r apart. The electric field
is zero at a point P between the particles on the line segment connecting them. We conclude
that:
A. q1 and q2 must have the same magnitude and sign
B. P must be midway between the particles
C. q1 and q2 must have the same sign but may have different magnitudes
D. q1 and q2 must have equal magnitudes and opposite signs
E. q1 and q2 must have opposite signs and may have different magnitudes
ans: C
19. The diagrams below depict four different charge distributions. The charge particles are all the
same distance from the origin. The electric field at the origin:
• 5q
•
2q
•
−3q
• 5q
•
3q
1
A.
B.
C.
D.
E.
• 5q
•
3q
2
•
2q
•
−2q
• 5q
3
• 5q
•
2q
•
2q
• 5q
4
is greatest for situation 1
is greatest for situation 3
is zero for situation 4
is downward for situation 1
is downward for situation 3
ans: C
20. The diagram shows a particle with positive charge Q and a particle with negative charge −Q.
The electric field at point P on the perpendicular bisector of the line joining them is:
−Q •
×P
+Q •
A.
B.
C.
D.
E.
336
↑
↓
→
←
zero
ans: A
Chapter 22:
ELECTRIC FIELDS
21. The diagram shows two identical particles, each with positive charge Q. The electric field at
point P on the perpendicular bisector of the line joining them is:
+Q •
×P
+Q •
A.
B.
C.
D.
E.
↑
↓
→
←
zero
ans: C
22. Two point particles, one with charge +8 × 10−9 C and the other with charge −2 × 10−9 C, are
separated by 4 m. The electric field in N/C midway between them is:
A. 9 × 109
B. 13, 500
C. 135, 000
D. 36 × 10−9
E. 22.5
ans: E
23. Two charged point particles are located at two vertices of an equilateral triangle and the electric
field is zero at the third vertex. We conclude:
A. the two particles have charges with opposite signs and the same magnitude
B. the two particles have charges with opposite signs and different magnitudes
C. the two particles have identical charges
D. the two particles have charges with the same sign but different magnitudes
E. at least one other charged particle is present
ans: E
24. Two point particles, with the same charge, are located at two vertices of an equilateral triangle.
A third charged particle is placed so the electric field at the third vertex is zero. The third
particle must:
A. be on the perpendicular bisector of the line joining the first two charges
B. be on the line joining the first two charges
C. have the same charge as the first two particles
D. have charge of the same magnitude as the first two charges but its charge may have a
different sign
E. be at the center of the triangle
ans: A
Chapter 22:
ELECTRIC FIELDS
337
25. Positive charge Q is uniformly distributed on a semicircular rod. What is the direction of the
electric field at point P, the center of the semicircle?
Q
A.
B.
C.
D.
E.
...................
........................
.............
...........
.
.
..
... ...
.. ..
.. ..
... ...
.... ...
... ...
... ...
... ...
......
.......
... ...
.......
...........
................
......... ...........
.............
•P
↑
↓
←
→
ans: D
26. Positive charge +Q is uniformly distributed on the upper half a semicircular rod and negative
charge −Q is uniformly distributed on the lower half. What is the direction of the electric field
at point P, the center of the semicircle?
+Q ...........................................................
... ...
.......
... ...
......
.
.
.
... ..
.. ..
..........
... ..
... ...
......
.......
... ...
........
............
...... ........
........ .............
..............
•P
−Q
A.
B.
C.
D.
E.
↑
↓
←
→
ans: B
27. Positive charge +Q is uniformly distributed on the upper half a rod and negative charge −Q
is uniformly distributed on the lower half. What is the direction of the electric field at point
P, on the perpendicular bisector of the rod?
+Q
−Q
A.
B.
C.
D.
E.
↑
↓
←
→
ans: B
338
Chapter 22:
ELECTRIC FIELDS
•P
28. The electric field due to a uniform distribution of charge on a spherical shell is zero:
A. everywhere
B. nowhere
C. only at the center of the shell
D. only inside the shell
E. only outside the shell
ans: D
29. A charged particle is placed in an electric field that varies with location. No force is exerted
on this charge:
A. at locations where the electric field is zero
B. at locations where the electric field strength is 1/(1.6 × 10−19 ) N/C
C. if the particle is moving along a field line
D. if the particle is moving perpendicularly to a field line
E. if the field is caused by an equal amount of positive and negative charge
ans: A
30. The magnitude of the force of a 400-N/C electric field on a 0.02-C point charge is:
A. 8.0 N
B. 8 × 10−5 N
C. 8 × 10−3 N
D. 0.08 N
E. 2 × 1011 N
ans: A
31. A 200-N/C electric field is in the positive x direction. The force on an electron in this field is:
A. 200 N in the positive x direction
B. 200 N in the negative x direction
C. 3.2 × 10−17 N in the positive x direction
D. 3.2 × 10−17 N in the negative x direction
E. 0
ans: D
32. An electron traveling north enters a region where the electric field is uniform and points north.
The electron:
A. speeds up
B. slows down
C. veers east
D. veers west
E. continues with the same speed in the same direction
ans: B
Chapter 22:
ELECTRIC FIELDS
339
33. An electron traveling north enters a region where the electric field is uniform and points west.
The electron:
A. speeds up
B. slows down
C. veers east
D. veers west
E. continues with the same speed in the same direction
ans: C
34. Two charged particles are arranged as shown. In which region could a third particle, with
charge +1 C, be placed so that the net electrostatic force on it is zero?
I
.....................
....
...
..
..
...
...
..
..
...
....... .........
........
+
2C
A.
B.
C.
D.
E.
II
.....................
....
...
..
..
...
...
..
..
...
....... .........
........
−
III
−4 C
I only
I and II only
lII only
I and III only
II only
ans: A
35. An electric dipole consists of a particle with a charge of +6×10−6 C at the origin and a particle
with a charge of −6 × 10−6 C on the x axis at x = 3 × 10−3 m. Its dipole moment is:
A. 1.8 × 10−8 C · m, in the positive x direction
B. 1.8 × 10−8 C · m, in the negative x direction
C. 0 because the net charge is 0
D. 1.8 × 10−8 C · m, in the positive y direction
E. 1.8 × 10−8 C · m, in the negative y direction
ans: B
36. The force exerted by a uniform electric field on a dipole is:
A. parallel to the dipole moment
B. perpendicular to the dipole moment
C. parallel to the electric field
D. perpendicular to the electric field
E. none of the above
ans: E
37. An
A.
B.
C.
D.
E.
electric field exerts a torque on a dipole only if:
the field is parallel to the dipole moment
the field is not parallel to the dipole moment
the field is perpendicular to the dipole moment
the field is not perpendicular to the dipole moment
the field is uniform
ans: B
340
Chapter 22:
ELECTRIC FIELDS
38. The torque exerted by an electric field on a dipole is:
A. parallel to the field and perpendicular to the dipole moment
B. parallel to both the field and dipole moment
C. perpendicular to both the field and dipole moment
D. parallel to the dipole moment and perpendicular to the field
E. not related to the directions of the field and dipole moment
ans: C
39. The diagrams show four possible orientations of an electric dipole in a uniform electric field E.
Rank them according to the magnitude of the torque exerted on the dipole by the field, least
to greatest.
p
.........................................................E
.
........................................
...
..
...
...
..
...
...................
.
......
A.
B.
C.
D.
E.
1
1, 2, 3, 4
4, 3, 2, 1
1, 2, 4, 3
3, 2 and 4 tie, then 1
1, 2 and 4 tie, then 3
ans: E
p
................................................E
.
...............................................
..
..
..
..
...
...................
......
...
2
p
E
..
...
.
..............................................
.....
.........................................................................
3
p
.........
.....
4
E
.......
.............................................................................................................
......
40. A uniform electric field of 300 N/C makes an angle of 25◦ with the dipole moment of an electric
dipole. If the torque exerted by the field has a magnitude of 2.5×10−7 N·m, the dipole moment
must be:
A. 8.3 × 10−10 C · m
B. 9.2 × 10−10 C · m
C. 2.0 × 10−9 C · m
D. 8.3 × 10−5 C · m
E. 1.8 × 10−4 C · m
ans: C
41. When the dipole moment of a dipole in a uniform electric field rotates to become more nearly
aligned with the field:
A. the field does positive work and the potential energy increases
B. the field does positive work and the potential energy decreases
C. the field does negative work and the potential energy increases
D. the field does negative work and the potential energy decreases
E. the field does no work
ans: B
Chapter 22:
ELECTRIC FIELDS
341
42. The dipole moment of a dipole in a 300-N/C electric field is initially perpendicular to the field,
but it rotates so it is in the same direction as the field. If the moment has a magnitude of
2 × 10−9 C · m, the work done by the field is:
A. −12 × 10−7 J
B. −6 × 10−7 J
C. 0
D. 6 × 10−7 J
E. 12 × 10−7 J
ans: D
43. An electric dipole is oriented parallel to a uniform electric field, as shown.
p
..................
E
.......
............................................................................................................
......
It is rotated to one of the five orientations shown below. Rank the final orientations according
to the change in the potential energy of the dipole-field system, most negative to most positive.
p
................................................E
.
.
...............................................
..
...
....
..................
.
......
...
A.
B.
C.
D.
E.
1
1, 2, 3, 4
4, 3, 2, 1
1, 2, 4, 3
3, 2 and 4 tie, then 1
1, 2 and 4 tie, then 3
ans: A
p
E
..
...
.
..............................................
.....
........................................................................
2
p
.........
.....
3
E
.......
............................................................................................................
......
p
................
E
.......
............................................................................................................
......
4
44. The purpose of Milliken’s oil drop experiment was to determine:
A. the mass of an electron
B. the charge of an electron
C. the ratio of charge to mass for an electron
D. the sign of the charge on an electron
E. viscosity
ans: B
45. A charged oil drop with a mass of 2 × 10−4 kg is held suspended by a downward electric field
of 300 N/C. The charge on the drop is:
A. +1.5 × 10−6 C
B. −1.5 × 10−6 C
C. +6.5 × 10−6 C
D. −6.5 × 10−6 C
E. 0
ans: D
342
Chapter 22:
ELECTRIC FIELDS
Chapter 23:
GAUSS’ LAW
1. A total charge of 6.3 × 10−8 C is distributed uniformly throughout a 2.7-cm radius sphere. The
volume charge density is:
A. 3.7 × 10−7 C/m3
3
B. 6.9 × 10−6 C/m
2
C. 6.9 × 10−6 C/m
3
D. 2.5 × 10−4 C/m
E. 7.6 × 10−4 C/m3
ans: E
2. Charge is placed on the surface of a 2.7-cm radius isolated conducting sphere. The surface
2
charge density is uniform and has the value 6.9 × 10−6 C/m . The total charge on the sphere
is:
A. 5.6 × 10−10 C
B. 2.1 × 10−8 C
C. 4.7 × 10−8 C
D. 6.3 × 10−8 C
E. 9.5 × 10−3 C
ans: D
3. A spherical shell has an inner radius of 3.7 cm and an outer radius of 4.5 cm. If charge is
distributed uniformly throughout the shell with a volume density of 6.1 × 10−4 C/m3 the total
charge is:
A. 1.0 × 10−7 C
B. 1.3 × 10−7 C
C. 2.0 × 10−7 C
D. 2.3 × 10−7 C
E. 4.0 × 10−7 C
ans: A
4. A cylinder has a radius of 2.1 cm and a length of 8.8 cm. Total charge 6.1×10−7 C is distributed
uniformly throughout. The volume charge density is:
3
A. 5.3 × 10−5 C/m
2
B. 5.3 × 10−5 C/m
3
C. 8.5 × 10−4 C/m
D. 5.0 × 10−3 C/m3
3
E. 6.3 × 10−2 C/m
ans: D
Chapter 23:
GAUSS’ LAW
343
5. When a piece of paper is held with one face perpendicular to a uniform electric field the flux
through it is 25 N · m2 /C. When the paper is turned 25◦ with respect to the field the flux
through it is:
A. 0
B. 12 N · m2 /C
C. 21 N · m2 /C
D. 23 N · m2 /C
E. 25 N · m2 /C
ans: D
6. The flux of the electric field (24 N/C) î + (30 N/C) ĵ + (16 N/C) k̂ through a 2.0 m2 portion of
the yz plane is:
A. 32 N · m2 /C
B. 34 N · m2 /C
C. 42 N · m2 /C
D. 48 N · m2 /C
E. 60 N · m2 /C
ans: D
7. Consider Gauss’s law: E · dA = q/ 0 . Which of the following is true?
A.
B.
C.
D.
E.
E must be the electric field due to the enclosed charge
If q = 0, then E = 0 everywhere on the Gaussian surface
If the three particles inside have charges of +q, +q, and −2q, then the integral is zero
on the surface E is everywhere parallel to dA
If a charge is placed outside the surface, then it cannot affect E at any point on the surface
ans: C
8. A charged point particle is placed at the center of a spherical Gaussian surface. The electric
flux ΦE is changed if:
A. the sphere is replaced by a cube of the same volume
B. the sphere is replaced by a cube of one-tenth the volume
C. the point charge is moved off center (but still inside the original sphere)
D. the point charge is moved to just outside the sphere
E. a second point charge is placed just outside the sphere
ans: D
9. Choose the INCORRECT statement:
A. Gauss’ law can be derived from Coulomb’s law
B. Gauss’ law states that the net number of lines crossing any closed surface in an outward
direction is proportional to the net charge enclosed within the surface
C. Coulomb’s law can be derived from Gauss’ law and symmetry
D. Gauss’ law applies to a closed surface of any shape
E. According to Gauss’ law, if a closed surface encloses no charge, then the electric field must
vanish everywhere on the surface
ans: E
344
Chapter 23:
GAUSS’ LAW
10. The outer surface of the cardboard center of a paper towel roll:
A. is a possible Gaussian surface
B. cannot be a Gaussian surface because it encloses no charge
C. cannot be a Gaussian surface since it is an insulator
D. cannot be a Gaussian surface because it is not a closed surface
E. none of the above
ans: D
11. A physics instructor in an anteroom charges an electrostatic generator to 25 µC, then carries
it into the lecture hall. The net electric flux in N · m2 /C through the lecture hall walls is:
A. 0
B. 25 × 10−6
C. 2.2 × 105
D. 2.8 × 106
E. can not tell unless the lecture hall dimensions are given
ans: D
12. A point particle with charge q is placed inside the cube but not at its center. The electric flux
through any one side of the cube:
A. is zero
B. is q/ 0
C. is q/4 0
D. is q/6 0
E. cannot be computed using Gauss’ law
ans: E
13. A particle with charge 5.0-µC is placed at the corner of a cube. The total electric flux in
N · m2 /C through all sides of the cube is:
A. 0
B. 7.1 × 104
C. 9.4 × 104
D. 1.4 × 105
E. 5.6 × 105
ans: E
14. A point particle with charge q is at the center of a Gaussian surface in the form of a cube. The
electric flux through any one face of the cube is:
A. q/ 0
B. q/4π 0
C. q/3 0
D. q/6 0
E. q/12 0
ans: D
Chapter 23:
GAUSS’ LAW
345
15. The table below gives the electric flux in N · m2 /C through the ends and round surfaces of four
Gaussian surfaces in the form of cylinders. Rank the cylinders according to the charge inside,
from the most negative to the most positive.
cylinder
cylinder
cylinder
cylinder
A.
B.
C.
D.
E.
1, 2, 3,
4, 3, 2,
3, 4, 2,
3, 1, 4,
4, 3, 1,
ans: E
1:
2:
3:
4:
left end
+2 × 10−9
+3 × 10−9
−2 × 10−9
+2 × 10−9
right end
+4 × 10−9
−2 × 10−9
−5 × 10−9
−5 × 10−9
rounded surface
−6 × 10−9
+6 × 10−9
+3 × 10−9
−3 × 10−9
4
1
1
2
2
16. A conducting sphere of radius 0.01 m has a charge of 1.0 × 10−9 C deposited on it. The
magnitude of the electric field in N/C just outside the surface of the sphere is:
A. 0
B. 450
C. 900
D. 4500
E. 90, 000
ans: C
17. A round wastepaper basket with a 0.15-m radius opening is in a uniform electric field of
300 N/C, perpendicular to the opening. The total flux through the sides and bottom, in
N · m2 C, is:
A. 0
B. 4.2
C. 21
D. 280
E. can not tell without knowing the areas of the sides and bottom
ans: C
18. 10 C of charge are placed on a spherical conducting shell. A particle with a charge of −3 C is
placed at the center of the cavity. The net charge on the inner surface of the shell is:
A. −7 C
B. −3 C
C. 0 C
D. +3 C
E. +7 C
ans: D
346
Chapter 23:
GAUSS’ LAW
19. 10 C of charge are placed on a spherical conducting shell. A particle with a charge of −3 C is
placed at the center of the cavity. The net charge on the outer surface of the shell is:
A. −7 C
B. −3 C
C. 0 C
D. +3 C
E. +7 C
ans: E
20. A 30-N/C uniform electric field points perpendicularly toward the left face of a large neutral
2
conducting sheet. The surface charge density in C/m on the left and right faces, respectively,
are:
A. −2.7 × 10−9 C/m2 ; +2.7 × 10−9 C/m2
2
2
B. +2.7 × 10−9 C/m ; −2.7 × 10−9 C/m
2
2
C. −5.3 × 10−9 C/m ; +5.3 × 10−9 C/m
2
2
D. +5.3 × 10−9 C/m ; −5.3 × 10−9 C/m
E. 0; 0
ans: A
21. A solid insulating sphere of radius R contains positive charge that is distributed with a volume
charge density that does not depend on angle but does increase with distance from the sphere
center. Which of the graphs below might give the magnitude E of the electric field as a function
of the distance r from the center of the sphere?
E ...
......
......
......
...
...
...
.......................... r
R
A
E
E .........................
...
...
....
.....
......
E
r
R
B
.
......
... .....
....
.
.......
..
..
.
.
.
.
......
r
R
D
E
....
... .....
.
.. .....
..
......
.
.
.
...
..
.
.
..
r
R
C
....
.....
.. ....
.. ......
.. ......
..
.........................
r
R
E
ans: D
Chapter 23:
GAUSS’ LAW
347
22. Which of the following graphs represents the magnitude of the electric field as a function of
the distance from the center of a solid charged conducting sphere of radius R?
E ...
......
......
......
...
...
...
.......................... r
R
A
E
E .........................
...
...
....
.....
......
E
r
......
... .....
.
.
....
...
.....
..
.....
.
.
.
.
...
r
R
B
.....
... ......
. ......
........
..
.
.
.
.
.
.....
R
D
R
C
E
r
....
....
.. ....
.. ......
.. .......
.
.........................
r
R
E
ans: E
23. Charge Q is distributed uniformly throughout an insulating sphere of radius R. The magnitude
of the electric field at a point R/2 from the center is:
A. Q/4π 0 R2
B. Q/π 0 R2
C. 3Q/4π 0 R2
D. Q/8π 0 R2
E. none of these
ans: D
24. Positive charge Q is distributed uniformly throughout an insulating sphere of radius R, centered
at the origin. A particle with positive charge Q is placed at x = 2R on the x axis. The
magnitude of the electric field at x = R/2 on the x axis is:
A. Q/4π 0 R2
B. Q/8π 0 R2
C. Q/72π 0 R2
D. 17Q/72π 0 R2
E. none of these
ans: C
25. Charge Q is distributed uniformly throughout a spherical insulating shell. The net electric flux
in N · m2 /C through the inner surface of the shell is:
A. 0
B. Q/ 0
C. 2Q/ 0
D. Q/4π 0
E. Q/2π 0
ans: A
348
Chapter 23:
GAUSS’ LAW
26. Charge Q is distributed uniformly throughout a spherical insulating shell. The net electric flux
in N · m2 /C through the outer surface of the shell is:
A. 0
B. Q/ 0
C. 2Q/ 0
D. Q/4 0
E. Q/2π 0
ans: B
27. A 3.5-cm radius hemisphere contains a total charge of 6.6 × 10−7 C. The flux through the
rounded portion of the surface is 9.8 × 104 N · m2 /C. The flux through the flat base is:
A. 0
B. +2.3 × 104 N · m2 /C
C. −2.3 × 104 N · m2 /C
D. −9.8 × 104 N · m2 /C
E. +9.8 × 104 N · m2 /C
ans: C
28. Charge is distributed uniformly along a long straight wire. The electric field 2 cm from the
wire is 20 N/C. The electric field 4 cm from the wire is:
A. 120 N/C
B. 80 N/C
C. 40 N/C
D. 10 N/C
E. 5 N/C
ans: D
29. Positive charge Q is placed on a conducting spherical shell with inner radius R1 and outer
radius R2 . A particle with charge q is placed at the center of the cavity. The magnitude of the
electric field at a point in the cavity, a distance r from the center, is:
A. zero
B. Q/4π 0 R12
C. q/4π 0 r 2
D. (q + Q)/4π 0 r 2
E. (q + Q)/4π 0 (R12 − r 2 )
ans: C
30. Positive charge Q is placed on a conducting spherical shell with inner radius R1 and outer
radius R2 . A point charge q is placed at the center of the cavity. The magnitude of the electric
field at a point outside the shell, a distance r from the center, is:
A. zero
B. Q/4π 0 r 2
C. q/4π 0 r 2
D. (q + Q)/4π 0 r 2
E. (q + Q)/4π 0 (R12 − r 2 )
ans: D
Chapter 23:
GAUSS’ LAW
349
31. Positive charge Q is placed on a conducting spherical shell with inner radius R1 and outer
radius R2 . A point charge q is placed at the center of the cavity. The magnitude of the electric
field produced by the charge on the inner surface at a point in the interior of the conductor, a
distance r from the center, is:
A. 0
B. Q/4vπ 0 R12
C. Q/4π 0 R22
D. q/4π 0 r 2
E. Q/4π 0 r 2
ans: D
32. A long line of charge with λf charge per unit length runs along the cylindrical axis of a cylindrical shell which carries a charge per unit length of λc . The charge per unit length on the
inner and outer surfaces of the shell, respectively are:
A. λf and λc
B. −λf and λc + λf
C. −λf and λc − λc
D. λf + λc and λc − λf
E. λf − λc and λc + λf
ans: B
33. Charge is distributed uniformly on the surface of a large flat plate. The electric field 2 cm from
the plate is 30 N/C. The electric field 4 cm from the plate is:
A. 120 N/C
B. 80 N/C
C. 30 N/C
D. 15 N/C
E. 7.5 N/C
ans: C
34. Two large insulating parallel plates carry charge of equal magnitude, one positive and the other
negative, that is distributed uniformly over their inner surfaces. Rank the points 1 through 5
according to the magnitude of the electric field at the points, least to greatest.
•
1
A.
B.
C.
D.
E.
350
1, 2, 3, 4, 5
2, then 1, 3, and 4 tied, then 5
1, 4, and 5 tie, then 2 and 3 tie
2 and 3 tie, then 1 and 4 tie, then 5
2 and 3 tie, then 1, 4, and 5 tie
ans: C
Chapter 23:
GAUSS’ LAW
+
+
+
+ ••
+ 23
+
+
−
−
−
−
−
−
−
• •
4 5
35. Two large parallel plates carry positive charge of equal magnitude that is distributed uniformly
over their inner surfaces. Rank the points 1 through 5 according to the magnitude of the electric
field at the points, least to greatest.
•
1
A.
B.
C.
D.
E.
+
+
+
+ ••
+ 23
+
+
+
+
+
+
+
+
+
• •
4 5
1, 2, 3, 4, 5
5, 4, 3, 2, 1
1, 4, and 5 tie, then 2 and 3 tie
2 and 3 tie, then 1 and 4 tie, then 5
2 and 3 tie, then 1, 4, and 5 tie
ans: E
36. A particle with charge Q is placed outside a large neutral conducting sheet. At any point in
the interior of the sheet the electric field produced by charges on the surface is directed:
A. toward the surface
B. away from the surface
C. toward Q
D. away from Q
E. none of the above
ans: C
37. A hollow conductor is positively charged. A small uncharged metal ball is lowered by a silk
thread through a small opening in the top of the conductor and allowed to touch its inner
surface. After the ball is removed, it will have:
A. a positive charge
B. a negative charge
C. no appreciable charge
D. a charge whose sign depends on what part of the inner surface it touched
E. a charge whose sign depends on where the small hole is located in the conductor
ans: C
38. A spherical conducting shell has charge Q. A particle with charge q is placed at the center of
the cavity. The charge on the inner surface of the shell and the charge on the outer surface of
the shell, respectively, are:
A. 0, Q
B. q, Q − q
C. Q, 0
D. −q, Q + q
E. −q, 0
ans: D
Chapter 23:
GAUSS’ LAW
351
Chapter 24:
ELECTRIC POTENTIAL
1. An electron moves from point i to point f , in the direction of a uniform electric field. During
this displacement:
E
.....
.................................................................................................................................................. .................
....
•
i
•
f
A. the work done by the field is positive and the potential energy of the electron-field
increases
B. the work done by the field is negative and the potential energy of the electron-field
increases
C. the work done by the field is positive and the potential energy of the electron-field
decreases
D. the work done by the field is negative and the potential energy of the electron-field
decreases
E. the work done by the field is positive and the potential energy of the electron-field
does not change
ans: B
system
system
system
system
system
2. A particle with a charge of 5.5 × 10−8 C is 3.5 cm from a particle with a charge of −2.3 × 10−8 C.
The potential energy of this two-particle system, relative to the potential energy at infinite
separation, is:
A. 3.2 × 10−4 J
B. −3.2 × 10−4 J
C. 9.3 × 10−3 J
D. −9.3 × 10−3 J
E. zero
ans: B
3. A particle with a charge of 5.5 × 10−8 C is fixed at the origin. A particle with a charge of
−2.3 × 10−8 C is moved from x = 3.5 cm on the x axis to y = 4.3 cm on the y axis. The change
in potential energy of the two-particle system is:
A. 3.1 × 10−3 J
B. −3.1 × 10−3 J
C. 6.0 × 10−5 J
D. −6.0 × 10−5 J
E. 0
ans: C
352
Chapter 24:
ELECTRIC POTENTIAL
4. A particle with a charge of 5.5 × 10−8 C charge is fixed at the origin. A particle with a charge
of −2.3 × 10−8 C charge is moved from x = 3.5 cm on the x axis to y = 3.5 cm on the y axis.
The change in the potential energy of the two-particle system is:
A. 3.2 × 10−4 J
B. −3.2 × 10−4 J
C. 9.3 × 10−3 J
D. −9.3 × 10−3 J
E. 0
ans: E
5. Three particles lie on the x axis: particle 1, with a charge of 1 × 10−8 C is at x = 1 cm, particle
2, with a charge of 2 × 10−8 C, is at x = 2 cm, and particle 3, with a charge of −3 × 10−8 C,
is at x = 3 cm. The potential energy of this arrangement, relative to the potential energy for
infinite separation, is:
A. +4.9 × 10−4 J
B. −4.9 × 10−4 J
C. +8.5 × 10−4 J
D. −8.5 × 10−4 J
E. zero
ans: B
6. Two identical particles, each with charge q, are placed on the x axis, one at the origin and the
other at x = 5 cm. A third particle, with charge −q, is placed on the x axis so the potential
energy of the three-particle system is the same as the potential energy at infinite separation.
Its x coordinate is:
A. 13 cm
B. 2.5 cm
C. 7.5 cm
D. 10 cm
E. −5 cm
ans: A
7. Choose the correct statement:
A. A proton tends to go from a region of low potential to a region of high potential
B. The potential of a negatively charged conductor must be negative
C. If E = 0 at a point P then V must be zero at P
D. If V = 0 at a point P then E must be zero at P
E. None of the above are correct
ans: E
8. If 500 J of work are required to carry a charged particle between two points with a potential
difference of 20 V, the magnitude of the charge on the particle is:
A. 0.040 C
B. 12.5 C
C. 20 C
D. cannot be computed unless the path is given
E. none of these
ans: B
Chapter 24:
ELECTRIC POTENTIAL
353
9. The potential difference between two points is 100 V. If a particle with a charge of 2 C is
transported from one of these points to the other, the magnitude of the work done is:
A. 200 J
B. 100 J
C. 50 J
D. 100 J
E. 2 J
ans: A
10. During a lightning discharge, 30 C of charge move through a potential difference of 1.0 × 108 V
in 2.0 × 10−2 s. The energy released by this lightning bolt is:
A. 1.5 × 1011 J
B. 3.0 × 109 J
C. 6.0 × 107 J
D. 3.3 × 106 J
E. 1500 J
ans: B
11. Points R and T are each a distance d from each of two particles with charges of equal magnitudes
and opposite signs as shown. If k = 1/4π 0 , the work required to move a particle with a negative
charge q from R to T is:
R
•
................ ................
... . . ......
...
....
.
.
....
.
....
....
...
....
....
...
...
.
....
.
..
...
.
.
.
....
..
.
.
.... .
.
..
.
.
.
.
.
........
................ ....
.
.
.
.
.
.
.
.
.
.
.
.. ..
.. ..
.... .....
..... ....
....
.
... ....
...... ........
...............
.
.
.
...........
............ ...
..
. ....
...
...
.
.
..
....
....
....
....
....
....
....
....
....
.
.
....
...
....
...
... . . ......
.
.
................ .............
.
d
d
− −Q
Q +
d
d
•
T
A.
B.
C.
D.
E.
354
0
kqQ/d2
kqQ/d√
kqQ/( 2d)
kQq/(2d)
ans: A
Chapter 24:
ELECTRIC POTENTIAL
12. Points R and T are each a distance d from each of two particles with equal positive charges as
shown. If k = 1/4π 0 , the work required to move a particle with charge q from R to T is:
R
•
.
............. ..............
..... .......
....
....
.
.
....
.
...
....
....
....
...
...
....
.
....
.
...
....
.
.
...
..
.
.
.
.... .
.......
.
.
.
................ ......
.
.
.
.
.
.
.
.
.
.
.
.
.
... ...
..... ......
..... .....
....
.
...
.
..... .....
.................
............
............. .......
.
.
. ....
... .
.
.
...
.
..
....
....
....
....
....
...
....
....
.
....
.
.
..
....
....
....
....
... .
..
. ....
............... ..............
d
d
Q +
+ Q
d
d
•
T
A.
B.
C.
D.
E.
0
kQq/d2
kQq/d√
kQq/( 2d)
kQq/(2d)
ans: A
13. Two particle with charges Q and −Q are fixed at the vertices of an equilateral triangle with
sides of length a. If k = 1/4π 0 , the work required to move a particle with charge q from the
other vertex to the center of the line joining the fixed particles is:
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
• q
•
•
•
•
•
•
•
•
..•
.•
•
•
•
•
•
.•
•
•
•
•
...
.•
.•
... ....
...
..
.
...
..
.
...
...
...
..
...
.
..
...
.
...
..
.
...
..
.
...
..
.
...
..
...
.
.
.
...
.
...
...
.
...
..
.
...
..
.
...
..
...
.
.
.......
.
.
................
.
..... .......
.
......................................................................... ....
.
....
...
...
.... .....
.
.............
........
a
Q
A.
B.
C.
D.
E.
a
a
−Q
0
kQq/a
kQq/a2
2kQq/a
√
2kQq/a
ans: A
Chapter 24:
ELECTRIC POTENTIAL
355
14. A particle with mass m and charge −q is projected with speed v0 into the region between
two parallel plates as shown. The potential difference between the two plates is V and their
separation is d. The change in kinetic energy of the particle as it traverses this region is:
0
V
m, −q
•
•
•
•
•
•
•
•••••••••••••••••• ............................................
•
•
•
•
v0
←
− d −
→
A.
B.
C.
D.
E.
−qV /d
2qV /mv02
qV
mv02 /2
none of these
ans: C
15. An electron is accelerated from rest through a potential difference V . Its final speed is proportional to:
A. V
B. √
V2
C.
V
D. 1/V
√
E. 1/ V
ans: C
16. In separate experiments, four different particles each start from far away with the same speed
and impinge directly on a gold nucleus. The masses and charges of the particles are
particle 1: mass m0 , charge q0
particle 2: mass 2m0 , charge 2q0
particle 3: mass 2m0 , charge q0 /2
particle 4: mass m0 /2, charge 2q0
Rank the particles according to the distance of closest approach to the gold nucleus, from
smallest to largest.
A. 1, 2, 3, 4
B. 4, 3, 2, 1
C. 3, 1 and 2 tie, then 4
D. 4, 1 and 2 tie, then 1
E. 1 and 2 tie, then 3, 4
ans: C
356
Chapter 24:
ELECTRIC POTENTIAL
17. Two large parallel conducting plates are separated by a distance d, placed in a vacuum, and
connected to a source of potential difference V . An oxygen ion, with charge 2e, starts from
rest on the surface of one plate and accelerates to the other. If e denotes the magnitude of the
electron charge, the final kinetic energy of this ion is:
A. eV /2
B. eV /d
C. eV d
D. V d/e
E. 2eV
ans: E
18. An
A.
B.
C.
D.
E.
electron volt is :
the force acting on an electron in a field of 1 N/C
the force required to move an electron 1 meter
the energy gained by an electron in moving through a potential difference of 1 volt
the energy needed to move an electron through 1 meter in any electric field
the work done when 1 coulomb of charge is moved through a potential difference of 1 volt.
ans: C
19. An electron has charge −e and mass me . A proton has charge e and mass 1840me . A “proton
volt” is equal to:
A. 1 eV
B. 1840 eV
C. (1/1840)
eV
√
1840
eV
D.
√
E. (1/ 1840) eV
ans: A
20. Two conducting spheres, one having twice the diameter of the other, are separated by a distance
large compared to their diameters. The smaller sphere (1) has charge q and the larger sphere
(2) is uncharged. If the spheres are then connected by a long thin wire:
d
....
....
......... ............
...
.......... .....
...
.... ....
..
... ...
..
.. ...
...
........ ...
.
.
.
......
......
....................
1
q
A.
B.
C.
D.
E.
...................................
.....
.......
.....
.........
.....
....
...
...
....
...
...
...
.
.
...
.
...
... ...
...
.. ....
...
.
...
.... ....
...
...
..
...
...
..
...
...
...
.
....
.
.
..
.
......
.
.
.
.
..........
........
...
.
.
.
.
.
.
.
.
.....................
..
2
2d
1 and 2 have the same potential
2 has twice the potential of 1
2 has half the potential of 1
1 and 2 have the same charge
all of the charge is dissipated
ans: A
Chapter 24:
ELECTRIC POTENTIAL
357
21. Two conducting spheres are far apart. The smaller sphere carries a total charge Q. The larger
sphere has a radius that is twice that of the smaller and is neutral. After the two spheres are
connected by a conducting wire, the charges on the smaller and larger spheres, respectively,
are:
A. Q/2 and Q/2
B. Q/3 and 2Q/3
C. 2Q/3 and Q/3
D. zero and Q
E. 2Q and −Q
ans: B
22. Three possible configurations for an electron e and a proton p are shown below. Take the zero
of potential to be at infinity and rank the three configurations according to the potential at S,
from most negative to most positive.
←
− d −
→←−−− D −−−→
•
•
×
e
p
S
1
←−−− D −−−→
←
− d −
→
•
•
×
e
p
S
2
←
− d−
→
•
↑ ×S
p
|
|
D
|
|
↓ •e
3
A.
B.
C.
D.
E.
1, 2, 3
3, 2, 1
2, 3, 1
1 and 2 tie, then 3
1 and 3 tie, then 2
ans: D
23. A conducting sphere with radius R is charged until the magnitude of the electric field just
outside its surface is E. The electric potential of the sphere, relative to the potential far away,
is:
A. zero
B. E/R
C. E/R2
D. ER
E. ER2
ans: D
358
Chapter 24:
ELECTRIC POTENTIAL
2
24. A 5-cm radius conducting sphere has a surface charge density of 2 × 10−6 C/m on its surface.
Its electric potential, relative to the potential far away, is:
A. 1.1 × 104 V
B. 2.2 × 104 V
C. 2.3 × 105 V
D. 3.6 × 105 V
E. 7.2 × 106 V
ans: A
25. A hollow metal sphere is charged to a potential V . The potential at its center is:
A. V
B. 0
C. −V
D. 2V
E. πV
ans: A
26. Positive charge is distributed uniformly throughout a non-conducting sphere. The highest
electric potential occurs:
A. at the center
B. at the surface
C. halfway between the center and surface
D. just outside the surface
E. far from the sphere
ans: A
27. A total charge of 7 × 10−8 C is uniformly distributed throughout a non-conducting sphere with
a radius of 5 cm. The electric potential at the surface, relative to the potential far away, is
about:
A. −1.3 × 104 V
B. 1.3 × 104 V
C. 7.0 × 105 V
D. −6.3 × 104 V
E. 0
ans: B
28. Eight identical spherical raindrops are each at a potential V , relative to the potential far away.
They coalesce to make one spherical raindrop whose potential is:
A. V /8
B. V /2
C. 2V
D. 4V
E. 8V
ans: D
Chapter 24:
ELECTRIC POTENTIAL
359
29. A metal sphere carries a charge of 5 × 10−9 C and is at a potential of 400 V, relative to the
potential far away. The potential at the center of the sphere is:
A. 400 V
B. −400 V
C. 2 × 10−6 V
D. 0
E. none of these
ans: A
30. A 5-cm radius isolated conducting sphere is charged so its potential is +100 V, relative to the
potential far away. The charge density on its surface is:
2
A. +2.2 × 10−7 C/m
B. −2.2 × 10−7 C/m2
2
C. +3.5 × 10−7 C/m
2
D. −3.5 × 10−7 C/m
2
E. +1.8 × 10−8 C/m
ans: E
31. A conducting sphere has charge Q and its electric potential is V , relative to the potential far
away. If the charge is doubled to 2Q, the potential is:
A. V
B. 2V
C. 4V
D. V /2
E. V /4
ans: B
32. The potential difference between the ends of a 2-meter stick that is parallel to a uniform electric
field is 400 V. The magnitude of the electric field is:
A. zero
B. 100 V/m
C. 200 V/m
D. 400 V/m
E. 800 V/m
ans: E
33. In a certain region of space the electric potential increases uniformly from east to west and
does not vary in any other direction. The electric field:
A. points east and varies with position
B. points east and does not vary with position
C. points west and varies with position
D. points west and does not vary with position
E. points north and does not vary with position
ans: B
360
Chapter 24:
ELECTRIC POTENTIAL
34. If the electric field is in the positive x direction and has a magnitude given by E = Cx2 , where
C is a constant, then the electric potential is given by V =:
A. 2Cx
B. −2Cx
C. Cx3 /3
D. −Cx3 /3
E. −3Cx3
ans: D
35. An electron goes from one equipotential surface to another along one of the four paths shown
below. Rank the paths according to the work done by the electric field, from least to greatest.
1
.............................................................................
2
............................
3
........................................................................
.
............................
4
......................
..... ...
.............................................
90 V 80 V 70 V 60 V 50 V
A.
B.
C.
D.
E.
1, 2, 3, 4
4, 3, 2, 1
1, 3, 4 and 2 tie
4 and 2 tie, then 3, then 1
4, 3, 1, 2
ans: D
36. The work required to carry a particle with a charge of 6.0 C from a 5.0-V equipotential surface
to a 6.0-V equipotential surface and back again to the 5.0-V surface is:
A. 0
B. 1.2 × 10−5 J
C. 3.0 × 10−5 J
D. 6.0 × 10−5 J
E. 6.0 × 10−6 J
ans: A
37. The equipotential surfaces associated with a charged point particles are:
A. radially outward from the particle
B. vertical planes
C. horizontal planes
D. concentric spheres centered at the particle
E. concentric cylinders with the particle on the axis.
ans: D
Chapter 24:
ELECTRIC POTENTIAL
361
38. The electric field in a region around the origin is given by E = C(x î + y ĵ), where C is a
constant. The equipotential surfaces in that region are:
A. concentric cylinders with axes along the z axis
B. concentric cylinders with axes along the x axis
C. concentric spheres centered at the origin
D. planes parallel to the xy plane
E. planes parallel to the yz plane
ans: A
39. The electric potential in a certain region of space is given by V = −7.5x2 + 3x, where V is in
volts and x is in meters. In this region the equipotential surfaces are:
A. planes parallel to the x axis
B. planes parallel to the yz plane
C. concentric spheres centered at the origin
D. concentric cylinders with the x axis as the cylinder axis
E. unknown unless the charge is given
ans: B
40. In the diagram, the points 1, 2, and 3 are all the same very large distance from a dipole. Rank
the points according to the values of the electric potential at them, from the most negative to
the most positive.
2•
.
p ......
1•
A.
B.
C.
D.
E.
362
1, 2, 3
3, 2, 1
2, 3, 1
1, 3, 2
1 and 2 tie, then 3
ans: D
Chapter 24:
ELECTRIC POTENTIAL
•3
41. A particle with charge q is to be brought from far away to a point near an electric dipole. No
work is done if the final position of the particle is on:
A. the line through the charges of the dipole
B. a line that is perpendicular to the dipole moment
C. a line that makes an angle of 45◦ with the dipole moment
D. a line that makes an angle of 30◦ with the dipole moment
E. none of the above
ans: B
42. Equipotential surfaces associated with an electric dipole are:
A. spheres centered on the dipole
B. cylinders with axes along the dipole moment
C. planes perpendicular to the dipole moment
D. planes parallel to the dipole moment
E. none of the above
ans: E
43. The diagram shows four pairs of large parallel conducting plates. The value of the electric
potential is given for each plate. Rank the pairs according to the magnitude of the electric field
between the plates, least to greatest.
−20 V
+70 V
1
A.
B.
C.
D.
E.
1, 2, 3,
4, 3, 2,
2, 3, 1,
2, 4, 1,
3, 2, 4,
ans: D
+20 V
+70 V
−10 V
2
+90 V
3
+30 V
+90 V
4
4
1
4
3
1
Chapter 24:
ELECTRIC POTENTIAL
363
Chapter 25:
CAPACITANCE
1. The units of capacitance are equivalent to:
A. J/C
B. V/C
C. J2 /C
D. C/J
E. C2 /J
ans: E
2. A farad is the same as a:
A. J/V
B. V/J
C. C/V
D. V/C
E. N/C
ans: C
3. A capacitor C “has a charge Q”. The actual charges on its plates are:
A. Q, Q
B. Q/2, Q/2
C. Q, −Q
D. Q/2, −Q/2
E. Q, 0
ans: C
4. Each plate of a capacitor stores a charge of magnitude 1 mC when a 100-V potential difference
is applied. The capacitance is:
A. 5 µF
B. 10 µF
C. 50 µF
D. 100 µF
E. none of these
ans: B
5. To
A.
B.
C.
D.
E.
364
charge a 1-F capacitor with 2 C requires a potential difference of:
2V
0.2 V
5V
0.5 V
none of these
ans: A
Chapter 25:
CAPACITANCE
6. The capacitance of a parallel-plate capacitor with plate area A and plate separation d is given
by:
A. 60 d/A
B. 60 d/2A
C. 60 A/d
D. 60 A/2d
E. Ad/60
ans: C
7. The capacitance of a parallel-plate capacitor is:
A. proportional to the plate area
B. proportional to the charge stored
C. independent of any material inserted between the plates
D. proportional to the potential difference of the plates
E. proportional to the plate separation
ans: A
8. The plate areas and plate separations of five parallel plate capacitors are
capacitor 1: area A0 , separation d0
capacitor 2: area 2A0 , separation 2d0
capacitor 3: area 2A0 , separation d0 /2
capacitor 4: area A0 /2, separation 2d0
capacitor 5: area A0 , separation d0 /2
Rank these according to their capacitances, least to greatest.
A. 1, 2, 3, 4, 5
B. 5, 4, 3, 2, 1
C. 5, 3 and 4 tie, then 1, 2
D. 4, 1 and 2 tie, then 5, 3
E. 3, 5, 1 and 2 tie, 1, 4
ans: D
9. The capacitance of a parallel-plate capacitor can be increased by:
A. increasing the charge
B. decreasing the charge
C. increasing the plate separation
D. decreasing the plate separation
E. decreasing the plate area
ans: D
10. If both the plate area and the plate separation of a parallel-plate capacitor are doubled, the
capacitance is:
A. doubled
B. halved
C. unchanged
D. tripled
E. quadrupled
ans: C
Chapter 25:
CAPACITANCE
365
11. If the plate area of an isolated charged parallel-plate capacitor is doubled:
A. the electric field is doubled
B. the potential difference is halved
C. the charge on each plate is halved
D. the surface charge density on each plate is doubled
E. none of the above
ans: B
12. If the plate separation of an isolated charged parallel-plate capacitor is doubled:
A. the electric field is doubled
B. the potential difference is halved
C. the charge on each plate is halved
D. the surface charge density on each plate is doubled
E. none of the above
ans: E
13. Pulling the plates of an isolated charged capacitor apart:
A. increases the capacitance
B. increases the potential difference
C. does not affect the potential difference
D. decreases the potential difference
E. does not affect the capacitance
ans: B
14. If the charge on a parallel-plate capacitor is doubled:
A. the capacitance is halved
B. the capacitance is doubled
C. the electric field is halved
D. the electric field is doubled
E. the surface charge density is not changed on either plate
ans: D
15. A parallel-plate capacitor has a plate area of 0.2 m2 and a plate separation of 0.1 mm. To
obtain an electric field of 2.0 × 106 V/m between the plates, the magnitude of the charge on
each plate should be:
A. 8.9 × 10−7 C
B. 1.8 × 10−6 C
C. 3.5 × 10−6 C
D. 7.1 × 10−6 C
E. 1.4 × 10−5 C
ans: D
366
Chapter 25:
CAPACITANCE
16. A parallel-plate capacitor has a plate area of 0.2 m2 and a plate separation of 0.1 mm. If the
charge on each plate has a magnitude of 4 × 10−6 C the potential difference across the plates
is approximately:
A. 0
B. 4 × 10−2 V
C. 1 × 102 V
D. 2 × 102 V
E. 4 × 108 V
ans: D
17. The capacitance of a spherical capacitor with inner radius a and outer radius b is proportional
to:
A. a/b
B. b − a
C. b2 − a2
D. ab/(b − a)
E. ab/(b2 − a2 )
ans: D
18. The capacitance of a single isolated spherical conductor with radius R is proportional to:
A. R
B. R2
C. 1/R
D. 1/R2
E. none of these
ans: A
19. Two conducting spheres have radii of R1 and R2 , with R1 greater than R2 . If they are far
apart the capacitance is proportional to:
A. R1 R2 /(R1 − R2 )
B. R12 − R22
C. (R1 − R2 )/R1 R2
D. R12 + R22
E. none of these
ans: A
20. The capacitance of a cylindrical capacitor can be increased by:
A. decreasing both the radius of the inner cylinder and the length
B. increasing both the radius of the inner cylinder and the length
C. increasing the radius of the outer cylindrical shell and decreasing the length
D. decreasing the radius of the inner cylinder and increasing the radius of the outer cylindrical
shell
E. only by decreasing the length
ans: B
Chapter 25:
CAPACITANCE
367
21. A battery is used to charge a series combination of two identical capacitors. If the potential
difference across the battery terminals is V and total charge Q flows through the battery during
the charging process then the charge on the positive plate of each capacitor and the potential
difference across each capacitor are:
A. Q/2 and V /2, respectively
B. Q and V , respectively
C. Q/2 and V , respectively
D. Q and V /2, respectively
E. Q and 2V , respectively
ans: D
22. A battery is used to charge a parallel combination of two identical capacitors. If the potential
difference across the battery terminals is V and total charge Q flows through the battery during
the charging process then the charge on the positive plate of each capacitor and the potential
difference across each capacitor are:
A. Q/2 and V /2, respectively
B. Q and V , respectively
C. Q/2 and V , respectively
D. Q and V /2, respectively
E. Q and 2V , respectively
ans: C
23. A 2-µF and a 1-µF capacitor are connected in series and a potential difference is applied across
the combination. The 2-µF capacitor has:
A. twice the charge of the 1-µF capacitor
B. half the charge of the 1-µF capacitor
C. twice the potential difference of the 1-µF capacitor
D. half the potential difference of the 1-µF capacitor
E. none of the above
ans: D
24. A 2-µF and a 1-µF capacitor are connected in parallel and a potential difference is applied
across the combination. The 2-µF capacitor has:
A. twice the charge of the 1-µF capacitor
B. half the charge of the 1-µF capacitor
C. twice the potential difference of the 1-µF capacitor
D. half the potential difference of the 1-µF capacitor
E. none of the above
ans: A
25. Let Q denote charge, V denote potential difference, and U denote stored energy. Of these
quantities, capacitors in series must have the same:
A. Q only
B. V only
C. U only
D. Q and U only
E. V and U only
ans: A
368
Chapter 25:
CAPACITANCE
26. Let Q denote charge, V denote potential difference, and U denote stored energy. Of these
quantities, capacitors in parallel must have the same:
A. Q only
B. V only
C. U only
D. Q and U only
E. V and U only
ans: B
27. Capacitors C1 and C2 are connected in parallel. The equivalent capacitance is given by:
A. C1 C2 /(C1 + C2 )
B. (C1 + C2 )/C1 C2
C. 1/(C1 + C2 )
D. C1 /C2
E. C1 + C2
ans: E
28. Capacitors C1 and C2 are connected in series. The equivalent capacitance is given by:
A. C1 C2 /(C1 + C2 )
B. (C1 + C2 )/C1 C2
C. 1/(C1 + C2 )
D. C1 /C2
E. C1 + C2
ans: A
29. Capacitors C1 and C2 are connected in series and a potential difference is applied to the
combination. If the capacitor that is equivalent to the combination has the same potential
difference, then the charge on the equivalent capacitor is the same as:
A. the charge on C1
B. the sum of the charges on C1 and C2
C. the difference of the charges on C1 and C2
D. the product of the charges on C1 and C2
E. none of the above
ans: A
30. Capacitors C1 and C2 are connected in parallel and a potential difference is applied to the
combination. If the capacitor that is equivalent to the combination has the same potential
difference, then the charge on the equivalent capacitor is the same as:
A. the charge on C1
B. the sum of the charges on C1 and C2
C. the difference of the charges on C1 and C2
D. the product of the charges on C1 and C2
E. none of the above
ans: B
Chapter 25:
CAPACITANCE
369
31. Two identical capacitors are connected in series and two, each identical to the first, are conthe equivalent
nected in parallel. The equivalent capacitance of the series connection is
capacitance of parallel connection.
A. twice
B. four times
C. half
D. one-fourth
E. the same as
ans: D
32. Two identical capacitors, each with capacitance C, are connected in parallel and the combination is connected in series to a third identical capacitor. The equivalent capacitance of this
arrangement is:
A. 2C/3
B. C
C. 3C/2
D. 2C
E. 3C
ans: A
33. A 2-µF and a 1-µF capacitor are connected in series and charged from a battery. They store
charges P and Q, respectively. When disconnected and charged separately using the same
battery, they have charges R and S, respectively. Then:
A. R > S > Q = P
B. P > Q > R = S
C. R > P = Q > S
D. R = P > S = Q
E. R > P > S = Q
ans: A
34. Capacitor C1 is connected alone to a battery and charged until the magnitude of the charge
on each plate is 4.0 × 10−8 C. Then it is removed from the battery and connected to two other
capacitors C2 and C3 , as shown. The charge on the positive plate of C1 is then 1.0 × 10−8 C.
The charges on the positive plates of C2 and C3 are:
C1
A.
B.
C.
D.
E.
370
q2 = 3.0 × 10−8 C
q2 = 2.0 × 10−8 C
q2 = 5.0 × 10−8 C
q2 = 3.0 × 10−8 C
q2 = 1.0 × 10−8 C
ans: A
Chapter 25:
and
and
and
and
and
q3
q3
q3
q3
q3
= 3.0 × 10−8 C
= 2.0 × 10−8 C
= 1.0 × 10−8 C
= 1.0 × 10−8 C
= 3.0 × 10−8 C
CAPACITANCE
C2
C3
35. Each of the four capacitors shown is 500 µF. The voltmeter reads 1000 V. The magnitude of
the charge, in coulombs, on each capacitor plate is:
.......
...... ........
...
...
....
..
...
....................
V
A.
B.
C.
D.
E.
0.2
0.5
20
50
none of these
ans: B
36. The diagram shows four 6-µF capacitors. The capacitance between points a and b is:
a
b
A.
B.
C.
D.
E.
3 µF
4 µF
6 µF
9 µF
1 µF
ans: C
37. Each of the two 25-µF capacitors shown is initially uncharged. How many coulombs of charge
pass through the ammeter A after the switch S is closed?
.
...
...
....
...
.
.
.
....
S
4000 V
........................
....
...
..
...
....
..
..
...
..
....
.
.
.
....................
A
A.
B.
C.
D.
E.
0.10
0.20
10
0.05
none of these
ans: B
Chapter 25:
CAPACITANCE
371
38. A 20-F capacitor is charged to 200 V. Its stored energy is:
A. 4000 J
B. 4 J
C. 0.4 J
D. 2000 J
E. 0.1 J
ans: C
39. A charged capacitor stores 10 C at 40 V. Its stored energy is:
A. 400 J
B. 4 J
C. 0.2 J
D. 2.5 J
E. 200 J
ans: E
40. A 2-µF and a 1-µF capacitor are connected in series and charged by a battery. They store
energies P and Q, respectively. When disconnected and charged separately using the same
battery, they store energies R and S, respectively. Then:
A. R > P > S > Q
B. P > Q > R > S
C. R > P > Q > S
D. P > R > S > Q
E. R > S > Q > P
ans: E
41. The quantity (1/2)60 E 2 has the significance of:
A. energy/farad
B. energy/coulomb
C. energy
D. energy/volume
E. energy/volt
ans: D
42. Capacitors A and B are identical. Capacitor A is charged so it stores 4 J of energy and capacitor
B is uncharged. The capacitors are then connected in parallel. The total stored energy in the
capacitors is now:
A. 16 J
B. 8 J
C. 4 J
D. 2 J
E. 1 J
ans: D
372
Chapter 25:
CAPACITANCE
43. To store a total of 0.040 J of energy in the two identical capacitors shown, each should have a
capacitance of:
200 V
A.
B.
C.
D.
E.
0.10 µF
0.50 µF0.10 µF
1.0 µJ
1.5 µF
2.0 µF
ans: C
44. A battery is used to charge a parallel-plate capacitor, after which it is disconnected. Then the
plates are pulled apart to twice their original separation. This process will double the:
A. capacitance
B. surface charge density on each plate
C. stored energy
D. electric field between the two places
E. charge on each plate
ans: C
45. A parallel-plate capacitor has a plate area of 0.3 m2 and a plate separation of 0.1 mm. If the
charge on each plate has a magnitude of 5 × 10−6 C then the force exerted by one plate on the
other has a magnitude of about:
A. 0
B. 5 N
C. 9 N
D. 1 × 104 N
E. 9 × 105 N
ans: B
46. A certain capacitor has a capacitance of 5.0 µF. After it is charged to 5.0 µC and isolated, the
plates are brought closer together so its capacitance becomes 10 µF. The work done by the
agent is about:
A. zero
B. 1.25 × 10−6 J
C. −1.25 × 10−6 J
D. 8.3 × 10−7 J
E. −8.3 × 10−7 J
ans: C
Chapter 25:
CAPACITANCE
373
47. A dielectric slab is slowly inserted between the plates of a parallel plate capacitor, while the
potential difference between the plates is held constant by a battery. As it is being inserted:
A. the capacitance, the potential difference between the plates, and the charge on the positive
plate all increase
B. the capacitance, the potential difference between the plates, and the charge on the positive
plate all decrease
C. the potential difference between the plates increases, the charge on the positive plate decreases, and the capacitance remains the same
D. the capacitance and the charge on the positive plate decrease but the potential difference
between the plates remains the same
E. the capacitance and the charge on the positive plate increase but the potential difference
between the plates remains the same
ans: E
48. An air-filled parallel-plate capacitor has a capacitance of 1 pF. The plate separation is then
doubled and a wax dielectric is inserted, completely filling the space between the plates. As a
result, the capacitance becomes 2 pF. The dielectric constant of the wax is:
A. 0.25
B. 0.5
C. 2.0
D. 4.0
E. 8.0
ans: D
49. One of materials listed below is to be placed between two identical metal sheets, with no, air
gap, to form a parallel-plate capacitor. Which produces the greatest capacitance?
A. material of thickness 0.1 mm and dielectric constant 2
B. material of thickness 0.2 mm and dielectric constant 3
C. material of thickness 0.3 mm and dielectric constant 2
D. material of thickness 0.4 mm and dielectric constant 8
E. material of thickness 0.5 mm and dielectric constant 11
ans: E
50. Two capacitors are identical except that one is filled with air and the other with oil. Both
capacitors carry the same charge. The ratio of the electric fields Eair /Eoil is:
A. between 0 and 1
B. 0
C. 1
D. between 1 and infinity
E. infinite
ans: D
374
Chapter 25:
CAPACITANCE
51. A parallel-plate capacitor, with air dielectric, is charged by a battery, after which the battery
is disconnected. A slab of glass dielectric is then slowly inserted between the plates. As it is
being inserted:
A. a force repels the glass out of the capacitor
B. a force attracts the glass into the capacitor
C. no force acts on the glass
D. a net charge appears on the glass
E. the glass makes the plates repel each other
ans: B
52. Two parallel-plate capacitors with the same plate separation but different capacitance are
connected in parallel to a battery. Both capacitors are filled with air. The quantity that is
NOT the same for both capacitors when they are fully charged is:
A. potential difference
B. energy density
C. electric field between the plates
D. charge on the positive plate
E. dielectric constant
ans: D
53. Two parallel-plate capacitors with the same plate area but different capacitance are connected
in parallel to a battery. Both capacitors are filled with air. The quantity that is the same for
both capacitors when they are fully charged is:
A. potential difference
B. energy density
C. electric field between the plates
D. charge on the positive plate
E. plate separation
ans: A
54. Two parallel-plate capacitors with different plate separation but the same capacitance are
connected in series to a battery. Both capacitors are filled with air. The quantity that is NOT
the same for both capacitors when they are fully charged is:
A. potential difference
B. stored energy
C. electric field between the plates
D. charge on the positive plate
E. dielectric constant
ans: C
55. Two parallel-plate capacitors with different capacitance but the same plate separation are
connected in series to a battery. Both capacitors are filled with air. The quantity that is the
same for both capacitors when they are fully charged is:
A. potential difference
B. stored energy
C. energy density
D. electric field between the plates
E. charge on the positive plate
ans: E
Chapter 25:
CAPACITANCE
375
Chapter 26:
CURRENT AND RESISTANCE
1. A car battery is rated at 80 A · h. An ampere-hour is a unit of:
A. power
B. energy
C. current
D. charge
E. force
ans: D
2. Current has units:
A. kilowatt·hour
B. coulomb/second
C. coulomb
D. volt
E. ohm
ans: B
3. Current has units:
A. kilowatt·hour
B. ampere
C. coulomb
D. volt
E. ohm
ans: B
4. The units of resistivity are:
A. ohm
B. ohm·meter
C. ohm/meter
D. ohm/meter2
E. none of these
ans: B
5. The rate at which electrical energy is used may be measured in:
A. watt/second
B. watt·second
C. watt
D. joule·second
E. kilowatt·hour
ans: C
376
Chapter 26:
CURRENT AND RESISTANCE
6. Energy may be measured in:
A. kilowatt
B. joule·second
C. watt
D. watt·second
E. volt/ohm
ans: D
7. Which one of the following quantities is correctly matched to its unit?
A. Power – kW·h
B. Energy – kW
C. Potential difference – J/C
D. Current – A/s
E. Resistance – V/C
ans: C
8. Current is a measure of:
A. force that moves a charge past a point
B. resistance to the movement of a charge past a point
C. energy used to move a charge past a point
D. amount of charge that moves past a point per unit time
E. speed with which a charge moves past a point
ans: D
9. A 60-watt light bulb carries a current of 0.5 A. The total charge passing through it in one hour
is:
A. 120 C
B. 3600 C
C. 3000 C
D. 2400 C
E. 1800 C
ans: E
10. A 10-ohm resistor has a constant current. If 1200 C of charge flow through it in 4 minutes what
is the value of the current?
A. 3.0 A
B. 5.0 A
C. 11 A
D. 15 A
E. 20 A
ans: D
Chapter 26:
CURRENT AND RESISTANCE
377
11. Conduction electrons move to the right in a certain wire. This indicates that:
A. the current density and electric field both point right
B. the current density and electric field both point left
C. the current density points right and the electric field points left
D. the current density points left and the electric field points right
E. the current density points left but the direction of the electric field is unknown
ans: B
12. Two wires made of different materials have the same uniform current density. They carry the
same current only if:
A. their lengths are the same
B. their cross-sectional areas are the same
C. both their lengths and cross-sectional areas are the same
D. the potential differences across them are the same
E. the electric fields in them are the same
ans: B
13. A wire with a length of 150 m and a radius of 0.15 mm carries a current with a uniform current
2
density of 2.8 × 107 A/m . The current is:
A. 0.63 A2
B. 2.0 A
C. 5.9 A2
D. 296 A
E. 400 A2
ans: B
14. In a conductor carrying a current we expect the electron drift speed to be:
A. much greater than the average electron speed
B. much less than the average electron speed
C. about the same as the average electron speed
D. less than the average electron speed at low temperature and greater than the average
electron speed at high temperature
E. less than the average electron speed at high temperature and greater than the average
electron speed at low temperature
ans: B
15. Two substances are identical except that the electron mean free time for substance A is twice
the electron mean free time for substance B. If the same electric field exists in both substances
the electron drift speed in A is:
A. the same as in B
B. twice that in B
C. half that in B
D. four times that in B
E. one-fourth that in B
ans: B
378
Chapter 26:
CURRENT AND RESISTANCE
16. The current is zero in a conductor when no potential difference is applied because:
A. the electrons are not moving
B. the electrons are not moving fast enough
C. for every electron with a given velocity there is another with a velocity of equal magnitude
and opposite direction.
D. equal numbers of electrons and protons are moving together
E. otherwise Ohm’s law would not be valid
ans: C
17. The current density is the same in two wires. Wire A has twice the free-electron concentration
of wire B. The drift speed of electrons in A is:
A. twice that of electrons in B
B. four times that of electrons in B
C. half that of electrons in B
D. one-fourth that of electrons in B
E. the same as that of electrons in B
ans: C
18. Copper contains 8.4×1028 free electrons/m3 . A copper wire of cross-sectional area 7.4×10−7 m2
carries a current of 1 A. The electron drift speed is approximately:
A. 3 × 108 m/s
B. 103 m/s
C. 1 m/s
D. 10−4 m/s
E. 10−23 m/s
ans: D
$
n is a vector element of area then the integral Jn · dA
n over an
19. If Jn is the current density and dA
area represents:
A. the electric flux through the area
B. the average current density at the position of the area
C. the resistance of the area
D. the resistivity of the area
E. the current through the area
ans: E
20. If the potential difference across a resistor is doubled:
A. only the current is doubled
B. only the current is halved
C. only the resistance is doubled
D. only the resistance is halved
E. both the current and resistance are doubled
ans: A
Chapter 26:
CURRENT AND RESISTANCE
379
21. Five cylindrical wires are made of the same material. Their lengths and radii are
wire 1: length f, radius r
wire 2: length f/4, radius r/2
wire 3: length f/2, radius r/2
wire 4: length f, radius r/2
wire 5: length 5f, radius 2r
Rank the wires according to their resistances, least to greatest.
A. 1, 2, 3, 4, 5
B. 5, 4, 3, 2, 1
C. 1 and 2 tie, then 5, 3, 4
D. 1, 3, 4, 2, 5
E. 1, 2, 4, 3, 5
ans: C
22. Of
A.
B.
C.
D.
E.
the following, the copper conductor that has the least resistance is:
thin, long and hot
thick, short and cool
thick, long and hot
thin, short and cool
thin, short and hot
ans: B
23. A cylindrical copper rod has resistance R. It is reformed to twice its original length with no
change of volume. Its new resistance is:
A. R
B. 2R
C. 4R
D. 8R
E. R/2
ans: C
24. The resistance of a rod does NOT depend on:
A. its temperature
B. its material
C. its length
D. its conductivity
E. the shape of its (fixed) cross-sectional area
ans: E
25. A certain wire has resistance R. Another wire, of the same material, has half the length and
half the diameter of the first wire. The resistance of the second wire is:
A. R/4
B. R/2
C. R
D. 2R
E. 4R
ans: D
380
Chapter 26:
CURRENT AND RESISTANCE
26. A nichrome wire is 1 m long and 1 × 10−6 m2 in cross-sectional area. When connected to a
potential difference of 2 V, a current of 4 A exists in the wire. The resistivity of this nichrome
is:
A. 10−7 Ω · m
B. 2 × 10−7 Ω · m
C. 4 × 10−7 Ω · m
D. 5 × 10−7 Ω · m
E. 8 × 10−7 Ω · m
ans: D
27. Two conductors are made of the same material and have the same length. Conductor A is a
solid wire of diameter 1 m. Conductor B is a hollow tube of inside diameter 1 m and outside
diameter 2 m. The ratio of their resistance, RA /RB , is:
A. √
1
2
B.
C. 2
D. 3
E. 4
ans: D
28. Conductivity is:
A. the same as resistivity, it is just more convenient to use for good conductors
B. expressed in Ω−1
C. equal to 1/resistance
D. expressed in (Ω · m)−1
E. not a meaningful quantity for an insulator
ans: D
29. A certain sample carries a current of 4 A when the potential difference is 2 V and a current of
10 A when the potential difference is 4 V. This sample:
A. obeys Ohm’s law
B. has a resistance of 0.5 Ω at 1 V
C. has a resistance of 2.5 Ω at 1 V
D. has a resistance of 2.5 Ω at 2 V
E. does not have a resistance
ans: B
30. A current of 0.5 A exists in a 60-ohm lamp. The applied potential difference is:
A. 15 V
B. 30 V
C. 60 V
D. 120 V
E. none of these
ans: B
Chapter 26:
CURRENT AND RESISTANCE
381
31. Which of the following graphs best represents the current-voltage relationship of an incandescent light bulb?
i
.............
.....
.
.
.
...
...
.
.
.
..
.. .
i
i
.......
.........
.
.
.
.
.
.
.
.......
........
V
V
..
..
.
...
...
.
.
..
....
.
.
.
.
.
.........
B
A
i.
...
...
...
....
....
.....
.......
.........
V
C
i
..............................................
V
V
E
D
ans: A
32. Which of the following graphs best represents the current-voltage relationship for a device that
obeys Ohm’s law?
i
.......
.......
.
.
.
.
.
....
...
.
..
.. .
i
V
A
i.
...
...
...
....
....
.....
.......
.........
i
..
.....
.
.
.
....
.....
.
.
.
...
.....
.
.
.
.
....
V
B
.
..
.
..
...
.
.
..
....
.
.
.
.
.
...........
V
C
i
..............................................
V
D
V
E
ans: B
33. Two wires are made of the same material and have the same length but different radii. They
are joined end-to-end and a potential difference is maintained across the combination. Of the
following the quantity that is the same for both wires is:
A. potential difference
B. current
C. current density
D. electric field
E. conduction electron drift speed
ans: B
382
Chapter 26:
CURRENT AND RESISTANCE
34. For
A.
B.
C.
D.
E.
an ohmic substance the resistivity is the proportionality constant for:
current and potential difference
current and electric field
current density and potential difference
current density and electric field
potential difference and electric field
ans: D
35. For
A.
B.
C.
D.
E.
an ohmic resistor, resistance is the proportionality constant for:
potential difference and electric field
current and electric field
current and length
current and cross-sectional area
current and potential difference
ans: E
36. For
A.
B.
C.
D.
E.
an ohmic substance, the resistivity depends on:
the electric field
the potential difference
the current density
the electron mean free time
the cross-sectional area of the sample
ans: D
37. For
A.
B.
C.
D.
E.
a cylindrical resistor made of ohmic material, the resistance does NOT depend on:
the current
the length
the cross-sectional area
the resistivity
the electron drift velocity
ans: A
38. For
A.
B.
C.
D.
E.
an ohmic substance, the electron drift velocity is proportional to:
the cross-sectional area of the sample
the length of the sample
the mass of an electron
the electric field in the sample
none of the above
ans: D
Chapter 26:
CURRENT AND RESISTANCE
383
39. You wish to triple the rate of energy dissipation in a heating device. To do this you could
triple:
A. the potential difference keeping the resistance the same
B. the current keeping the resistance the same
C. the resistance keeping the potential difference the same
D. the resistance keeping the current the same
E. both the potential difference and current
ans: D
40. A student kept her 60-watt, 120-volt study lamp turned on from 2:00 PM until 2:00 AM. How
many coulombs of charge went through it?
A. 150
B. 3, 600
C. 7, 200
D. 18, 000
E. 21, 600
ans: E
41. A flat iron is marked “120 V, 600 W”. In normal use, the current in it is:
A. 2 A
B. 4 A
C. 5 A
D. 7.2 A
E. 0.2 A
ans: C
42. An certain resistor dissipates 0.5 W when connected to a 3 V potential difference. When connected to a 1 V potential difference, this resistor will dissipate:
A. 0.5 W
B. 0.167 W
C. 1.5 W
D. 0.056 W
E. none of these
ans: D
43. An
A.
B.
C.
D.
E.
ordinary light bulb is marked “60 W, 120 V”. Its resistance is:
60 Ω
120 Ω
180 Ω
240 Ω
15 Ω
ans: D
384
Chapter 26:
CURRENT AND RESISTANCE
44. The mechanical equivalent of heat is 1 cal = 4.18 J. The specific heat of water is 1 cal/g · K. An
electric immersion water heater, rated at 400 W, should heat a kilogram of water from 10◦ C
to 30◦ C in about:
A. 3.5 min
B. 1 min
C. 15 min
D. 45 min
E. 15 s
ans: A
45. It is better to send 10, 000 kW of electric power long distances at 10, 000 V rather than at 220 V
because:
A. there is less heating in the transmission wires
B. the resistance of the wires is less at high voltages
C. more current is transmitted at high voltages
D. the insulation is more effective at high voltages
E. the iR drop along the wires is greater at high voltage
ans: A
46. Suppose the electric company charges 10 cents per kW·h. How much does it cost to use a
125 W lamp 4 hours a day for 30 days?
A. $1.20
B. $1.50
C. $1.80
D. $7.20
E. none of these
ans: B
47. A certain x-ray tube requires a current of 7 mA at a voltage of 80 kV. The rate of energy
dissipation (in watts) is:
A. 560
B. 5600
C. 26
D. 11.4
E. 87.5
ans: A
48. The mechanical equivalent of heat is 1 cal = 4.18 J. A heating coil, connected to a 120-V source,
provides 60, 000 calories in 10 minutes. The current in the coil is:
A. 0.83 A
B. 2 A
C. 3.5 A
D. 20 A
E. 50 A
ans: C
Chapter 26:
CURRENT AND RESISTANCE
385
49. You buy a “75 W” light bulb. The label means that:
A. no matter how you use the bulb, the power will be 75 W
B. the bulb was filled with 75 W at the factory
C. the actual power dissipated will be much higher than 75 W since most of the power appears
as heat
D. the bulb is expected to burn out after you use up its 75 W
E. none of the above
ans: E
50. A current of 0.3 A is passed through a lamp for 2 minutes using a 6-V power supply. The energy
dissipated by this lamp during the 2 minutes is:
A. 1.8 J
B. 12 J
C. 20 J
D. 36 J
E. 216 J
ans: E
386
Chapter 26:
CURRENT AND RESISTANCE
Chapter 27:
CIRCUITS
1. “The sum of the currents into a junction equals the sum of the currents out of the junction” is
a consequence of:
A. Newton’s third law
B. Ohm’s law
C. Newton’s second law
D. conservation of energy
E. conservation of charge
ans: E
2. “The sum of the emf’s and potential differences around a closed loop equals zero” is a consequence of:
A. Newton’s third law
B. Ohm’s law
C. Newton’s second law
D. conservation of energy
E. conservation of charge
ans: D
3. A portion of a circuit is shown, with the values of the currents given for some branches. What
is the direction and value of the current i?
↑2 A
→
5A
A.
B.
C.
D.
E.
↓4 A
i
↑3 A
↑2 A
↓, 6 A
↑, 6 A
↓, 4 A
↑, 4 A
↓, 2 A
ans: A
4. Four wires meet at a junction. The first carries 4 A into the junction, the second carries 5 A
out of the junction, and the third carries 2 A out of the junction. The fourth carries:
A. 7 A out of the junction
B. 7 A into the junction
C. 3 A out of the junction
D. 3 A into the junction
E. 1 A into the junction
ans: D
Chapter 27:
CIRCUITS
387
5. In the context of the loop and junctions rules for electrical circuits a junction is:
A. where a wire is connected to a resistor
B. where a wire is connected to a battery
C. where only two wires are joined
D. where three or more wires are joined
E. where a wire is bent
ans: D
6. For any circuit the number of independent equations containing emf’s, resistances, and currents
equals:
A. the number of junctions
B. the number of junctions minus 1
C. the number of branches
D. the number of branches minus 1
E. the number of closed loops
ans: C
7. If a circuit has L closed loops, B branches, and J junctions the number of independent loop
equations is:
A. B − J + 1
B. B − J
C. B
D. L
E. L − J
ans: A
8. A battery is connected across a series combination of two identical resistors. If the potential
difference across the terminals is V and the current in the battery is i, then:
A. the potential difference across each resistor is V and the current in each resistor is i
B. the potential difference across each resistor is V /2 and the current in each resistor is i/2
C. the potential difference across each resistor is V and the current in each resistor is i/2
D. the potential difference across each resistor is V /2 and the current in each resistor is i
E. none of the above are true
ans: D
9. A battery is connected across a parallel combination of two identical resistors. If the potential
difference across the terminals is V and the current in the battery is i, then:
A. the potential difference across each resistor is V and the current in each resistor is i
B. the potential difference across each resistor is V /2 and the current in each resistor is i/2
C. the potential difference across each resistor is V and the current in each resistor is i/2
D. the potential difference across each resistor is V /2 and the current in each resistor is i
E. none of the above are true
ans: C
388
Chapter 27:
CIRCUITS
10. A total resistance of 3.0 Ω is to be produced by combining an unknown resistor R with a 12 Ω
resistor. What is the value of R and how is it to be connected to the 12 Ω resistor?
A. 4.0 Ω, parallel
B. 4.0 Ω, series
C. 2.4 Ω, parallel
D. 2.4 Ω, series
E. 9.0 Ω, series
ans: A
11. By using only two resistors, R1 and R2 , a student is able to obtain resistances of 3 Ω, 4 Ω, 12 Ω,
and 16 Ω. The values of R1 and R2 (in ohms) are:
A. 3, 4
B. 2, 12
C. 3, 16
D. 4, 12
E. 4, 16
ans: D
12. Four 20-Ω resistors are connected in parallel and the combination is connected to a 20-V emf
device. The current in the device is:
A. 0.25 A
B. 1.0 A
C. 4.0 A
D. 5.0 A
E. 100 A
ans: C
13. Four 20-Ω resistors are connected in parallel and the combination is connected to a 20-V emf
device. The current in any one of the resistors is:
A. 0.25 A
B. 1.0 A
C. 4.0 A
D. 5.0 A
E. 100 A
ans: B
14. Four 20-Ω resistors are connected in series and the combination is connected to a 20-V emf
device. The current in any one of the resistors is:
A. 0.25 A
B. 1.0 A
C. 4.0 A
D. 5.0 A
E. 100 A
ans: A
Chapter 27:
CIRCUITS
389
15. Four 20-Ω resistors are connected in series and the combination is connected to a 20-V emf
device. The potential difference across any one of the resistors is:
A. 1 V
B. 4 V
C. 5 V
D. 20 V
E. 80 V
ans: C
16. Nine identical wires, each of diameter d and length L, are connected in parallel. The combination has the same resistance as a single similar wire of length L but whose diameter is:
A. 3d
B. 9d
C. d/3
D. d/9
E. d/81
ans: A
17. Nine identical wires, each of diameter d and length L, are connected in series. The combination
has the same resistance as a single similar wire of length L but whose diameter is:
A. 3d
B. 9d
C. d/3
D. d/9
E. d/81
ans: C
18. Two wires made of the same material have the same lengths but different diameters. They are
connected in parallel to a battery. The quantity that is NOT the same for the wires is:
A. the end-to-end potential difference
B. the current
C. the current density
D. the electric field
E. the electron drift velocity
ans: B
19. Two wires made of the same material have the same lengths but different diameters. They are
connected in series to a battery. The quantity that is the same for the wires is:
A. the end-to-end potential difference
B. the current
C. the current density
D. the electric field
E. the electron drift velocity
ans: B
390
Chapter 27:
CIRCUITS
20. The equivalent resistance between points 1 and 2 of the circuit shown is:
1Ω
1Ω
. . .
.........................
. . .
. . .
.........................
. . .
•1
...........................
. . .
...........................
. . .
2Ω
2Ω
•2
..........
..
............
..
............
....
..........
.
......
1 Ω .........................
A.
B.
C.
D.
E.
4Ω
3Ω
4Ω
5Ω
6Ω
7Ω
ans: C
21. Each of the resistors in the diagram has a resistance of 12 Ω. The resistance of the entire circuit
is:
. . .
......................
. . .
. . .
......................
. . .
. . .
.........................
. . .
•
. . .
.........................
. . .
. . .
.........................
. . .
A.
B.
C.
D.
E.
•
•
. . .
.........................
. . .
. . .
.........................
. . .
•
•
. . .
.........................
. . .
•
. . .
.........................
. . .
•
. . .
.........................
. . .
5.76 Ω
25 Ω
48 Ω
120 Ω
none of these
ans: B
22. The resistance of resistor 1 is twice the resistance of resistor 2. The two are connected in
parallel and a potential difference is maintained across the combination. Then:
A. the current in 1 is twice that in 2
B. the current in 1 is half that in 2
C. the potential difference across 1 is twice that across 2
D. the potential difference across 1 is half that across 2
E. none of the above are true
ans: B
Chapter 27:
CIRCUITS
391
23. The resistance of resistor 1 is twice the resistance of resistor 2. The two are connected in series
and a potential difference is maintained across the combination. Then:
A. the current in 1 is twice that in 2
B. the current in 1 is half that in 2
C. the potential difference across 1 is twice that across 2
D. the potential difference across 1 is half that across 2
E. none of the above are true
ans: C
24. Resistor 1 has twice the resistance of resistor 2. The two are connected in series and a potential
difference is maintained across the combination. The rate of thermal energy generation in 1 is:
A. the same as that in 2
B. twice that in 2
C. half that in 2
D. four times that in 2
E. one-fourth that in 2
ans: B
25. Resistor 1 has twice the resistance of resistor 2. The two are connected in parallel and a potential difference is maintained across the combination. The rate of thermal energy generation
in 1 is:
A. the same as that in 2
B. twice that in 2
C. half that in 2
D. four times that in 2
E. one-fourth that in 2
ans: C
26. The emf of a battery is equal to its terminal potential difference:
A. under all conditions
B. only when the battery is being charged
C. only when a large current is in the battery
D. only when there is no current in the battery
E. under no conditions
ans: D
27. The terminal potential difference of a battery is less than its emf:
A. under all conditions
B. only when the battery is being charged
C. only when the battery is being discharged
D. only when there is no current in the battery
E. under no conditions
ans: C
392
Chapter 27:
CIRCUITS
28. A battery has an emf of 9 V and an internal resistance of 2 Ω. If the potential difference across
its terminals is greater than 9 V:
A. it must be connected across a large external resistance
B. it must be connected across a small external resistance
C. the current must be out of the positive terminal
D. the current must be out of the negative terminal
E. the current must be zero
ans: D
29. A battery with an emf of 24 V is connected to a 6-Ω resistor. As a result, current of 3 A exists
in the resistor. The terminal potential difference of the battery is:
A. 0
B. 6 V
C. 12 V
D. 18 V
E. 24 V
ans: D
30. In the diagram R1 > R2 > R3 . Rank the three resistors according to the current in them, least
to greatest.
R1
.. .. ..
............................
. . .
..........
......
............
......
............
..
.....
E
R2
.. .. ..
............................
. . .
R3
A.
B.
C.
D.
E.
1, 2, 3
3, 2, 1
1, 3, 2
3, 1, 3
All are the same
ans: E
31. Resistances of 2.0 Ω, 4.0 Ω, and 6.0 Ω and a 24-V emf device are all in parallel. The current in
the 2.0-Ω resistor is:
A. 12 A
B. 4.0 A
C. 2.4 A
D. 2.0 A
E. 0.50 A
ans: A
Chapter 27:
CIRCUITS
393
32. Resistances of 2.0 Ω, 4.0 Ω, and 6.0 Ω and a 24-V emf device are all in series. The potential
difference across the 2.0-Ω resistor is:
A. 4 V
B. 8 V
C. 12 V
D. 24 V
E. 48 V
ans: A
33. A battery with an emf of 12 V and an internal resistance of 1 Ω is used to charge a battery with
an emf of 10 V and an internal resistance of 1 Ω. The current in the circuit is:
A. 1 A
B. 2 A
C. 4 A
D. 11 A
E. 22 A
ans: A
34. In the diagram, the current in the 3-Ω resistor is 4 A. The potential difference between points
1 and 2 is:
3Ω
A.
B.
C.
D.
E.
2Ω
.. .. ..
.........................
.. .. ..
1•
.. .. ..
.........................
.. .. ..
•2
0.75 V
0.8 V
1.25 V
12 V
20 V
ans: E
35. The current in the 5.0-Ω resistor in the circuit shown is:
. . .
.........................
6.0 Ω
12 V
A.
B.
C.
D.
E.
394
0.42 A
0.67 A
1.5 A
2.4 A
3.0 A
ans: C
Chapter 27:
CIRCUITS
. .
............................
...............................
4.0 Ω
12 Ω
. . .
.........................
. . .
.........................
3.0 Ω
5.0 Ω
36. A 3-Ω and a 1.5-Ω resistor are wired in parallel and the combination is wired in series to a 4-Ω
resistor and a 10-V emf device. The current in the 3-Ω resistor is:
A. 0.33 A
B. 0.67 A
C. 2.0 A
D. 3.3 A
E. 6.7 A
ans: B
37. A 3-Ω and a 1.5-Ω resistor are wired in parallel and the combination is wired in series to a 4-Ω
resistor and a 10-V emf device. The potential difference across the 3-Ω resistor is:
A. 2.0 V
B. 6.0 V
C. 8.0 V
D. 10 V
E. 12 V
ans: A
38. Two identical batteries, each with an emf of 18 V and an internal resistance of 1 Ω, are wired in
parallel by connecting their positive terminals together and connecting their negative terminals
together. The combination is then wired across a 4-Ω resistor. The current in the 4-Ω resistor
is:
A. 1.0 A
B. 2.0 A
C. 4.0 A
D. 3.6 A
E. 7.2 A
ans: C
39. Two identical batteries, each with an emf of 18 V and an internal resistance of 1 Ω, are wired in
parallel by connecting their positive terminals together and connecting their negative terminals
together. The combination is then wired across a 4-Ω resistor. The current in each battery is:
A. 1.0 A
B. 2.0 A
C. 4.0 A
D. 3.6 A
E. 7.2 A
ans: B
Chapter 27:
CIRCUITS
395
40. Two identical batteries, each with an emf of 18 V and an internal resistance of 1 Ω, are wired in
parallel by connecting their positive terminals together and connecting their negative terminals
together. The combination is then wired across a 4-Ω resistor. The potential difference across
the 4-Ω resistor is:
A. 4.0 V
B. 8.0 V
C. 14 V
D. 16 V
E. 29 V
ans: D
41. In the diagrams, all light bulbs are identical and all emf devices are identical. In which circuit
(A, B, C, D, E) will the bulbs glow with the same brightness as in circuit X?
....
.......................
..... ................... ....
... .. ......
................
.. ..
............
...................
..... ................ ....
....... .......
.............
.. .
....
.......................
..... ................... ....
... .. ......
................
.. ..
A
...
....
...
...................... ...................... ......................
..... .................... .... ..... .................... .... ..... .................... ....
... .. .. .... ... .. .. .... ... .. .. ....
................. ................. .................
. .
. ..
. ..
....
.......................
..... ................... ...
... .. .. ....
.................
.. ..
B
C
•
..........
..........................
..... ................ ...
.........................
..........
..........
..........................
..... ................ ...
.........................
..........
•
•
...........
...................
..... .................. ....
... ... ... ...
...............
. .
•
D
X
...........
........................
..... ................. ...
........................
.............
...........
...................
..... .................. ....
... ... ... ...
...............
. .
E
ans: D
42. In the diagrams, all light bulbs are identical and all emf devices are identical. In which circuit
(A, B, C, D, E) will the bulbs be dimmest?
..........
...............
.... .................... ...
... ... .......
..............
.. ..
.............. .............. ..............
... ........... ... ... ........... ... ... ........... ...
.... ................. .... .... ................ .... .... ................ ....
....... ... ... ....... ... ... ....... ... ...
............. .............. ..............
. .
. .
. .
..........
...............
.... .................... ...
... ... .......
..............
.. ..
A
•
..............
... ........... ...
.... ................. ....
....... ........
.............
. .
............
...................
.... ................. ....
....... .......
..............
. .
C
ans: D
396
Chapter 27:
CIRCUITS
•
B
•
•
..........
................
.... .................... ....
... ... ... ...
.............
.. ..
..........
................
.... .................... ....
... ... ... ...
.............
.. ..
D
•
..........
................
.... .................... ....
... ... ... ...
.............
.. ..
......
...................
..... ................. ...
... ... . ... ....
.................
.. ..
E
•
43. A 120-V power line is protected by a 15-A fuse. What is the maximum number of “120 V,
500 W” light bulbs that can be operated at full brightness from this line?
A. 1
B. 2
C. 3
D. 4
E. 5
ans: C
44. Two 110-V light bulbs, one “25 W” and the other “100 W”, are connected in series to a 110 V
source. Then:
A. the current in the 100-W bulb is greater than that in the 25-W bulb
B. the current in the 100-W bulb is less than that in the 25-W bulb
C. both bulbs will light with equal brightness
D. each bulb will have a potential difference of 55 V
E. none of the above
ans: E
45. A resistor with resistance R1 and a resistor with resistance R2 are connected in parallel to an
ideal battery with emf E. The rate of thermal energy generation in the resistor with resistance
R1 is:
A. E 2 /R1
B. E 2 R1 /(R1 + R2 )2
C. E 2 /(R1 + R2 )
D. E 2 /R2
E. E 2 R1 /R22
ans: A
46. In an antique automobile, a 6-V battery supplies a total of 48 W to two identical headlights in
parallel. The resistance (in ohms) of each bulb is:
A. 0.67
B. 1.5
C. 3
D. 4
E. 8
ans: B
47. Resistor 1 has twice the resistance of resistor 2. They are connected in parallel to a battery.
The ratio of the thermal energy generation rate in 1 to that in 2 is:
A. 1 : 4
B. 1 : 2
C. 1 : 1
D. 2 : 1
E. 4 : 1
ans: B
Chapter 27:
CIRCUITS
397
48. A series circuit consists of a battery with internal resistance r and an external resistor R. If
these two resistances are equal (r = R) then the thermal energy generated per unit time by
the internal resistance r is:
A. the same as by R
B. half that by R
C. twice that by R
D. one-third that by R
E. unknown unless the emf is given
ans: A
49. The positive terminals of two batteries with emf’s of E1 and E2 , respectively, are connected
together. Here E2 > E1 . The circuit is completed by connecting the negative terminals. If
each battery has an internal resistance r, the rate with which electrical energy is converted to
chemical energy in the smaller battery is:
A. E12 /r
B. E12 /2r
C. (E2 − E1 )E1 /r
D. (E2 − E1 )E1 /2r
E. E22 /2r
ans: D
50. In the figure, voltmeter V1 reads 600 V, voltmeter V2 reads 580 V, and ammeter A reads 100 A.
The power wasted in the transmission line connecting the power house to the consumer is:
power
house
•
398
1 kW
2 kW
58 kW
59 kW
60 kW
ans: B
Chapter 27:
CIRCUITS
A
......
...... ........
...
..
....
..
.... 1.....
...............
V
•
A.
B.
C.
D.
E.
.................
....
..
..
.....
...
..
...... .......
.......
......
...... ........
...
..
....
..
.... 2.....
...............
V
transmission line
•
consumer
•
51. The circuit shown was wired for the purpose of measuring the resistance of the lamp L. Inspection shows that:
..
..........
.......
...
.
.
...... ....... .......
.
. ... ... ... ... ... ...
..... ..... .....
•
R
...................
...
...
....
.
...
..
...... .......
.......
L
•
...................
...
...
.....
.
...
..
...... .......
........
•
...................
...
...
....
.
...
..
...... .......
.......
A
to 120 V
A.
B.
C.
D.
E.
•
V
voltmeter V and rheostat R should be interchanged
the circuit is satisfactory
the ammeter A should be in parallel with R, not L
the meters, V and A, should be interchanged
L and V should be interchanged
ans: D
52. When switch S is open, the ammeter in the circuit shown reads 2.0 A. When S is closed, the
ammeter reading:
15 Ω
.. .. ..
.........................
.. .. ..
•
...................
...
..
.
.....
...
...
...... .........
.....
A
20 Ω
...........
.....
............
......
............
..
......
...........
.....
............
.....
............
..
......
60 Ω
• ...........
..
....
S
•
A.
B.
C.
D.
E.
increases slightly
remains the same
decreases slightly
doubles
halves
ans: A
53. A certain galvanometer has a resistance of 100 Ω and requires 1 mA for full scale deflection. To
make this into a voltmeter reading 1 V full scale, connect a resistance of:
A. 1000 Ω in parallel
B. 900 Ω in series
C. 1000 Ω in series
D. 10 Ω in parallel
E. 0.1 Ω in series
ans: B
Chapter 27:
CIRCUITS
399
54. To
A.
B.
C.
D.
E.
make a galvanometer into an ammeter, connect:
a high resistance in parallel
a high resistance in series
a low resistance in series
a low resistance in parallel
a source of emf in series
ans: D
55. A certain voltmeter has an internal resistance of 10, 000 Ω and a range from 0 to 100 V. To
give it a range from 0 to 1000 V, one should connect:
A. 100, 000 Ω in series
B. 100, 000 Ω in parallel
C. 1000 Ω in series
D. 1000 Ω in parallel
E. 90, 000 Ω in series
ans: E
56. A certain ammeter has an internal resistance of 1 Ω and a range from 0 to 50 mA. To make its
range from 0 to 5 A, use:
A. a series resistance of 99 Ω
B. an extremely large (say 106 Ω ) series resistance
C. a resistance of 99 Ω in parallel
D. a resistance of 1/99 Ω in parallel
E. a resistance of 1/1000 Ω in parallel
ans: D
57. A galvanometer has an internal resistance of 12 Ω and requires 0.01 A for full scale deflection.
To convert it to a voltmeter reading 3 V full scale, one must use a series resistance of:
A. 102 Ω
B. 288 Ω
C. 300 Ω
D. 360 Ω
E. 412 Ω
ans: B
58. A certain voltmeter has an internal resistance of 10, 000 Ω and a range from 0 to 12 V. To
extend its range to 120 V, use a series resistance of:
A. 1, 111 Ω
B. 90, 000 Ω
C. 100, 000 Ω
D. 108, 000 Ω
E. 120, 000 Ω
ans: B
400
Chapter 27:
CIRCUITS
59. Four circuits have the form shown in the diagram. The capacitor is initially uncharged and the
switch S is open.
S
• •
....
....
....
....
.
R
... ... ...
.. ....... ....... ......
.. .. ..
E
C
The values of the emf E, resistance R, and capacitance C for each of the circuits are
circuit 1: E = 18 V, R = 3 Ω, C = 1 µF
circuit 2: E = 18 V, R = 6 Ω, C = 9 µF
circuit 3: E = 12 V, R = 1 Ω, C = 7 µF
circuit 4: E = 10 V, R = 5 Ω, C = 7 µF
Rank the circuits according to the current just after switch S is closed least to greatest.
A. 1, 2, 3, 4
B. 4, 3, 2, 1
C. 4, 2, 3, 1
D. 4, 2, 1, 3
E. 3, 1, 2, 4
ans: D
60. Four circuits have the form shown in the diagram. The capacitor is initially uncharged and the
switch S is open.
S
• •
....
....
....
....
.
E
R
.. .. ..
.........................
.. .. ..
C
The values of the emf E, resistance R, and capacitance C for each of the circuits are
circuit 1: E = 18 V, R = 3 Ω, C = 1 µF
circuit 2: E = 18 V, R = 6 Ω, C = 9 µF
circuit 3: E = 12 V, R = 1 Ω, C = 7 µF
circuit 4: E = 10 V, R = 5 Ω, C = 7 µF
Rank the circuits according to the time after switch S is closed for the capacitors to reach half
their final charges, least to greatest.
A. 1, 2, 3, 4
B. 4, 3, 2, 1
C. 1, 3, 4, 2
D. 1 and 2 tied, then 4, 3
E. 4, 3, then 1 and 2 tied
ans: C
Chapter 27:
CIRCUITS
401
61. The time constant RC has units of:
A. second/farad
B. second/ohm
C. 1/second
D. second/watt
E. none of these
ans: E
62. In the circuit shown, both resistors have the same value R. Suppose switch S is initially closed.
When it is then opened, the circuit has a time constant τa . Conversely, suppose S is initially
open. When it is then closed, the circuit has a time constant τb . The ratio τa /τb is:
. . .
.........................
•
R
C
R
.
.....
......
......
S
..........
..
............
.
............
.....
E
•
A.
B.
C.
D.
E.
1
2
0.5
0.667
1.5
ans: B
63. In the circuit shown, the capacitor is initially uncharged. At time t = 0, switch S is closed. If
τ denotes the time constant, the approximate current through the 3 Ω resistor when t = τ /10
is:
. . .
.........................
. . .
•
S •
6Ω
....
....
....
....
.
10 V
A.
B.
C.
D.
E.
402
0.38 A
0.50 A
0.75 A
1.0 A
1.5 A
ans: D
Chapter 27:
CIRCUITS
6 µF
..........
..
............
..
............
.....
3Ω
64. Suppose the current charging a capacitor is kept constant. Which graph below correctly gives
the potential difference V across the capacitor as a function of time?
V
.............
.....
.
.
.
...
...
.
.
.
..
.. .
V
V
...........................................
t
t
A
....
.....
.
.
.
....
.....
.
.
...
....
.
.
.
..
B
V
.
..
.
..
...
.
.
..
....
.
.
.
.
.............
D
C
V
t
t
..
..
..
..
..
..
..
t
E
ans: C
65. A charged capacitor is being discharged through a resistor. At the end of one time constant
the charge has been reduced by (1 − 1/e) = 63% of its initial value. At the end of two time
constants the charge has been reduced by what percent of its initial value?
A. 82%
B. 86%
C. 100%
D. Between 90% and 100%
E. Need to know more data to answer the question
ans: B
66. An initially uncharged capacitor C is connected in series with resistor R. This combination is
then connected to a battery of emf V0 . Sufficient time elapses so that a steady state is reached.
Which of the following statements is NOT true?
A. The time constant is independent of V0
B. The final charge on C is independent of R
C. The total thermal energy generated by R is independent of R
D. The total thermal energy generated by R is independent of V0
E. The initial current (just after the battery was connected) is independent of C
ans: C
67. A certain capacitor, in series with a resistor, is being charged. At the end of 10 ms its charge
is half the final value. The time constant for the process is about:
A. 0.43 ms
B. 2.3 ms
C. 6.9 ms
D. 10 ms
E. 14 ms
ans: E
Chapter 27:
CIRCUITS
403
68. A certain capacitor, in series with a 720-Ω resistor, is being charged. At the end of 10 ms its
charge is half the final value. The capacitance is about:
A. 9.6 µF
B. 14 µF
C. 20 µF
D. 7.2 F
E. 10 F
ans: C
69. In the capacitor discharge formula q = q0 e−t/RC the symbol t represents:
A. the time constant
B. the time it takes for C to lose the fraction 1/e of its initial charge
C. the time it takes for C to lose the fraction (1 − 1/e) of its initial charge
D. the time it takes for C to lose essentially all of its initial charge
E. none of the above
ans: E
404
Chapter 27:
CIRCUITS
Chapter 28:
MAGNETIC FIELDS
1. Units of a magnetic field might be:
A. C·m/s
B. C·s/m
C. C/kg
D. kg/C·s
E. N/C·m
ans: D
2. In the formula F = qv × B:
A. F must be perpendicular to v but not necessarily to B
B. F must be perpendicular to B but not necessarily to v
C. v must be perpendicular to B but not necessarily to F
D. all three vectors must be mutually perpendicular
E. F must be perpendicular to both v and B
ans: E
3. An electron moves in the negative x direction, through a uniform magnetic field in the negative
y direction. The magnetic force on the electron is:
y
..
...
..
...
...
...
...
.
...
...
....
...
....
...
....
... .......
... .....
..
......................................................................................................................................
.. ...
.
.
.
.. ...
.
.
.
..
....
....
....
....
....
..
...
.
.
.
...
..
.
.
....
.
..
.
.
..
.
..
.
.
.
...
....
....
..
..
v
...........................•...
...
.
........
. B
x
z
A.
B.
C.
D.
E.
4. At
A.
B.
C.
D.
E.
in the negative x direction
in the positive y direction
in the negative y direction
in the positive z direction
in the negative z direction
ans: E
any point the magnetic field lines are in the direction of:
the magnetic force on a moving positive charge
the magnetic force on a moving negative charge
the velocity of a moving positive charge
the velocity of a moving negative charge
none of the above
ans: E
Chapter 28:
MAGNETIC FIELDS
405
5. The magnetic force on a charged particle is in the direction of its velocity if:
A. it is moving in the direction of the field
B. it is moving opposite to the direction of the field
C. it is moving perpendicular to the field
D. it is moving in some other direction
E. never
ans: E
6. A magnetic field exerts a force on a charged particle:
A. always
B. never
C. if the particle is moving across the field lines
D. if the particle is moving along the field lines
E. if the particle is at rest
ans: C
7. The direction of the magnetic field in a certain region of space is determined by firing a test
charge into the region with its velocity in various directions in different trials. The field direction
is:
A. one of the directions of the velocity when the magnetic force is zero
B. the direction of the velocity when the magnetic force is a maximum
C. the direction of the magnetic force
D. perpendicular to the velocity when the magnetic force is zero
E. none of the above
ans: A
8. An electron is moving north in a region where the magnetic field is south. The magnetic force
exerted on the electron is:
A. zero
B. up
C. down
D. east
E. west
ans: A
9. A magnetic field CANNOT:
A. exert a force on a charged particle
B. change the velocity of a charged particle
C. change the momentum of a charged particle
D. change the kinetic energy of a charged particle
E. change the trajectory of a charged particle
ans: D
406
Chapter 28:
MAGNETIC FIELDS
10. A proton (charge e), traveling perpendicular to a magnetic field, experiences the same force as
an alpha particle (charge 2e) which is also traveling perpendicular to the same field. The ratio
of their speeds, vproton /valpha , is:
A. 0.5
B. 1
C. 2
D. 4
E. 8
ans: C
11. A hydrogen atom that has lost its electron is moving east in a region where the magnetic field
is directed from south to north. It will be deflected:
A. up
B. down
C. north
D. south
E. not at all
ans: A
12. A beam of electrons is sent horizontally down the axis of a tube to strike a fluorescent screen
at the end of the tube. On the way, the electrons encounter a magnetic field directed vertically
downward. The spot on the screen will therefore be deflected:
A. upward
B. downward
C. to the right as seen from the electron source
D. to the left as seen from the electron source
E. not at all
ans: C
13. An electron (charge = −1.6 × 10−19 C) is moving at 3 × 105 m/s in the positive x direction. A
magnetic field of 0.8 T is in the positive z direction. The magnetic force on the electron is:
A. 0
B. 4 × 10−14 N, in the positive z direction
C. 4 × 10−14 N, in the negative z direction
D. 4 × 10−14 N, in the positive y direction
E. 4 × 10−14 N, in the negative y direction
ans: D
14. At one instant an electron (charge = −1.6×10−19 C) is moving in the xy plane, the components
of its velocity being vx = 5 × 105 m/s and vy = 3 × 105 m/s. A magnetic field of 0.8 T is in the
positive x direction. At that instant the magnitude of the magnetic force on the electron is:
A. 0
B. 2.6 × 10−14 N
C. 3.8 × 10−14 N
D. 6.4 × 10−14 N
E. 1.0 × 10−13 N
ans: C
Chapter 28:
MAGNETIC FIELDS
407
15. At one instant an electron (charge = −1.6×10−19 C) is moving in the xy plane, the components
of its velocity being vx = 5 × 105 m/s and vy = 3 × 105 m/s. A magnetic field of 0.8 T is in the
positive x direction. At that instant the magnitude of the magnetic force on the electron is:
A. 0
B. 3.8 × 10−14 N
C. 5.1 × 10−14 N
D. 6.4 × 10−14 N
E. 7.5 × 10−14 N
ans: B
16. An electron travels due north through a vacuum in a region of uniform magnetic field B that
is also directed due north. It will:
A. be unaffected by the field
B. speed up
C. slow down
D. follow a right-handed corkscrew path
E. follow a left-handed corkscrew path
ans: A
17. At one instant an electron is moving in the positive x direction along the x axis in a region
where there is a uniform magnetic field in the positive z direction. When viewed from a point
on the positive z axis, it subsequent motion is:
A. straight ahead
B. counterclockwise around a circle in the xy plane
C. clockwise around a circle in the xy plane
D. in the positive z direction
E. in the negative z direction
ans: B
18. A uniform magnetic field is directed into the page. A charged particle, moving in the plane of
the page, follows a clockwise spiral of decreasing radius as shown. A reasonable explanation is:
⊗
⊗
⊗
⊗
.................................
.........
....... .
.......
...... ..
......
............................... ...................
....
.
.
.
.
.
.
.
.
......
..
... ..........
.... ......
.
.
.
.
...
.
.
.
.
.
.
..
.
.
.
.
.
..
..
.
.
.
.
.
.
.
.
.
.
.....
...
... ..... ....
...
...
.....
.... .... .... ................ .... .... ....
..
..
..
.
... ... ... ...
..
.
.
..
.
...
..
..
.. .... .... ....
.. .... ....
.
....
... ....
..
...
...
.
.
.
.
.
....................
.
...
.
...
.
.
.
.
.
.
..
.
... .........
..... ....
...
...............................
...
.....
.....
......
......
.
.......
.
.
.
.
.
.............................
⊗
A.
B.
C.
D.
E.
408
⊗
MAGNETIC FIELDS
•
⊗
⊗
⊗
⊗
⊗
⊗
⊗
B
⊗
the charge is positive and slowing down
the charge is negative and slowing down
the charge is positive and speeding up
the charge is negative and speeding up
none of the above
ans: B
Chapter 28:
⊗
⊗
particle
19. An electron and a proton each travel with equal speeds around circular orbits in the same
uniform magnetic field, as shown in the diagram (not to scale). The field is into the page on
the diagram. Because the electron is less massive than the proton and because the electron is
negatively charged and the proton is positively charged:
•
•
.....................
.........
......
.....
...
....
...
..
...
.
...
.....
..
...
...
...
...
..
.
.
...
.
.
...
.
.
.
.
.....
.......
.....
............................
⊗
B
..............................
...............
.........
........
.......
.......
......
......
.....
.
.
.
.
....
....
.
....
.
..
.
...
.
..
...
.
.
...
...
.
...
..
...
.
...
....
..
...
..
..
...
..
..
...
..
...
..
.
...
....
...
...
...
.
...
..
...
...
...
...
...
...
...
.
....
..
....
...
......
.....
......
......
.......
......
.
.
.
.
.
..........
.
.
..........................................
A. the electron travels clockwise around the smaller circle and the proton travels counterclockwise around the larger circle
B. the electron travels counterclockwise around the smaller circle and the proton travels clockwise around the larger circle
C. the electron travels clockwise around the larger circle and the proton travels counterclockwise around the smaller circle
D. the electron travels counterclockwise around the larger circle and the proton travels clockwise around the smaller circle
E. the electron travels counterclockwise around the smaller circle and the proton travels counterclockwise around the larger circle
ans: A
20. An electron is launched with velocity v in a uniform magnetic field B. The angle θ between
v and B is between 0 and 90◦ . As a result, the electron follows a helix, its velocity vector v
returning to its initial value in a time interval of:
A. 2πm/eB
B. 2πmv/eB
C. 2πmv sin θ/eB
D. 2πmv cos θ/eB
E. none of these
ans: A
21. An electron and a proton are both initially moving with the same speed and in the same
direction at 90◦ to the same uniform magnetic field. They experience magnetic forces, which
are initially:
A. identical
B. equal in magnitude but opposite in direction
C. in the same direction and differing in magnitude by a factor of 1840
D. in opposite directions and differing in magnitude by a factor of 1840
E. equal in magnitude but perpendicular to each other.
ans: B
Chapter 28:
MAGNETIC FIELDS
409
22. An electron enters a region of uniform perpendicular E and B fields. It is observed that the
velocity v of the electron is unaffected. A possible explanation is:
A. v is parallel to E and has magnitude E/B
B. v is parallel to B
C. v is perpendicular to both E and B and has magnitude B/E
D. v is perpendicular to both E and B and has magnitude E/B
E. the given situation is impossible
ans: D
23. A charged particle is projected into a region of uniform, parallel, E and B fields. The force on
the particle is:
A. zero
B. at some angle < 90◦ with the field lines
C. along the field lines
D. perpendicular to the field lines
E. unknown (need to know the sign of the charge)
ans: B
24. A uniform magnetic field is in the positive z direction. A positively charged particle is moving
in the positive x direction through the field. The net force on the particle can be made zero
by applying an electric field in what direction?
A. Positive y
B. Negative y
C. Positive x
D. Negative x
E. Positive z
ans: B
25. An electron is traveling in the positive x direction. A uniform electric field E is in the negative
y direction. If a uniform magnetic field with the appropriate magnitude and direction also
exists in the region, the total force on the electron will be zero. The appropriate direction for
the magnetic field is:
y
v
•..........................
.
........
.E
A.
B.
C.
D.
E.
410
the positive y direction
the negative y direction
into the page
out of the page
the negative x direction
ans: C
Chapter 28:
MAGNETIC FIELDS
x
26. An ion with a charge of +3.2×10−19 C is in a region where a uniform electric field of 5×104 V/m
is perpendicular to a uniform magnetic field of 0.8 T. If its acceleration is zero then its speed
must be:
A. 0
B. 1.6 × 104 m/s
C. 4.0 × 104 m/s
D. 6.3 × 104 m/s
E. any value but 0
ans: D
27. The current is from left to right in the conductor shown. The magnetic field is into the page
and point S is at a higher potential than point T. The charge carriers are:
S
•
.....
...........................................................................
....
i
•
T
A.
B.
C.
D.
E.
positive
negative
neutral
absent
moving near the speed of light
ans: A
28. Electrons (mass m, charge −e) are accelerated from rest through a potential difference V and
are then deflected by a magnetic field B that is perpendicular to their velocity. The radius of
the resulting electron trajectory is:
0
A. ( √2eV /m)/B
B. B0 2eV /m
C. ( √2mV /e)/B
D. B 2mV /e
E. none of these
ans: C
29. In a certain mass spectrometer, an ion beam passes through a velocity filter consisting of
mutually perpendicular fields E and B. The beam then enters a region of another magnetic
field B perpendicular to the beam. The radius of curvature of the resulting ion beam is
proportional to:
A. EB /B
B. EB/B
C. BB /E
D. B/EB
E. E/BB
ans: E
Chapter 28:
MAGNETIC FIELDS
411
30. A cyclotron operates with a given magnetic field and at a given frequency. If R denotes the
radius of the final orbit, the final particle energy is proportional to:
A. 1/R
B. R
C. R2
D. R3
E. R4
ans: C
31. J. J. Thomson’s experiment, involving the motion of an electron beam in mutually perpendicular E and B fields, gave the value of:
A. mass of an electron
B. charge of an electron
C. Earth’s magnetic field
D. charge/mass ratio for electrons
E. Avogadro’s number
ans: D
32. The diagram shows a straight wire carrying a flow of electrons into the page. The wire is
between the poles of a permanent magnet. The direction of the magnetic force exerted on the
wire is:
N
A.
B.
C.
D.
E.
412
↑
↓
←
→
into the page
ans: A
Chapter 28:
MAGNETIC FIELDS
....
...... .......
..
.....
.... .....
.........
S
33. The figure shows the motion of electrons in a wire that is near the N pole of a magnet. The
wire will be pushed:
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
•••
...
...
...
•
...
•
...
•
...
•
•
•
•
•
...
•
•
•
...
•
•
•
•
•
•
•
...
•
•
•
...
••• •••••••••••
...
...
••• ••••••• .....................
...
...
...
..
...
•
.
.
.
.
•
.
.... ......
.
.
...
...
•••
..
...
...
.......
.............. ...
...
.
...
.......
.
...
....... .........
.......
...
.
.
.
.
.
.
.
.
.
.
.
.
...
...
...
.... ...........
.
.
.
.
.
.
.
.
.
.
...
.
.
... ......
.... .............
.
.
.
...
.
...........
.
.
... ......... ..
...
...
.......
..
.
...
...... . ......
....
...
...
...................... .......
.
...
... .........................................
...
.
.
...
.
. ...... .. .......
.
.
.
.
...
.
.......
....
.
.
.
.
.
.
.
.
.
.
.
.
.
.
... ........
....
....
.
.
.
.
.
.
.
.
.
.
.........
.
.
.
..
...
.......
.......
....... ................
.......
........
...
.......
..... .... ............ .... ....
.......
... .. ............
.........
...... ........
....
A.
B.
C.
D.
E.
electron
flow
toward the magnet
away from the magnet
downwards
upwards
along its length
ans: D
34. The diagram shows a straight wire carrying current i in a uniform magnetic field. The magnetic
force on the wire is indicated by an arrow but the magnetic field is not shown. Of the following
possibilities, the direction of the magnetic field is:
i
..
.......................................................................
..
...
...
...
...
...
...
...
.
..........
.......
...
A.
B.
C.
D.
E.
F
opposite the direction of the current
opposite the direction of F
in the direction of F
into the page
out of the page
ans: E
Chapter 28:
MAGNETIC FIELDS
413
35. The figure shows a uniform magnetic field B directed to the left and a wire carrying a current
into the page. The magnetic force acting on the wire is:
....
...................................................................................................................................................................................................................
....
....
...................................................................................................................................................................................................................
....
B
i
....
...................................................................................................................................................................................................................
....
....
...................................................................................................................................................................................................................
....
A.
B.
C.
D.
E.
toward
toward
toward
toward
zero
ans: A
the
the
the
the
top of the page
bottom of the page
left
right
36. A loop of wire carrying a current of 2.0 A is in the shape of a right triangle with two equal sides,
each 15 cm long. A 0.7 T uniform magnetic field is parallel to the hypotenuse. The resultant
magnetic force on the two equal sides has a magnitude of:
A. 0
B. 0.21 N
C. 0.30 N
D. 0.41 N
E. 0.51 N
ans: A
37. A loop of wire carrying a current of 2.0 A is in the shape of a right triangle with two equal
sides, each 15 cm long. A 0.7 T uniform magnetic field is in the plane of the triangle and is
perpendicular to the hypotenuse. The magnetic force on either of the two equal sides has a
magnitude of:
A. zero
B. 0.105 N
C. 0.15 N
D. 0.21 N
E. 0.25 N
ans: C
38. A current is clockwise around the outside edge of this page and a uniform magnetic field is
directed parallel to the page, from left to right. If the magnetic force is the only force acting
on the page, the page will turn so the right edge:
A. moves toward you
B. moves away from you
C. moves to your right
D. moves to your left
E. does not move
ans: A
414
Chapter 28:
MAGNETIC FIELDS
39. A square loop of wire lies in the plane of the page and carries a current I as shown. There is a
uniform magnetic field B parallel to the side MK as indicated. The loop will tend to rotate:
R
.
.
K .......................................................................................... L
...
...
...
...
..
..
..
..
.
..
.. B ....
..
...
..
..
..
...
..
..
..
... Q
..
..
P ...
..
..
..
..
.. .........
..
....
.... I
..
..
I .....
...
..
..
..
.
..
..
..
................................................................................
.
.
M
N
.
.
S
A.
B.
C.
D.
E.
about PQ with KL coming out of the page
about PQ with KL going into the page
about RS with MK coming out of the page
about RS with MK going into the page
about an axis perpendicular to the page.
ans: A
40. The units of magnetic dipole moment are:
A. ampere
B. ampere·meter
C. ampere·meter2
D. ampere/meter
E. ampere/meter2
ans: C
41. You are facing a loop of wire which carries a clockwise current of 3.0 A and which surrounds
an area of 5.8 × 10−2 m2 . The magnetic dipole moment of the loop is:
A. 3.0 A · m2 , away from you
B. 3.0 A · m2 , toward you
C. 0.17 A · m2 , away from you
D. 0.17 A · m2 , toward you
E. 0.17 A · m2 , left to right
ans: C
42. The magnetic torque exerted on a flat current-carrying loop of wire by a uniform magnetic
field B is:
A. maximum when the plane of the loop is perpendicular to B
B. maximum when the plane of the loop is parallel to B
C. dependent on the shape of the loop for a fixed loop area
D. independent of the orientation of the loop
E. such as to rotate the loop around the magnetic field lines
ans: B
Chapter 28:
MAGNETIC FIELDS
415
43. A circular loop of wire with a radius of 20 cm lies in the xy plane and carries a current of 2 A,
counterclockwise when viewed from a point on the positive z axis. Its magnetic dipole moment
is:
A. 0.25 A · m2 , in the positive z direction
B. 0.25 A · m2 , in the negative z direction
C. 2.5 A · m2 , in the positive z direction
D. 2.5 A · m2 , in the negative z direction
E. 0.25 A · m2 , in the xy plane
ans: A
44. The diagrams show five possible orientations of a magnetic dipole µ in a uniform magnetic field
B. For which of these does the magnetic torque on the dipole have the greatest magnitude?
. µ
....... .......
........................................
................................................ B
..
A
µ
.............................
..
........................................................................................
..
B
µ .........
..
.....
....
..
........................................................................................
..
B
B
C
........ µ
......
.....
..
..
........................................................................................
..
B
D
µ
............................
..
........................................................................................
..
B
E
ans: A
45. The magnetic dipole moment of a current-carrying loop of wire is in the positive z direction.
If a uniform magnetic field is in the positive x direction the magnetic torque on the loop is:
A. 0
B. in the positive y direction
C. in the negative y direction
D. in the positive z direction
E. in the negative z direction
ans: B
46. For a loop of current-carrying wire in a uniform magnetic field the potential energy is a minimum
if the magnetic dipole moment of the loop is:
A. in the same direction as the field
B. in the direction opposite to that of the field
C. perpendicular to the field
D. at an angle of 45◦ to the field
E. none of the above
ans: A
47. The diagrams show five possible orientations of a magnetic dipole µ in a uniform magnetic field
B. For which of these is the potential energy the greatest?
. µ
...... ........
........................................
............................................... B
..
A
µ
.............................
..
........................................................................................
..
B
B
ans: E
416
Chapter 28:
µ .........
..
.....
....
..
........................................................................................
..
MAGNETIC FIELDS
C
B
........ µ
......
.....
..
..
........................................................................................
..
D
B
µ
............................
..
........................................................................................
..
E
B
48. A loop of current-carrying wire has a magnetic dipole moment of 5 × 10−4 A · m2 . The moment
initially is aligned with a 0.5-T magnetic field. To rotate the loop so its dipole moment is
perpendicular to the field and hold it in that orientation, you must do work of:
A. 0
B. 2.5 × 10−4 J
C. −2.5 × 10−4 J
D. 1.0 × 10−3 J
E. −1.0 × 10−3 J
ans: B
Chapter 28:
MAGNETIC FIELDS
417
Chapter 29:
MAGNETIC FIELDS DUE TO CURRENTS
1. Suitable units for µ0 are:
A. tesla
B. newton/ampere2
C. weber/meter
D. kilogram·ampere/meter
E. tesla·meter/ampere
ans: E
2. A “coulomb” is:
A. one ampere per second
B. the quantity of charge that will exert a force of 1 N on a similar charge at a distance of 1 m
C. the amount of current in each of two long parallel wires, separated by 1 m, that produces
a force of 2 × 10−7 N/m
D. the amount of charge that flows past a point in one second when the current is 1 A
E. an abbreviation for a certain combination of kilogram, meter and second
ans: D
3. Electrons are going around a circle in a counterclockwise direction as shown. At the center of
the circle they produce a magnetic field that is:
..........
................ ...........................
.......
......
......
....
.
.
.
.
.
...
...
....
...
...
.
...
..
.
..
...
....
...
..............
.....
....
.
... ....
...
...........
..
...
...
...
..
.
.
...
.
...
...
....
...
.....
....
......
......
.
.
.
........
.
.
........................................
− electron
A.
B.
C.
D.
E.
418
into the page
out of the page
to the left
to the right
zero
ans: A
Chapter 29:
MAGNETIC FIELDS DUE TO CURRENTS
4. In the figure, the current element i df, the point P, and the three vectors (1, 2, 3) are all in the
plane of the page. The direction of dB, due to this current element, at the point P is:
3...
..
....
.......
..........
..
...
..
.
...
...
....
.
...
..................
...
... ..
.
.
...
.
.
...
....
....
...
...
...
....
...
.
...
.
.
...
....
...
...
...
...
....
...
.
...
.
... .......
.... .....
..
.................................................................................................................
..
i
................................................ ......
... ...
...
...
.... ....
.......................................
.
.
.
..
.
... ................................................... .....
df
2
•
P
A.
B.
C.
D.
E.
1
in the direction marked “1”
in the direction marked “2”
in the direction marked “3”
out of the page
into the page
ans: E
5. The magnitude of the magnetic field at point P, at the center of the semicircle shown, is given
by:
.. i
...................................
.
.
.
.
.
.
.....
...
...
..........
...
.. . ..............
...
...
....
..
....
.. ..
........................................ R ....•...
....................................
P
A.
B.
C.
D.
E.
2µ0 i/R
µ0 i/R
µ0 i/4πR
µ0 i/2R
µ0 i/4R
ans: E
Chapter 29:
MAGNETIC FIELDS DUE TO CURRENTS
419
6. The diagrams show three circuits consisting of concentric circular arcs (either half or quarter
circles of radii r, 2r, and 3r) and radial lengths. The circuits carry the same current. Rank
them according to the magnitudes of the magnetic fields they produce at C, least to greatest.
..............................
............
.......
.......
......
......
.....
.....
.....
.
.
.
....
...
.
.
...
...
...
.
.
...
.
.
.
...
....
...
...
...
...
..
..
...
..................................... ...
.................................................. ..
.
...
.
.
.
...
.
.
.
.....
........................
1
C
•
A.
B.
C.
D.
E.
..............................
............
.......
.......
......
......
.....
.....
.....
.
.
.
....
...
.
.
...
...
...
.
.
...
.
.
.
...
....
...
........................
.
.
.
.
...
...
...
...
.
.
...
..
...
..
...
....
..
..................................... .
................................................. ..
2
•
C
..............................
............
.......
.......
......
......
.....
.....
.....
.
.
.
....
.....
.
.
.
.
.
...
.
.
.
.
.
.
.
.
.
.
...
..
......
.
...
.
...
.
.
.
.
.
...
....
...
.
.
.
.
.
...
..
...
.
.
.
....
.........
.
...
.....
...
....
...
...
...
...
..
...
...
...
....................................... ....
....................
3
•
C
1, 2, 3
3, 2, 1
1, 3, 2
2, 3, 1
2, 1, 3
ans: B
7. Lines of the magnetic field produced by a long straight wire carrying a current are:
A. in the direction of the current
B. opposite to the direction of the current
C. radially outward from the wire
D. radially inward toward the wire
E. circles that are concentric with the wire
ans: E
8. In an overhead straight wire, the current is north. The magnetic field due to this current, at
our point of observation, is:
A. east
B. up
C. north
D. down
E. west
ans: E
9. A wire carrying a large current i from east to west is placed over an ordinary magnetic compass.
The end of the compass needle marked “N” will point:
A. north
B. south
C. east
D. west
E. the compass will act as an electric motor, hence the needle will keep rotating
ans: B
420
Chapter 29:
MAGNETIC FIELDS DUE TO CURRENTS
10. The magnetic field outside a long straight current-carrying wire depends on the distance R
from the wire axis according to:
A. R
B. 1/R
C. 1/R2
D. 1/R3
E. 1/R3/2
ans: B
11. Which graph correctly gives the magnitude of the magnetic field outside an infinitely long
straight current-carrying wire as a function of the distance r from the wire?
B
B
.
..
.
..
...
.
.
..
....
.
.
.
.
.
...........
r
A
B.
...
...
...
....
....
.....
......
..........
D
B
..
....
.
.
...
.....
.
.
.
...
.....
.
.
.
.
...
r
B
r
..........
......
.
.
.
...
...
.
.
...
..
.
.
r
C
B ..
.....
.....
.....
.....
.....
.....
.....
..
r
E
ans: D
12. The magnetic field a distance 2 cm from a long straight current-carrying wire is 2.0 × 10−5 T.
The current in the wire is:
A. 0.16 A
B. 1.0 A
C. 2.0 A
D. 4.0 A
E. 25 A
ans: C
13. Two long parallel straight wires carry equal currents in opposite directions. At a point midway
between the wires, the magnetic field they produce is:
A. zero
B. non-zero and along a line connecting the wires
C. non-zero and parallel to the wires
D. non-zero and perpendicular to the plane of the two wires
E. none of the above
ans: D
Chapter 29:
MAGNETIC FIELDS DUE TO CURRENTS
421
14. Two long straight wires are parallel and carry current in the same direction. The currents are
8.0 and 12 A and the wires are separated by 0.40 cm. The magnetic field in tesla at a point
midway between the wires is:
A. 0
B. 4.0 × 10−4
C. 8.0 × 10−4
D. 12 × 10−4
E. 20 × 10−4
ans: B
15. Two long straight wires are parallel and carry current in opposite directions. The currents are
8.0 and 12 A and the wires are separated by 0.40 cm. The magnetic field in tesla at a point
midway between the wires is:
A. 0
B. 4.0 × 10−4
C. 8.0 × 10−4
D. 12 × 10−4
E. 20 × 10−4
ans: E
16. Two long straight current-carrying parallel wires cross the x axis and carry currents I and 3I
in the same direction, as shown. At what value of x is the net magnetic field zero?
x
0
1
3
.
......
........
....
A.
B.
C.
D.
E.
422
I
4
5
7
.
......
........
....
3I
0
1
3
5
7
ans: C
Chapter 29:
MAGNETIC FIELDS DUE TO CURRENTS
17. Two long straight wires pierce the plane of the paper at vertices of an equilateral triangle as
shown below. They each carry 2 A, out of the paper. The magnetic field at the third vertex
(P) has magnitude (in T):
P
....
... ...
... ....
...
...
.
...
...
...
..
...
...
.
...
.
...
...
.
...
..
.
...
.
.
...
.
..
...
.
.
...
...
.
...
.
.
.
...
...
...
.
.
...
.
.
.•
..
.•
.
•
•
•
•
.•
•
•
•
•
•
•
.
•
•
•
•
.•
•
•
•
•
•
•
•
•
•
•
•
•
•
..•
.•
•
•
•
•
•
•
•
•
•
•
.•
.•
..•
......................................................................................•
•
•
•
•
•
•
•
•
•
•
•
•
•
4 cm
2 A •••••••••••••••••••••••
A.
B.
C.
D.
E.
4 cm
4 cm
• 2A
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
1.0 × 10−5
1.7 × 10−5
2.0 × 10−5
5.0 × 10−6
8.7 × 10−6
ans: B
18. The diagram shows three equally spaced wires that are perpendicular to the page. The currents
are all equal, two being out of the page and one being into the page. Rank the wires according
to the magnitudes of the magnetic forces on them, from least to greatest.
.................
...
..
....
.
.... ......
.........
.................
...
..
....
.
.... ......
.........
.................
...
..
....
.
.... ......
.........
1
2
3
·
A.
B.
C.
D.
E.
×
·
1, 2, 3
2, 1 and 3 tie
2 and 3 tie, then 1
1 and 3 tie, then 2
3, 2, 1
ans: B
19. Two parallel wires carrying equal currents of 10 A attract each other with a force of 1 mN. If
both currents are doubled, the force of attraction will be:
A. 1 mN
B. 4 mN
C. 0.5 mN
D. 0.25 mN
E. 2 mN
ans: B
Chapter 29:
MAGNETIC FIELDS DUE TO CURRENTS
423
20. Two parallel long wires carry the same current and repel each other with a force F per unit
length. If both these currents are doubled and the wire separation tripled, the force per unit
length becomes:
A. 2F/9
B. 4F/9
C. 2F/3
D. 4F/3
E. 6F
ans: D
21. Two parallel wires, 4 cm apart, carry currents of 2 A and 4 A respectively, in the same direction.
The force per unit length in N/m of one wire on the other is:
A. 1 × 10−3 , repulsive
B. 1 × 10−3 , attractive
C. 4 × 10−5 , repulsive
D. 4 × 10−5 , attractive
E. none of these
ans: D
22. Two parallel wires, 4 cm apart, carry currents of 2 A and 4 A respectively, in opposite directions.
The force per unit length in N/m of one wire on the other is:
A. 1 × 10−3 , repulsive
B. 1 × 10−3 , attractive
C. 4 × 10−5 , repulsive
D. 4 × 10−5 , attractive
E. none of these
ans: C
23. Four long straight wires carry equal currents into the page as shown. The magnetic force
exerted on wire F is:
F
A.
B.
C.
D.
E.
424
north
east
south
west
zero
ans: B
Chapter 29:
N
W
E
S
MAGNETIC FIELDS DUE TO CURRENTS
24. A constant current is sent through a helical coil. The coil:
A. tends to get shorter
B. tends to get longer
C. tends to rotate about its axis
D. produces zero magnetic field at its center
E. none of the above
ans: A
25. The diagram shows three arrangements of circular loops, centered on vertical axes and carrying identical currents in the directions indicated. Rank the arrangements according to the
magnitudes of the magnetic fields at the midpoints between the loops on the central axes.
............................................
.......
....
...
...
.....
..
....
...
.
.......
.
.
.
............................................
.....
•
A.
B.
C.
D.
E.
............................................
.......
....
...
...
.....
..
....
...
.
.......
.
.
.
............................................
.....
•
..........
................... ..........................
........
............................. .......
...... .............
...... ....
.... ..
.... ......
..
.
..... .....
...
..
... ....
.. ....
.
.
.... .......
.
.
.
...
. ...
......
.
......... ............................................. .............
.................................................
......
•
...........................................
.......
....
...
....
.
.....
...
....
....
.......
.
.
.
.
.
.........................................
......
...........................................
.......
....
...
....
.
.....
...
....
....
....... .
.
.
.
.
.
.........................................
.
.
...
...........................................
.......
....
...
....
.
.....
...
....
....
.......
.
.
.
.
.
.........................................
......
1
2
3
1, 2, 3
2, 1, 3
2, 3, 1
3, 2, 1
3, 1, 2
ans: C
26. Helmholtz coils are commonly used in the laboratory because the magnetic field between them:
A. can be varied more easily than the fields of other current arrangements
B. is especially strong
C. nearly cancels Earth’s magnetic field
D. is parallel to the plane of the coils
E. is nearly uniform
ans: E
27. If the radius of a pair of Helmholtz coils is R then the distance between the coils is:
A. R/4
B. R/2
C. R
D. 2R
E. 4R
ans: C
Chapter 29:
MAGNETIC FIELDS DUE TO CURRENTS
425
28. If R is the distance from a magnetic dipole, then the magnetic field it produces is proportional
to:
A. R
B. 1/R
C. R2
D. 1/R2
E. 1/R3
ans: E
29. A square loop of current-carrying wire with edge length a is in the xy plane, the origin being
at its center. Along which of the following lines can a charge move without experiencing a
magnetic force?
A. x = 0, y = a/2
B. x = a/2, y = a/2
C. x = a/2, y = 0
D. x = 0, y = 0
E. x = 0, z = 0
ans: D
30. In Ampere’s law, B · ds = µ0 i, the integration must be over any:
A. surface
B. closed surface
C. path
D. closed path
E. closed path that surrounds all the current producing B
ans: D
31. In Ampere’s law, B · ds = µ0 i, the symbol ds is:
A. an infinitesimal piece of the wire that carries current i
B. in the direction of B
C. perpendicular to B
D. a vector whose magnitude is the length of the wire that carries current i
E. none of the above
ans: E
32. In Ampere’s law, B · ds = µ0 i, the direction of the integration around the path:
A. must be clockwise
B. must be counterclockwise
C. must be such as to follow the magnetic field lines
D. must be along the wire in the direction of the current
E. none of the above
ans: E
426
Chapter 29:
MAGNETIC FIELDS DUE TO CURRENTS
33. A long straight wire carrying a 3.0 A current enters a room through a window 1.5 m high and
1.0 m wide. The path integral B · ds around the window frame has the value (in T·m):
A. 0.20
B. 2.5 × 10−7
C. 3.0 × 10−7
D. 3.8 × 10−6
E. none of these
ans: D
34. Two long straight wires enter a room through a door. One carries a current of 3.0 A into
the
room while the other carries a current of 5.0 A out. The magnitude of the path integral B · ds
around the door frame is:
A. 2.5 × 10−6 T · m
B. 3.8 × 10−6 T · m
C. 6.3 × 10−6 T · m
D. 1.0 × 10−5 T · m
E. none of these
ans: A
35. If the magnetic field B is uniform over the area bounded by a circle with radius R, the net
current through the circle is:
A. 0
B. 2πRB/µ0
C. πR2 B/µ0
D. RB/2µ0
E. 2RB/µ0
ans: A
36. The magnetic field at any point is given by B = Ar × k̂, where r is the position vector of the
point and A is a constant. The net current through a circle of radius R, in the xy plane and
centered at the origin is given by:
A. πAR2 /µ0
B. 2πAR/µ0
C. 4πAR3 /3µ0
D. 2πAR2 /µ0
E. πAR2 /2µ0
ans: D
Chapter 29:
MAGNETIC FIELDS DUE TO CURRENTS
427
37. A hollow cylindrical conductor (inner radius = a, outer radius = b) carries a current i uniformly
spread over its cross section. Which graph below correctly gives B as a function of the distance
r from the center of the cylinder?
B
B ...............................
...
...
...
...
...
...
...
..................................
..
...
..
...
...
..
...
..
...
..
....
..
........
r
a
b
B
r
a
b
.........
.... .....
.
.
.
...
..
...
...
...
....
..
......
..
..... r
a
b
B
A
B
.....
... ....
.
.
... .....
...
...
.
.
.
...
...
....
.
.
.
........
...
r
a
b
D
C
B
.....................................
...
...
.
.
.
...
...
.
...
.
.
.
...
..
.
....
.
..
.......
.
.
... r
..
a
b
E
ans: C
38. A long straight cylindrical shell carries current i parallel to its axis and uniformly distributed
over its cross section. The magnitude of the magnetic field is greatest:
A. at the inner surface of the shell
B. at the outer surface of the shell
C. inside the shell near the middle
D. in hollow region near the inner surface of the shell
E. near the center of the hollow region
ans: B
39. A long straight cylindrical shell has inner radius Ri and outer radius Ro . It carries current
i, uniformly distributed over its cross section. A wire is parallel to the cylinder axis, in the
hollow region (r < Ri ). The magnetic field is zero everywhere outside the shell (r > Ro ). We
conclude that the wire:
A. is on the cylinder axis and carries current i in the same direction as the current in the shell
B. may be anywhere in the hollow region but must be carrying current i in the direction
opposite to that of the current in the shell
C. may be anywhere in the hollow region but must be carrying current i in the same direction
as the current in the shell
D. is on the cylinder axis and carries current i in the direction opposite to that of the current
in the shell
E. does not carry any current
ans: D
428
Chapter 29:
MAGNETIC FIELDS DUE TO CURRENTS
40. A long straight cylindrical shell has inner radius Ri and outer radius Ro . It carries a current i,
uniformly distributed over its cross section. A wire is parallel to the cylinder axis, in the hollow
region (r < Ri ). The magnetic field is zero everywhere in the hollow region. We conclude that
the wire:
A. is on the cylinder axis and carries current i in the same direction as the current in the shell
B. may be anywhere in the hollow region but must be carrying current i in the direction
opposite to that of the current in the shell
C. may be anywhere in the hollow region but must be carrying current i in the same direction
as the current in the shell
D. is on the cylinder axis and carries current i in the direction opposite to that of the current
in the shell
E. does not carry any current
ans: E
41. The magnetic field B inside a long ideal solenoid is independent of:
A. the current
B. the core material
C. the spacing of the windings
D. the cross-sectional area of the solenoid
E. the direction of the current
ans: D
42. Two long ideal solenoids (with radii 20 mm and 30 mm, respectively) have the same number
of turns of wire per unit length. The smaller solenoid is mounted inside the larger, along a
common axis. The magnetic field within the inner solenoid is zero. The current in the inner
solenoid must be:
A. two-thirds the current in the outer solenoid
B. one-third the current in the outer solenoid
C. twice the current in the outer solenoid
D. half the current in the outer solenoid
E. the same as the current in the outer solenoid
ans: E
43. Magnetic field lines inside the solenoid shown are:
.........................................
.............
.......
.......
....
....
...
.....
.
....
...........
..... ....
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
...............................................
............................................................................................................................
.......
..
.
......
.......
..... .......
...... ...
..... ...
... .......
....................
.
....... .
....... ..................... .................................. ...............
......
.........................
..
.
.
.
...
..
... .. .
.... ......................................................................... ..........
..
...
...
............
........
........ ....
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.................................................................................... ................................... .................................
..
....
...
..
..
.....
..
.....
...
.
.
........
.
.
.
.
..................... .......................
..........
I
I
A.
B.
C.
D.
E.
clockwise circles as one looks down the axis from the top of the page
counterclockwise circles as one looks down the axis from the top of the page
toward the top of the page
toward the bottom of the page
in no direction since B = 0
ans: C
Chapter 29:
MAGNETIC FIELDS DUE TO CURRENTS
429
44. Solenoid 2 has twice the radius and six times the number of turns per unit length as solenoid
1. The ratio of the magnetic field in the interior of 2 to that in the interior of 1 is:
A. 2
B. 4
C. 6
D. 1
E. 1/3
ans: C
45. A solenoid is 3.0 cm long and has a radius of 0.50 cm. It is wrapped with 500 turns of wire
carrying a current of 2.0 A. The magnetic field at the center of the solenoid is:
A. 9.9 × 10−8 T
B. 1.3 × 10−3 T
C. 4.2 × 10−2 T
D. 16 T
E. 20 T
ans: C
46. A toroid with a square cross section carries current i. The magnetic field has its largest
magnitude:
A. at the center of the hole
B. just inside the toroid at its inner surface
C. just inside the toroid at its outer surface
D. at any point inside (the field is uniform)
E. none of the above
ans: B
47. A toroid has a square cross section with the length of an edge equal to the radius of the inner
surface. The ratio of the magnitude of the magnetic field at the inner surface to the magnitude
of the field at the outer surface is:
A. 1/4
B. 1/2
C. 1
D. 2
E. 4
ans: D
430
Chapter 29:
MAGNETIC FIELDS DUE TO CURRENTS
Chapter 30:
INDUCTION AND INDUCTANCE
1. The normal to a certain 1-m2 area makes an angle of 60◦ with a uniform magnetic field.
The magnetic flux through this area is the same as the flux through a second area that is
perpendicular to the field if the second area is:
A. 0.866 m2
B. 1.15 m2
C. 0.5 m2
D. 2 m2
E. 1 m2
ans: C
2. Suppose this page is perpendicular to a uniform magnetic field and the magnetic flux through
it is 5 Wb. If the page is turned by 30◦ around an edge the flux through it will be:
A. 2.5 Wb
B. 4.3 Wb
C. 5 Wb
D. 5.8 Wb
E. 10 Wb
ans: B
3. A 2-T uniform magnetic field makes an angle of 30◦ with the z axis. The magnetic flux through
a 3-m2 portion of the xy plane is:
A. 2.0 Wb
B. 3.0 Wb
C. 5.2 Wb
D. 6.0 Wb
E. 12 Wb
ans: C
4. A uniform magnetic field makes an angle of 30◦ with the z axis. If the magnetic flux through
a 1-m2 portion of the xy plane is 5 Wb then the magnetic flux through a 2-m2 portion of the
same plane is:
A. 2.5 Wb
B. 4.3 Wb
C. 5 Wb
D. 5.8 Wb
E. 10 Wb
ans: E
5. 1 weber is the same as:
A. 1 V/s
B. 1 T/s
C. 1 T/m
D. 1 T · m2
2
E. 1 T/m
ans: D
Chapter 30:
INDUCTION AND INDUCTANCE
431
6. 1 weber is the same as:
A. 1 V · s
B. 1 T · s
C. 1 T/m
D. 1 V/s
E. 1 T/m2
ans: A
7. The units of motional emf are:
A. volt/second
B. volt·meter/second
C. volt/tesla
D. tesla/second
E. tesla·meter2 /second
ans: E
8. Faraday’s law states that an induced emf is proportional to:
A. the rate of change of the magnetic field
B. the rate of change of the electric field
C. the rate of change of the magnetic flux
D. the rate of change of the electric flux
E. zero
ans: C
9. The emf that appears in Faraday’s law is:
A. around a conducting circuit
B. around the boundary of the surface used to compute the magnetic flux
C. throughout the surface used to compute the magnetic flux
D. perpendicular to the surface used to compute the magnetic flux
E. none of the above
ans: B
10. If the magnetic flux through a certain region is changing with time:
A. energy must be dissipated as heat
B. an electric field must exist at the boundary
C. a current must flow around the boundary
D. an emf must exist around the boundary
E. a magnetic field must exist at the boundary
ans: D
432
Chapter 30:
INDUCTION AND INDUCTANCE
11. A square loop of wire lies in the plane of the page. A decreasing magnetic field is directed into
the page. The induced current in the loop is:
A. counterclockwise
B. clockwise
C. zero
D. up the left edge and from right to left along the top edge
E. through the middle of the page
ans: B
12. As an externally generated magnetic field through a certain conducting loop increases in magnitude, the field produced at points inside the loop by the current induced in the loop must
be:
A. increasing in magnitude
B. decreasing in magnitude
C. in the same direction as the applied field
D. directed opposite to the applied field
E. perpendicular to the applied field
ans: D
13. At any instant of time the total magnetic flux through a stationary conducting loop is less in
magnitude than the flux associated with an externally applied field. This might occur because:
A. the applied field is normal to the loop and increasing in magnitude
B. the applied field is normal to the loop and decreasing in magnitude
C. the applied field is parallel to the plane of the loop and increasing in magnitude
D. the applied field is parallel to the plane of the loop and decreasing in magnitude
E. the applied field is tangent to the loop
ans: A
14. A long straight wire is in the plane of a rectangular conducting loop. The straight wire carries
a constant current i, as shown. While the wire is being moved toward the rectangle the current
in the rectangle is:
i
A.
B.
C.
D.
E.
..
......
... ...
zero
clockwise
counterclockwise
clockwise in the left side and counterclockwise in the right side
counterclockwise in the left side and clockwise in the right side
ans: C
Chapter 30:
INDUCTION AND INDUCTANCE
433
15. A long straight wire is in the plane of a rectangular conducting loop. The straight wire carries
an increasing current in the direction shown. The current in the rectangle is:
i
A.
B.
C.
D.
E.
.....
.. ..
.. ..
zero
clockwise
counterclockwise
clockwise in the left side and counterclockwise in the right side
counterclockwise in the left side and clockwise in the right side
ans: C
16. A long straight wire is in the plane of a rectangular conducting loop. The straight wire initially
carries a constant current i in the direction shown. While the current i is being shut off, the
current in the rectangle is:
i
A.
B.
C.
D.
E.
434
....
.....
.. ..
zero
clockwise
counterclockwise
clockwise in the left side and counterclockwise in the right side
counterclockwise in the left side and clockwise in the right side
ans: B
Chapter 30:
INDUCTION AND INDUCTANCE
17. A rectangular loop of wire is placed midway between two long straight parallel conductors as
shown. The conductors carry currents i 1 and i2 , as indicated. If i1 is increasing and i2 is
constant, then the induced current in the loop is:
.....
i1 ........
A.
B.
C.
D.
E.
...
.....
... ..
i2
zero
clockwise
counterclockwise
depends on i1 − i2
depends on i1 + i2
ans: C
18. You push a permanent magnet with its north pole away from you toward a loop of conducting
wire in front of you. Before the north pole enters the loop the current in the loop is:
A. zero
B. clockwise
C. counterclockwise
D. to your left
E. to your right
ans: C
19. A vertical bar magnet is dropped through the center of a horizontal loop of wire, with its north
pole leading. At the instant when the midpoint of the magnet is in the plane of the loop, the
induced current at point P, viewed from above, is:
A. maximum and clockwise
B. maximum and counterclockwise
C. not maximum but clockwise
D. not maximum but counterclockwise
E. essentially zero
ans: E
20. A circular loop of wire rotates about a diameter in a magnetic field that is perpendicular to
the axis of rotation. Looking in the direction of the field at the loop the induced current is:
A. always clockwise
B. always counterclockwise
C. clockwise in the lower half of the loop and counterclockwise in the upper half
D. clockwise in the upper half of the loop and counterclockwise in the lower half
E. sometimes clockwise and sometimes counterclockwise
ans: E
Chapter 30:
INDUCTION AND INDUCTANCE
435
21. In the experiment shown:
....
S..............
.......................................
.. ........ ........ ........ .....
...
.............................•
.•
............................................. •
... .. ... .. ... .. •
.
....
...... ...... ...... ...
.
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
....
.
.
............................................................................................................................................................................................
..
...
..
..
A.
B.
C.
D.
E.
......... ......... ......... .........
•......... ...................... ...................... ...................... •.................................................. ......
..
...
...
...
..
...
.........
.
.
.
.
.
.
...
.
.
...
...
.
...
...
.
..
..
...
.
...
..
...
...
..
.
...
.
.
...... ......
..........
...
...
...
...
...
...
...
...
..
.........................................................................................................................
G
there is a steady reading in G as long as S is closed
a motional emf is generated when S is closed
the current in the battery goes through G
there is a current in G just after S is opened or closed
since the two loops are not connected, the current in G is always zero
ans: D
22. The emf developed in a coil X due to the current in a neighboring coil Y is proportional to the:
A. magnetic field in X
B. rate of change of magnetic field in X
C. resistance of X
D. thickness of the wire in X
E. current in Y
ans: B
23. One hundred turns of insulated copper wire are wrapped around an iron core of cross-sectional
area 0.100 m2 . The circuit is completed by connecting the coil to a 10-Ω resistor. As the
magnetic field along the coil axis changes from 1.00 T in one direction to 1.00 T in the other
direction, the total charge that flows through the resistor is:
A. 10−2 C
B. 2 × 10−2 C
C. 1 C
D. 2 C
E. 0.20 C
ans: D
436
Chapter 30:
INDUCTION AND INDUCTANCE
24. In the circuit shown, there will be a non-zero reading in galvanometer G:
.............................................................................................................................
..
..
....
...
...
.
....
.........
...
..
...
.
...
.........................
........ ..
....
.
.
.
.
.
.
.
.
.
.
.
.
.
.....................
...
..
..
................................
....
..
..
...
...
........
.
....
..
....
.
.
.
.
.
....
..
...
....
....
.
...
...................................... ...
............................ ..
•
•
A.
B.
C.
D.
E.
S
•
•
.....................................................................................................
..
..
....
...
...
.
...
....
.
.
.
.
...
.
.
...
....
.
..........
.................
.
.
.
.
.
.
....
....
.
...................
.
...
..
.................
.
..
...
..................
...
...
... .............
...
.....
.
....................
..................
...
...
.....
...
.....
...
....
...
..
...
..
.......................................................................... ....
•
G
•
only just after S is closed
only just after S is opened
only while S is kept closed
never
only just after S is opened or closed
ans: E
25. A magnet moves inside a coil. Consider the following factors:
I. strength of the magnet
II. number of turns in the coil
III. speed at which the magnet moves
Which can affect the emf induced in the coil?
A. I only
B. II only
C. III only
D. I and II only
E. I, II, III
ans: E
26. The graph shows the magnitude B of a uniform magnetic field that is perpendicular to the
plane of a conducting loop. Rank the five regions indicated on the graph according to the
magnitude of the emf induced in the loop, from least to greatest.
B
2
.........................................................
.
.
.....
...
..... 3
...
.
.....
.
..
.....
.
.
1....
.....
.
.....
.
..
.....
.
.
.
.
.......
..
........ 4
.
.
.
.
........
..
........
.
.
........
.
....
...
t
A.
B.
C.
D.
E.
1, 2, 3,
2, 4, 3,
4, 3, 1,
1, 3, 4,
4, 3, 2,
ans: B
4
1
2
2
1
Chapter 30:
INDUCTION AND INDUCTANCE
437
27. The circuit shown is in a uniform magnetic field that is into the page. The current in the circuit
is 0.20 A. At what rate is the magnitude of the magnetic field changing? Is it increasing or
decreasing?:
←−− 12 cm −−→
↑
|
|
12 cm
|
|
↓
.. .. ..
...................................................................................................... ..
...
...
.. .. ..
...
...
...
...
....
....
...
...
...
...
...
...
...
...
...
...
.....
.....
...
...
...
...
....
....
...
...
...
...
...
...
...
...
.
...
.......................................... ........................................................
10 Ω
4V
A.
B.
C.
D.
E.
zero
140 T/s,
140 T/s,
420 T/s,
420 T/s,
ans: B
decreasing
increasing
decreasing
increasing
28. A changing magnetic field pierces the interior of a circuit containing three identical resistors.
Two voltmeters are connected to the same points, as shown. V1 reads 1 mV. V2 reads:
......................
....
...
..
.......................................... ....
..........................................................
...
....
....
.... 2 .....
..................
...
...
....
...
..
..
...
...
....
....
..
..
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
....................................................................... ....... ....... ................................. ...... ....... .............................................................. ..
.. .. ..
...
.. .. ..
...
..
.
....
...
...
.
.
...
...
.
...
...
.....
....
...
...
.
.
...
...
....
...
....
...
...
....
....
...
...
..
..
...
..
...
.
.
.
.
.
.
.
.
.
.
.
.
...
........................................................ ....... ....... ............................................... .
....
.. .. ..
...
...
...
...
...
...
...
...
...
...
...
...
...
.
.
.
.
.
.
.
.
.
.
.
.
.....
...
...
.....
.
.
.
.
...
..
................................................................................. ....
.
..........................................................................................................
...
.
...
1
.
.
.....
..................
V
R
•
R
⊗ ⊗ ⊗ ⊗ ⊗ ⊗
⊗ ⊗ ⊗ ⊗ ⊗
⊗ ⊗ ⊗ ⊗ ⊗ ⊗
R
V
A.
B.
C.
D.
E.
438
0
1/3 mV
1/2 mV
1 mV
2 mV
ans: E
Chapter 30:
INDUCTION AND INDUCTANCE
•
29. A circular loop of wire is positioned half in and half out of a square region of constant uniform
magnetic field directed into the page, as shown. To induce a clockwise current in this loop:
⊗
⊗
⊗
⊗
⊗
A.
B.
C.
D.
E.
⊗
⊗
⊗
⊗
⊗
⊗
⊗
y
⊗
⊗
⊗•••••••••••••••••••••••••••••••••••••••••
•
•
•
B ⊗ ⊗ ⊗ ⊗ ••••••••⊗ •••••••• loop
•
•
⊗ ⊗ ⊗ ⊗ ••••••••••••••••••••••••••••
⊗ ⊗ ⊗ ⊗ ⊗
⊗ ⊗ ⊗ ⊗
⊗ ⊗ ⊗ ⊗ ⊗
⊗
⊗
⊗
x
move it in +x direction
move it in +y direction
move it in −y direction
move it in −x direction
increase the strength of the magnetic field
ans: A
30. The four wire loops shown have edge lengths of either L, 2L, or 3L. They will move with the
same speed into a region of uniform magnetic field B, directed out of the page. Rank them
according to the maximum magnitude of the induced emf, least to greatest.
.....
.......................................................................
....
1
A.
B.
C.
D.
E.
2
3
4
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
1 and 2 tie, then 3 and 4 tie
3 and 4 tie, then 1 and 2 tie
4, 2, 3, 1
1, then 2 and 3 tie, then 4
1, 2, 3, 4
ans: D
Chapter 30:
INDUCTION AND INDUCTANCE
439
31. A square loop of wire moves with a constant speed v from a field-free region into a region
of constant uniform magnetic field, as shown. Which of the five graphs correctly shows the
induced current i in the loop as a function of time t?
⊗
⊗
v
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
.
•
•
•
• ................................................
....
•
•
•
•
•
..
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
⊗
⊗
⊗
i
.
.........
.
.
.
... ...
... ..
A
.....
.. .....
.. .....
.. ....
i
i
t
...
... ....
.
.
. .
... ..
... ..
......................
...
..
..
..
...
..
⊗
⊗
⊗
⊗
B
D
⊗
⊗
⊗
⊗
⊗
⊗
⊗
⊗
⊗
⊗
⊗
⊗
⊗
⊗
⊗
⊗
⊗
t
⊗
⊗
⊗
⊗
⊗
⊗
⊗
⊗
⊗
⊗
⊗
⊗ B
⊗
⊗
i
......................
...
..
..
..
...
..
i
... ....
... ...
... ....
......
⊗
t
......................
...
..
..
..
...
..
E
..............................
.
.
....
...
....
...
.
....
.
.
...
C
...
...
...
..
...
.
..
....................
t
t
ans: C
32. The figure shows a bar moving to the right on two conducting rails. To make an induced
current i in the direction indicated, a constant magnetic field in region A should be in what
direction?
i
.
..........................................................
..
i
...
...
...
...
...
.
..........
........
..
A
i
.......
..........
...
...
...
..
...
v
..
..................................................
..
..
..................................................
..
i
A.
B.
C.
D.
E.
440
Right
Left
Into the page
Out of the page
Impossible; this cannot be done with a constant magnetic field
ans: C
Chapter 30:
INDUCTION AND INDUCTANCE
33. A car travels northward at 75 km/h along a straight road in a region where Earth’s magnetic
field has a vertical component of 0.50 × 10−4 T. The emf induced between the left and right
side, separated by 1.7 m, is:
A. 0
B. 1.8 mV
C. 3.6 mV
D. 6.4 mV
E. 13 mV
ans: B
34. Coils P and Q each have a large number of turns of insulated wire. When switch S is closed,
the pointer of galvanometer G is deflected toward the left. With S now closed, to make the
pointer of G deflect toward the right one could:
..........................
... ... .... ....
... ... .... ....
.... ....
.. ..
.. ..
. .
... ...
.. ..
.. ..
... ...
.... ....
.. ..
... ...
... ...
... ...
... ...
.. ...
.
... ...
.. ...
.
... ...
.. ..
... ... .... ....
... ... ... ...
.... ...... ...
.................
.... ....
... ...
.. ...
......................................................................................................................................... ....
...
...
...
..
...
...
...
.........
...
.........
..
.
.
.
.
.
.
.
.
.....
.
...
...... ....... .......
.
.
.
.
... ... ... ... ... ... ............................................... .. ......................................
..... ..... .....
P
• •
S
R
A.
B.
C.
D.
E.
..........................
... ... .... ....
... ... .... ....
.... ....
.. ..
.. ..
. .
... ...
.. ..
.. ..
... ...
.... ....
.. ..
... ...
... ...
... ...
... ...
.. ...
.
... ...
.. ...
.
... ...
.. ..
... ... .... ....
... ... ... ...
.... ...... ...
................
.... ....
... ...
... ...
......................................................................................................................................................................
...
..
...
...
...
...
...
...
...
...
....................
.
...
...
...
.
........................................................ ....
........................................................ ..
...
.
....
.
.
.
..............
Q
G
move the slide of the rheostat R quickly to the right
move coil P toward coil Q
move coil Q toward coil P
open S
do none of the above
ans: D
35. A rod lies across frictionless rails in a constant uniform magnetic field B, as shown. The
rod moves to the right with speed v. In order for the emf around the circuit to be zero, the
magnitude of the magnetic field should:
...... ........................... v
.......................................................... ........................
.. ................................................. .....................
..
.. ... ⊗
⊗ .. ... ⊗
.. ..
.. ...
.. ..
⊗
.. ... ⊗
.. ..
⊗ ... .... ⊗
.. .. ⊗
. .............................................. ....................
.......................................................... ........................
......
A.
B.
C.
D.
E.
not change
increase linearly with time
decrease linearly with time
increase quadratically with time
decrease quadratically with time
ans: C
Chapter 30:
INDUCTION AND INDUCTANCE
441
36. A rectangular loop of wire has area A. It is placed perpendicular to a uniform magnetic field
B and then spun around one of its sides at frequency f . The maximum induced emf is:
A. BAf
B. BAf
C. 2BAf
D. 2πBAf
E. 4πBAf
ans: D
37. A rectangular loop of wire is placed perpendicular to a uniform magnetic field and then spun
around one of its sides at frequency f . The induced emf is a maximum when:
A. the flux is zero
B. the flux is a maximum
C. the flux is half its maximum value
D. the derivative of the flux with respect to time is zero
E. none of the above
ans: A
38. The diagram shows a circular loop of wire that rotates at a steady rate about a diameter O
that is perpendicular to a uniform magnetic field. The maximum induced emf occurs when the
point X on the loop passes:
e
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........
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........
........
...
........
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........
B
........
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........
........
...
........
a
b
c
d
e
ans: C
39. A copper hoop is held in a vertical east-west plane in a uniform magnetic field whose field lines
run along the north-south direction. The largest induced emf is produced when the hoop is:
A. rotated about a north-south axis
B. rotated about an east-west axis
C. moved rapidly, without rotation, toward the east
D. moved rapidly, without rotation, toward the south
E. moved rapidly, without rotation, toward the northwest
ans: B
442
Chapter 30:
INDUCTION AND INDUCTANCE
40. A 10-turn conducting loop with a radius of 3.0 cm spins at 60 revolutions per second in a
magnetic field of 0.50 T. The maximum emf generated is:
A. 0.014 V
B. 0.53 V
C. 5.3 V
D. 18 V
E. 180 V
ans: C
41. A single loop of wire with a radius of 7.5 cm rotates about a diameter in a uniform magnetic
field of 1.6 T. To produce a maximum emf of 1.0 V, it should rotate at:
A. 0
B. 2.7 rad/s
C. 5.6 rad/s
D. 35 rad/s
E. 71 rad/s
ans: D
42. A merry-go-round has an area of 300 m2 and spins at 2 rpm about a vertical axis at a place
where Earth’s magnetic field is vertical and has a magnitude of 5 × 10−5 T. The emf around
the rim is:
A. 0
B. 0.5 mV
C. 3.1 mV
D. 15 mV
E. 30 mV
ans: A
Chapter 30:
INDUCTION AND INDUCTANCE
443
43. A copper penny slides on a horizontal frictionless table. There is a square region of constant
uniform magnetic field perpendicular to the table, as shown. Which graph correctly shows the
speed v of the penny as a function of time t?
top view
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t
A
t
B
v
C
v
......................
.....................
...
....................
..................
......
.......
.......
............................
t
D
t
E
ans: D
44. A rod with resistance R lies across frictionless conducting rails in a constant uniform magnetic
field B, as shown. Assume the rails have negligible resistance. The magnitude of the force that
must be applied by a person to pull the rod to the right at constant speed v is:
↑
|
L
|
↓
A.
B.
C.
D.
E.
444
←−−− x −−−→
........ ..................................
.
............................................................................ ...........................v...
. ..
..
.
.. ................................................................... ...........................
.. ..
.. ...
.. ..
.. ...
.. ...
.. ..
.. ...
.. ..
.. ..
.. ...
. ..
.. ..
.. .................................................................. ..............................
............................................................................. .............................
........
0
BLv
BLv/R
B 2 L2 v/R
B 2 Lxv/R
ans: D
Chapter 30:
INDUCTION AND INDUCTANCE
45. A rod of length L and electrical resistance R moves through a constant uniform magnetic field
B, perpendicular to the rod. The force that must be applied by a person to keep the rod
moving with constant velocity v is:
A. 0
B. BLv
C. BLv/R
D. B 2 L2 v/R
E. B 2 L2 v 2 /R
ans: A
46. As a loop of wire with a resistance of 10 Ω moves in a constant non-uniform magnetic field, it
loses kinetic energy at a uniform rate of 4.0 mJ/s. The induced current in the loop:
A. is 0
B. is 2 mA
C. is 2.8 mA
D. is 20 mA
E. cannot be calculated from the given data
ans: D
47. As a loop of wire with a resistance of 10 Ω moves in a non-uniform magnetic field, it loses
kinetic energy at a uniform rate of 5 mJ/s. The induced emf in the loop:
A. is 0
B. is 0.2 V
C. is 0.28 V
D. is 2 V
E. cannot be calculated from the given data
ans: B
48. An
A.
B.
C.
D.
E.
electric field is associated with every:
magnetic field
time-dependent magnetic field
time-dependent magnetic flux
object moving in a magnetic field
conductor moving in a magnetic field
ans: B
49. A cylindrical region of radius R = 3.0 cm contains a uniform magnetic field parallel to its
axis. If the electric field induced at a point R/2 from the cylinder axis is 4.5 × 10−3 V/m the
magnitude of the magnetic field must be changing at the rate:
A. 0
B. 0.30 T/s
C. 0.60 T/s
D. 1.2 T/s
E. 2.4 T/s
ans: C
Chapter 30:
INDUCTION AND INDUCTANCE
445
50. A cylindrical region of radius R contains a uniform magnetic field parallel to its axis. The field
is zero outside the cylinder. If the magnitude of the field is changing at the rate dB/dt, the
electric field induced at a point 2R from the cylinder axis is:
A. zero
B. 2R dB/dt
C. R dB/dt
D. (R/2) dB/dt
E. (R/4) dB/dt
ans: E
51. A cylindrical region of radius R contains a uniform magnetic field, parallel to its axis, with
magnitude that is changing linearly with time. If r is the radial distance from the cylinder
axis, the magnitude of the induced electric field inside the cylinder is proportional to:
A. R
B. r
C. r 2
D. 1/r
E. 1/r2
ans: B
52. A cylindrical region of radius R contains a uniform magnetic field, parallel to its axis, with
magnitude that is changing linearly with time. If r is the radial distance from the cylinder
axis, the magnitude of the induced electric field outside the cylinder is proportional to:
A. R
B. r
C. r 2
D. 1/r
E. 1/r2
ans: D
53. The unit “henry” is equivalent to:
A. volt·second/ampere
B. volt/second
C. ohm
D. ampere·volt/second
E. ampere·second/volt
ans: A
446
Chapter 30:
INDUCTION AND INDUCTANCE
54. The diagram shows an inductor that is part of a circuit. The direction of the emf induced in
the inductor is indicated. Which of the following is possible?
E ◦−→
.......
.......
.......
.......
.. ...
.. ...
.. ...
.. ...
.. ... .. ... .. ... .. ...
....................................................... ..
.... . ... .... ... .... ... .... ...
........................................................
...
... .. ... .. ... .. ... ...
...
... ...
... ...
... ...
...
... ...
...
.
.
.
......
.....................................................................................................................
A.
B.
C.
D.
E.
The current is constant and rightward
The current is constant and leftward
The current is increasing and rightward
The current is increasing and leftward
None of the above
ans: D
55. A 10-turn ideal solenoid has an inductance of 3.5 mH. When the solenoid carries a current of
2.0 A the magnetic flux through each turn is:
A. 0
B. 3.5 × 10−4 wb
C. 7.0 × 10−4 wb
D. 7.0 × 10−3 wb
E. 7.0 × 10−2 wb
ans : C
56. A 10-turn ideal solenoid has an inductance of 4.0 mH. To generate an emf of 2.0 V the current
should change at a rate of:
A. zero
B. 5.0 A/s
C. 50 A/s
D. 250 A/s
E. 500 A/s
ans: E
57. A long narrow solenoid has length
area A. Its inductance is:
A. µ0 N 2 A
B. µ0 N 2 A/
C. µ0 N A/
D. µ0 N 2 /A
E. none of these
ans: B
and a total of N turns, each of which has cross-sectional
Chapter 30:
INDUCTION AND INDUCTANCE
447
58. A flat coil of wire, having 5 turns, has an inductance L. The inductance of a similar coil having
20 turns is:
A. 4L
B. L/4
C. 16L
D. L/16
E. L
ans: C
59. An inductance L, resistance R, and ideal battery of emf E are wired in series. A switch in the
circuit is closed at time 0, at which time the current is zero. At any later time t the current i
is given by:
A. (E/R)(1 − e−Lt/R )
B. (E/R)e−Lt/R
C. (E/R)(1 + e−Rt/L )
D. (E/R)e−Rt/L
E. (E/R)(1 − e−Rt/L )
ans: E
60. An inductance L, resistance R, and ideal battery of emf E are wired in series. A switch in the
circuit is closed at time 0, at which time the current is zero. At any later time t the emf of the
inductor is given by:
A. E(1 − e−Lt/R )
B. Ee−Lt/R
C. E(1 + e−Rt/L )
D. Ee−Rt/L
E. E(1 − e−Rt/L )
ans: D
61. An inductance L, resistance R, and ideal battery of emf E are wired in series. A switch in the
circuit is closed at time 0, at which time the current is zero. At any later time t the potential
difference across the resistor is given by:
A. E(1 − e−Lt/R )
B. Ee−Lt/R
C. E(1 + e−Rt/L )
D. Ee−Rt/L
E. E(1 − e−Rt/L )
ans: E
62. An 8.0-mH inductor and a 2.0-Ω resistor are wired in series to an ideal battery. A switch in
the circuit is closed at time 0, at which time the current is zero. The current reaches half its
final value at time:
A. 2.8 ms
B. 4.0 ms
C. 3 s
D. 170 s
E. 250 s
ans: A
448
Chapter 30:
INDUCTION AND INDUCTANCE
63. An 8.0-mH inductor and a 2.0-Ω resistor are wired in series to a 20-V ideal battery. A switch in
the circuit is closed at time 0, at which time the current is zero. After a long time the current
in the resistor and the current in the inductor are:
A. 0, 0
B. 10 A, 10 A
C. 2.5 A, 2.5 A
D. 10 A, 2.5 A
E. 10 A, 0
ans: B
64. An 8.0-mH inductor and a 2.0-Ω resistor are wired in series to a 20-V ideal battery. A switch in
the circuit is closed at time 0, at which time the current is zero. Immediately after the switch
is thrown the potential differences across the inductor and resistor are:
A. 0, 20 V
B. 20 V, 0
C. 10 V, 10 V
D. 16 V, 4 V
E. unknown since the rate of change of the current is not given
ans: B
65. An inductor with inductance L resistor with resistance R are wired in series to an ideal battery
with emf E. A switch in the circuit is closed at time 0, at which time the current is zero. A
long time after the switch is thrown the potential differences across the inductor and resistor:
A. 0, E
B. E, 0
C. E/2, E/2
D. (L/R)E, (R/L)E
E. cannot be computed unless the rate of change of the current is given
ans: A
66. If both the resistance and the inductance in an LR series circuit are doubled the new inductive
time constant will be:
A. twice the old
B. four times the old
C. half the old
D. one-fourth the old
E. unchanged
ans: E
Chapter 30:
INDUCTION AND INDUCTANCE
449
67. When the switch S in the circuit shown is closed, the time constant for the growth of current
in R2 is:
..
.....
...
....
...... ...... ......
.
.
.
............................... ..
.................................................. .. .... ... .... ... .... .... ......................
...
..... ........ ........ ........ .....
..
...... ..... ...... ......
...
....
...
...
...
..
...
..
...
...
...
...
..
..
...
.
.
.....
.........
.
....
.
.
...
.........
.
............
......
.
.
.
.
.
.
.
.
.
.
1 .............
2 .............
....
.....
.......
...
...
..
....
...
..
....
...
..
..
...
...
....
...
..
..
..
.
....................................................................................................................................................................................................................
S
L
R
A.
B.
C.
D.
E.
R
L/R1
L/R2
L/(R1 + R2 )
L(R1 + R2 )/(R1 R2 )
(L/R1 + L/R2 )/2
ans: B
68. The diagrams show three circuits with identical batteries, identical inductors, and identical
resistors. Rank them according to the current through the battery just after the switch is
closed, from least to greatest.
.. .. ..
.. .... ... .... ... .... ..
.. .. ..
.......
...
.
............................
..
.
.
.
.
.
.
.
.
.
.
....................
..
..............................
.
...
......
..
...
....
•..... •
A.
B.
C.
D.
E.
450
.. .. ..
.. .... ... .... ... .... ..
.. .. ..
.. .. ..
.........................
.. .. ..
1
..........
......
...........
.....
...........
..
.....
..
...
....
•..... •
2
3, 2, 1
2 and 3 ties, then 1
1, 3, 2
1, 2, 3
3, 1, 2
ans: C
Chapter 30:
INDUCTION AND INDUCTANCE
.. .. ..
.. .... ... .... ... .... ..
.. .. ..
.......
...
.
............................
..
.
.
.
.
.
.
.
.
.
.
....................
..
..............................
.
...
......
..........
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.....
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..
.....
..
...
....
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3
.......
...
.
............................
..
.
.
.
.
.
.
.
.
.
.
....................
..
..............................
.
...
......
69. Immediately after switch S in the circuit shown is closed, the current through the battery is:
.. .. ..
................................. .......................................................................................................... ..
...
..
.. .. ..
.
...
....
...
..
...
....
...
...
...
........
1
...
...
...
..
...
.
.....................
...........
.
...
......... ..
......
..
..
.
.
.
.
.
.
.
.
.
............
.
.
.
.
.
.
..................
..
2 ...................
..
...
.
................................
.......
...
...
...
...
..
.
...
.
.
.
.
...
.
.
..
....
....
...
....
....
...
...
....
...
..
...
...
.
....
.
.
.
.
.
.
..........................................
........................................................................................................
R
V0
R
L
S
A.
B.
C.
D.
E.
0
V0 /R1
V0 /R2
V0 /(R1 + R2 )
V0 (R1 + R2 )/(R1 R2 )
ans: D
70. A 3.5-mH inductor and a 4.5-mH inductor are connected in series. The equivalent inductance
is:
A. 2.0 mH
B. 0.51 mH
C. 0.13 mH
D. 1.0 mH
E. 8.0 mH
ans: E
71. A 3.5-mH inductor and a 4.5-mH inductor are connected in series and a time varying current
is established in them. When the total emf of the combination is 16 V, the emf of the larger
inductor is:
A. 7.0 V
B. 9.0 V
C. 2.3 V
D. 28 V
E. 36 V
ans: B
72. A 3.5-mH inductor and a 4.5-mH inductor are connected in parallel. The equivalent inductance
is:
A. 2.0 mH
B. 0.51 mH
C. 0.13 mH
D. 1.0 mH
E. 8.0 mH
ans: A
Chapter 30:
INDUCTION AND INDUCTANCE
451
73. A 3.5-mH inductor and a 4.5-mH inductor are connected in parallel. When the total emf of
the combination is 16 V, the rate of change of the current in the larger inductor is:
A. 2.0 × 103 A/s
B. 3.6 × 103 A/s
C. 4.6 × 103 A/s
D. 7.0 × 103 A/s
E. 8.1 × 103 A/s
ans: B
74. An inductor with inductance L and an inductor with inductance 2L are connected in parallel.
When the rate of change of the current in the larger inductor is 1200 A/s the rate of change of
the current in the smaller inductor is:
A. 400 A/s
B. 1200 A/s
C. 1600 A/s
D. 2000 A/s
E. 2400 A/s
ans: E
75. The stored energy in an inductor:
A. depends, in sign, upon the direction of the current
B. depends on the rate of change of current
C. is proportional to the square of the inductance
D. has units J/H
E. none of the above
ans: E
76. An inductance L and a resistance R are connected in series to an ideal battery. A switch in the
circuit is closed at time 0, at which time the current is zero. The energy stored in the inductor
is a maximum:
A. just after the switch is closed
B. at the time t = L/R after the switch is closed
C. at the time t = L/R after the switch is closed
D. at the time t = 2L/R after the switch is closed
E. a long time after the switch is closed
ans: E
77. An inductance L and a resistance R are connected in series to an ideal battery. A switch in
the circuit is closed at time 0, at which time the current is zero. The rate of increase of the
energy stored in the inductor is a maximum:
A. just after the switch is closed
B. at the time t = L/R after the switch is closed
C. at the time t = L/R after the switch is closed
D. at the time t = (L/R) ln 2 after the switch is closed
E. a long time after the switch is closed
ans: D
452
Chapter 30:
INDUCTION AND INDUCTANCE
78. In each of the following operations, energy is expended. The LEAST percentage of returnable
electrical energy will be yielded by:
A. charging a capacitor
B. charging a storage battery
C. sending current through a resistor
D. establishing a current through an inductor
E. moving a conducting rod through a magnetic field
ans: C
79. A current of 10 A in a certain inductor results in a stored energy of 40 J. When the current is
changed to 5 A in the opposite direction, the stored energy changes by:
A. 20 J
B. 30 J
C. 40 J
D. 50 J
E. 60 J
ans: B
80. A 6.0-mH inductor is in a series circuit with a resistor and an ideal battery. At the instant the
current in the circuit is 5.0 A the energy stored in the inductor is:
A. 0
B. 7.5 × 10−2 J
C. 15 × 10−2 J
D. 30 × 10−2 J
E. unknown since the rate of change of the current is not given
ans: B
81. A 6.0-mH inductor is in a circuit. At the instant the current is 5.0 A and its rate of change is
200 A/s, the rate with which the energy stored in the inductor is increasing is:
A. 7.5 × 10−2 W
B. 120 W
C. 240 W
D. 3.0 W
E. 6.0 W
ans: E
82. A 6.0-mH inductor and a 3.0-Ω resistor are wired in series to a 12-V ideal battery. A switch in
the circuit is closed at time 0, at which time the current is zero. 2.0 ms later the energy stored
in the inductor is:
A. 0
B. 2.5 × 10−2 J
C. 1.9 × 10−2 J
D. 3.8 × 10−2 J
E. 9.6 × 10−3 J
ans: C
Chapter 30:
INDUCTION AND INDUCTANCE
453
83. The quantity B 2 /µ0 has units of:
A. J
B. J/H
C. J/m
D. J/m3
E. H/m3
ans: D
84. A 0.20-cm radius cylinder, 3.0 cm long, is wrapped with wire to form an inductor. At the
instant the magnetic field in the interior is 5.0 mT the energy stored in the field is about:
A. 0
B. 3.8 × 10−6 J
C. 7.5 × 10−6 J
D. 7.5 × 10−4 J
E. 9.9 J
ans: B
85. In the diagram, assume that all the magnetic field lines generated by coil 1 pass through coil
2. Coil 1 has 100 turns and coil 2 has 400 turns. Then:
........................................... .......................................... ...
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#2
G
S
A.
B.
C.
D.
E.
454
the power supplied to coil 1 is equal to the power delivered by coil 2
the emf around coil 1 will be one-fourth the emf around coil 2
the current in coil 1 will be one-fourth the current in coil 2
the emfs will be the same in the two coils
none of the above
ans: E
Chapter 30:
INDUCTION AND INDUCTANCE
Chapter 31:
ELECTROMAGNETIC OSCILLATIONS
AND ALTERNATING CURRENT
1. A charged capacitor and an inductor are connected in series. At time t = 0 the current is zero,
but the capacitor is charged. If T is the period of the resulting oscillations, the next time after
t = 0 that the current is a maximum is:
A. T
B. T /4
C. T /2
D. T
E. 2T
ans: B
2. A charged capacitor and an inductor are connected in series. At time t = 0 the current is zero,
but the capacitor is charged. If T is the period of the resulting oscillations, the next time after
t = 0 that the charge on the capacitor is a maximum is:
A. T
B. T /4
C. T /2
D. T
E. 2T
ans: C
3. A charged capacitor and an inductor are connected in series. At time t = 0 the current is zero,
but the capacitor is charged. If T is the period of the resulting oscillations, the next time after
t = 0 that the voltage across the inductor is a maximum is:
A. T
B. T /4
C. T /2
D. T
E. 2T
ans: C
4. A charged capacitor and an inductor are connected in series. At time t = 0 the current is zero,
but the capacitor is charged. If T is the period of the resulting oscillations, the next time after
t = 0 that the energy stored in the magnetic field of the inductor is a maximum is:
A. T
B. T /4
C. T /2
D. T
E. 2T
ans: B
Chapter 31:
ELECTROMAGNETIC OSCILLATIONS & ALTERNATING CURRENT
455
5. A charged capacitor and an inductor are connected in series. At time t = 0 the current is zero,
but the capacitor is charged. If T is the period of the resulting oscillations, the next time after
t = 0 that the energy stored in the electric field of the capacitor is a maximum is:
A. T
B. T /4
C. T /2
D. T
E. 2T
ans: C
6. A capacitor in an LC oscillator has a maximum potential difference of 15 V and a maximum
energy of 360 µJ. At a certain instant the energy in the capacitor is 40 µJ. At that instant
what is the potential difference across the capacitor?
A. zero
B. 5 V
C. 10 V
D. 15 V
E. 20 V
ans: B
7. Which of the following has the greatest effect in decreasing the oscillation frequency of an LC
circuit? Using instead:
A. L/2 and C/2
B. L/2 and 2C
C. 2L and C/2
D. 2L and 2C
E. none of these
ans: D
8. We desire to make an LC circuit that oscillates at 100 Hz using an inductance of 2.5 H. We
also need a capacitance of:
A. 1 F
B. 1 mF
C. 1 µF
D. 100 µF
E. 1 pF
ans: C
9. An LC circuit consists of a 1-µF capacitor and a 4 mH inductor. Its oscillation frequency is
approximately:
A. 0.025 Hz
B. 25 Hz
C. 60 Hz
D. 2500 Hz
E. 15, 800 Hz
ans: D
456
Chapter 31:
ELECTROMAGNETIC OSCILLATIONS & ALTERNATING CURRENT
10. An
A.
B.
C.
D.
E.
LC circuit has an oscillation frequency of 105 Hz. If C = 0.1 µF, then L must be about:
10 mH
1 mH
25 µH
2.5 µH
1 pH
ans: C
11. In the circuit shown, switch S is first pushed up to charge the capacitor. When S is then pushed
down, the current in the circuit will oscillate at a frequency of:
..................................................................................
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......... ......... ......... .........
5 µF
V
•
50 mH
A.
B.
C.
D.
E.
318 Hz
0.01 Hz
12.500 Hz
2000 Hz
depends on V0
ans: A
•
•
S
12. Radio receivers are usually tuned by adjusting the capacitor of an LC circuit. If C = C1 for a
frequency of 600 kHz, then for a frequency of 1200 kHz one must adjust C to:
A. C1 /2
B. C1 /4
C. 2C1
D. √
4C1
E.
2C1
ans: B
13. An LC series circuit with an inductance L and a capacitance C has an oscillation frequency f .
Two inductors, each with inductance L, and two capacitors, each with capacitance C, are all
wired in series and the circuit is completed. The oscillation frequency is:
A. f /4
B. f /2
C. f
D. 2f
E. 4f
ans: C
Chapter 31:
ELECTROMAGNETIC OSCILLATIONS & ALTERNATING CURRENT
457
14. The electrical analog of a spring constant k is:
A. L
B. 1/L
C. C
D. 1/C
E. R
ans: D
15. Consider the mechanical system consisting of two springs and a block, as shown. Which one
of the five electrical circuits (A, B, C, D, E) is the analog of the mechanical system?
\ \
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k1
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D
E
ans: A
16. A 150-g block on the end of a spring with a spring constant of 35 N/m is pulled aside 25 cm
and released from rest. In the electrical analog the initial charge on the capacitor is:
A. 0.15 C
B. 6.67 C
C. 0.025 C
D. 40 C
E. 35 C
ans: C
458
Chapter 31:
ELECTROMAGNETIC OSCILLATIONS & ALTERNATING CURRENT
17. A 150-g block on the end of a spring with a spring constant of 35 N/m is pulled aside 25 cm
and released from rest. In the electrical analog the maximum charge on the capacitor is 0.25 C.
The maximum current in the LC circuit is:
A. 0.38 A
B. 0.025 A
C. 40 A
D. 2.3 A
E. 5.3 A
ans: A
18. A capacitor in an LC oscillator has a maximum potential difference of 15 V and a maximum
energy of 360 µJ. At a certain instant the energy in the capacitor is 40 µJ. At that instant
what is the potential difference across the capacitor?
A. zero
B. 5 V
C. 10 V
D. 15 V
E. 20 V
ans: B
19. A capacitor in an LC oscillator has a maximum potential difference of 15 V and a maximum
energy of 360 µJ. At a certain instant the energy in the capacitor is 40 µJ. At that instant
what is the emf induced in the inductor?
A. zero
B. 5 V
C. 10 V
D. 15 V
E. 20 V
ans: C
20. In an oscillating LC circuit, the total stored energy is U . The maximum energy stored in the
capacitor during one cycle is:
A. U/2
√
B. U/ 2
C. U
D. U/(2π)
E. U/π
ans: C
21. In an oscillating LC circuit, the total stored energy is U and the maximum charge on the
capacitor is Q. When the charge on the capacitor is Q/2, the energy stored in the inductor is:
A. U/2
B. U/4
C. (4/3)U
D. 3U/2
E. 3U/4
ans: E
Chapter 31:
ELECTROMAGNETIC OSCILLATIONS & ALTERNATING CURRENT
459
22. The total energy in an LC circuit is 5.0 × 10−6 J. If C = 15 µF the charge on the capacitor is:
A. 0.82 µC
B. 8.5 µC
C. 12 µC
D. 17 µC
E. 24 µC
ans: C
23. The total energy in an LC circuit is 5.0 × 10−6 J. If L = 25 mH the maximum current is:
A. 10 mA
B. 14 mA
C. 20 mA
D. 28 mA
E. 40 mA
ans: C
24. At time t = 0 the charge on the 50-µF capacitor in an LC circuit is 15 µC and there is no
current. If the inductance is 20 mH the maximum current is:
A. 15 nA
B. 15 µA
C. 6.7 mA
D. 15 mA
E. 15 A
ans: D
25. An LC circuit has an inductance of 20 mH and a capacitance of 5.0 µF. At time t = 0 the
charge on the capacitor is 3.0 µC and the current is 7.0 mA. The total energy is:
A. 4.1 × 10−7 J
B. 4.9 × 10−7 J
C. 9.0 × 10−7 J
D. 1.4 × 10−6 J
E. 2.8 × 10−6 J
ans: D
26. An LC circuit has a capacitance of 30 µF and an inductance of 15 mH. At time t = 0 the charge
on the capacitor is 10 µC and the current is 20 mA. The maximum charge on the capacitor is:
A. 8.9 µC
B. 10 µC
C. 12 µC
D. 17 µC
E. 24 µC
ans: D
460
Chapter 31:
ELECTROMAGNETIC OSCILLATIONS & ALTERNATING CURRENT
27. An LC circuit has an inductance of 15 mH and a capacitance of 10 µF. At one instant the
charge on the capacitor is 25 µC. At that instant the current is changing at the rate of:
A. 0
B. 1.7 × 10−8 A/s
C. 5.9 × 10−3 A/s
D. 3.8 × 10−2 A/s
E. 170 A/s
ans: E
28. An LC circuit has a capacitance of 30 µF and an inductance of 15 mH. At time t = 0 the
charge on the capacitor is 10 µC and the current is 20 mA. The maximum current is:
A. 18 mA
B. 20 mA
C. 25 mA
D. 35 mA
E. 42 mA
ans: C
29. The graphs show the total electromagnetic energy in two RLC circuits as functions of time.
Which of the following statements might be true?
E
....
......
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... ....
... ......
... ......
... .......
.... .......
.. 1
....
..... ...............
.......
............
...
.
2 ............................ .........
................
t
A.
B.
C.
D.
E.
Circuit
Circuit
Circuit
Circuit
Circuit
ans: A
1
1
1
1
1
has
has
has
has
has
a smaller resistance and a larger inductance
a larger resistance and a smaller inductance
the same resistance and a larger inductance
a larger resistance and a larger capacitance
the same resistance and a smaller capacitance
30. An RLC circuit has a resistance of 200 Ω and an inductance of 15 mH. Its oscillation frequency
is 7000 Hz. At time t = 0 the current is 25 mA and there is no charge on the capacitor. After
five complete cycles the current is:
A. zero
B. 1.8 × 10−6 A
C. 2.1 × 10−4 A
D. 2.3 × 10−3 A
E. 2.5 × 10−2 A
ans: C
Chapter 31:
ELECTROMAGNETIC OSCILLATIONS & ALTERNATING CURRENT
461
31. An RLC circuit has an inductance of 25 mH and a capacitance of 5.0 µF. The charge on the
capacitor does NOT oscillate but rather decays exponentially to zero. The resistance in the
circuit must be:
A. greater than or equal to 20, 000Ω
B. less than 20, 000Ω but greater than 10, 000Ω
C. less than 10, 000Ω but greater than 5, 000Ω
D. less than 5, 000Ω but greater than 0
E. 0
ans: A
32. A series circuit with an inductance of 15 mH, a capacitance of 35 µF, and a resistance of 5.0 Ω
contains a sinusoidal source of emf with a frequency of 500 Hz. The frequency with which the
charge on the capacitor oscillates is:
A. 500 Hz
B. 1.4 kHz
C. greater than 1.4 kHz
D. less than 500 Hz
E. between 500 Hz and 1.4 kHz
ans: A
33. The rapid exponential decay in just a few cycles of the charge on the plates of capacitor in an
RLC circuit might be due to:
A. a large inductance
B. a large capacitance
C. a small capacitance
D. a large resistance
E. a small resistance
ans: D
34. An RLC circuit has a capacitance of 12 µF, an inductance of 25 mH, and a resistance of 60Ω.
The current oscillates with an angular frequency of:
A. 1.2 × 103 rad/s
B. 1.4 × 103 rad/s
C. 1.8 × 103 rad/s
D. 2.2 × 103 rad/s
E. 2.6 × 103 rad/s
ans: B
35. The angular frequency of a certain RLC series circuit is ω0 . A source of sinusoidal emf, with
angular frequency 2ω, is inserted into the circuit. After transients die out the angular frequency
of the current oscillations is:
A. ω0 /2
B. ω0
C. 2ω0
D. 1.5ω0
E. 3ω0
ans: C
462
Chapter 31:
ELECTROMAGNETIC OSCILLATIONS & ALTERNATING CURRENT
36. The angular frequency of a certain RLC series circuit is ω0 . A source of sinusoidal emf, with
angular frequency ω, is inserted into the circuit and ω is varied while the amplitude of the
source is held constant. For which of the following values of ω is the amplitude of the current
oscillations the greatest?
A. ω0 /5
B. ω0 /2
C. ω0
D. 2ω0
E. None of them (they all produce the same current amplitude)
ans: C
37. An RLC circuit has a sinusoidal source of emf. The average rate at which the source supplies
energy is 5 nW. This must also be:
A. the average rate at which energy is stored in the capacitor
B. the average rate at which energy is stored in the inductor
C. the average rate at which energy is dissipated in the resistor
D. twice the average rate at which energy is stored in the capacitor
E. three times the average rate at which energy is stored in the inductor
ans: C
38. In a purely capacitive circuit the current:
A. leads the voltage by one-fourth of a cycle
B. leads the voltage by one-half of a cycle
C. lags the voltage by one-fourth of a cycle
D. lags the voltage by one-half of a cycle
E. is in phase with the potential difference across the plates
ans: A
39. In a purely resistive circuit the current:
A. leads the voltage by one-fourth of a cycle
B. leads the voltage by one-half of a cycle
C. lags the voltage by one-fourth of a cycle
D. lags the voltage by one-half of a cycle
E. is in phase with the voltage
ans: E
40. In a purely inductive circuit, the current lags the voltage by:
A. zero
B. one-fourth of a cycle
C. one-half of a cycle
D. three-fourths of a cycle
E. one cycle
ans: B
Chapter 31:
ELECTROMAGNETIC OSCILLATIONS & ALTERNATING CURRENT
463
41. A series RL circuit is connected to an emf source of angular frequency ω. The current:
A. leads the applied emf by tan−1 (ωL/R)
B. lags the applied emf by tan−1 (ωL/R)
C. lags the applied emf by tan−1 (ωR/L)
D. leads the applied emf by tan−1 (ωR/L)
E. is zero
ans: B
42. A series RC circuit is connected to an emf source having angular frequency ω. The current:
A. leads the source emf by tan−1 (1/ωCR)
B. lags the source emf by tan−1 (1/ωCR)
C. leads the source emf by tan−1 (ωCR)
D. lags the source emf by tan−1 (ωCR)
E. leads the source emf by π/4
ans: A
43. In an RLC series circuit, which is connected to a source of emf Em cos(ωt), the current lags
the voltage by 45◦ if:
A. R = 1/ωC − ωL
B. R = 1/ωL − ωC
C. R = ωL − 1/ωC
D. R = ωC − 1/ωL
E. ωL = 1/ωC
ans: C
44. A coil has a resistance of 60 Ω and an impedance of 100 Ω. Its reactance, in ohms, is:
A. 40
B. 60
C. 80
D. 117
E. 160
ans: C
45. The reactance in ohms of a 35-µF capacitor connected to a 400-Hz generator is:
A. 0
B. 0.014
C. 0.088
D. 11
E. 71
ans: D
464
Chapter 31:
ELECTROMAGNETIC OSCILLATIONS & ALTERNATING CURRENT
46. A 35-µF capacitor is connected to a source of sinusoidal emf with a frequency of 400 Hz and a
maximum emf of 20 V. The maximum current is:
A. 0
B. 0.28 A
C. 1.8 A
D. 230 A
E. 1400 A
ans: C
47. A 45-mH inductor is connected to a source of sinusoidal emf with a frequency of 400 Hz and a
maximum emf of 20 V. The maximum current is:
A. 0
B. 0.18 A
C. 1.1 A
D. 360 A
E. 2300 A
ans: B
48. The impedance of an RLC series circuit is definitely increased if:
A. C decreases
B. L increases
C. L decreases
D. R increases
E. R decreases
ans: D
49. An
is:
A.
B.
C.
D.
E.
RLC series circuit has R = 4 Ω, XC = 3 Ω, and XL = 6 Ω. The impedance of this circuit
5Ω
7Ω
9.8 Ω
13 Ω
7.8 Ω
ans: A
Chapter 31:
ELECTROMAGNETIC OSCILLATIONS & ALTERNATING CURRENT
465
50. The impedance of the circuit shown is:
50 Ω
0.20 H
150 µF
.
.. .. ..
......
......
.....
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...................................... ..
...
......
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......
......
.....
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...
..
...
....
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.
.
.
.
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.
....
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....
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.
...
...
..
.... .........
....
..
.
.
.
.
.
.
.
.
....................................................................................................................
... .......................................................................................................................
.
.
.
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.
...
.
.
.
....
.
.
..
.......
.....................
50 Hz, 240 Vrms
A.
B.
C.
D.
E.
21 Ω
50 Ω
63 Ω
65 Ω
98 Ω
ans: D
51. An electric motor, under load, has an effective resistance of 30 Ω and an inductive reactance of
40 Ω. When powered by a source with a maximum voltage of 420 V, the maximum current is:
A. 6.0 A
B. 8.4 A
C. 10.5 A
D. 12.0 A
E. 14.0 A
ans: B
52. An RL series circuit is connected to an ac generator with a maximum emf of 20 V. If the
maximum potential difference across the resistor is 16 V, then the maximum potential difference
across the inductor is:
A. 2 V
B. 4 V
C. 12 V
D. 25.6 V
E. 36 V
ans: C
53. When the amplitude of the oscillator in a series RLC circuit is doubled:
A. the impedance is doubled
B. the voltage across the capacitor is halved
C. the capacitive reactance is halved
D. the power factor is doubled
E. the current amplitude is doubled
ans: E
466
Chapter 31:
ELECTROMAGNETIC OSCILLATIONS & ALTERNATING CURRENT
54. When the frequency of the oscillator in a series RLC circuit is doubled:
A. the capacitive reactance is doubled
B. the capacitive reactance is halved
C. the impedance is doubled
D. the current amplitude is doubled
E. the current amplitude is halved
ans: B
55. In an RLC series circuit, the source voltage is leading the current at a given frequency f . If f
is lowered slightly, then the circuit impedance will:
A. increase
B. decrease
C. remain the same
D. need to know the amplitude of the source voltage
E. need to know whether the phase angle is larger or smaller than 45◦
ans: B
56. In the diagram, the function y(t) = ym sin(ωt) is plotted as a solid curve. The other three
curves have the form y(t) = ym sin(ωt + φ), where φ is between −π/2 and +π/2. Rank the
curves according to the value of φ, from the most negative to the most positive.
y(t)
. .... ................ ......................... ... .... ..... .... .
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...
..
t
...
..
...
..
...
.
..
.
...
...
A.
B.
C.
D.
E.
1, 2, 3
2, 3, 1
3, 2, 1
1, 3, 2
2, 1, 3
ans: D
Chapter 31:
ELECTROMAGNETIC OSCILLATIONS & ALTERNATING CURRENT
467
57. An RLC series circuit has L = 100 mH and C = 1 µF. It is connected to a 1000-Hz source and
the source emf is found to lead the current by 75◦ . The value of R is:
A. 12.6 Ω
B. 126 Ω
C. 175 Ω
D. 1750 Ω
E. 1810 Ω
ans: B
58. An RLC series circuit is driven by a sinusoidal emf with angular frequency ω d . If ωd is
increased without changing the amplitude of the emf the current amplitude increases. If L is
the inductance, C is the capacitance, and R is the resistance, this means that:
A. ωd L > 1/ωd C
B. ωd L < 1/ωd C
C. ωd L = 1/ωd C
D. ωd L > R
E. ωd L < R
ans: B
59. In a sinusoidally driven series RLC circuit, the inductive reactance is XL = 200 Ω, the capacitive reactance is XC = 100 Ω, and the resistance is R = 50 Ω. The current and applied emf
would be in phase if:
A. the resistance is increased to 100 Ω, with no other changes
B. the resistance is increased to 200 Ω, with no other changes
C. the inductance is reduced to zero, with no other changes
D. the capacitance is doubled, with no other changes
E. the capacitance is halved, with no other changes
ans: E
60. In a sinusoidally driven series RLC circuit the current lags the applied emf. The rate at which
energy is dissipated in the resistor can be increased by:
A. decreasing the capacitance and making no other changes
B. increasing the capacitance and making no other changes
C. increasing the inductance and making no other changes
D. increasing the driving frequency and making no other changes
E. decreasing the amplitude of the driving emf and making no other changes
ans: A
61. An
A.
B.
C.
D.
E.
RLC series circuit, connected to a source E, is at resonance. Then:
the voltage across R is zero
the voltage across R equals the applied voltage
the voltage across C is zero
the voltage across L equals the applied voltage
the applied voltage and current differ in phase by 90◦
ans: B
468
Chapter 31:
ELECTROMAGNETIC OSCILLATIONS & ALTERNATING CURRENT
62. An RLC series circuit is connected to an oscillator with a maximum emf of 100 V. If the
voltage amplitudes VR , VL , and VC are all equal to each other, then VR must be:
A. 33 V
B. 50 V
C. 67 V
D. 87 V
E. 100 V
ans: E
63. A resistor, an inductor, and a capacitor are connected in parallel to a sinusoidal source of emf.
Which of the following is true?
A. The currents in all branches are in phase.
B. The potential differences across all branches are in phase.
C. The current in the capacitor branch leads the current in the inductor branch by one-fourth
of a cycle
D. The potential difference across the capacitor branch leads the potential difference across
the inductor branch by one-fourth of a cycle.
E. The current in the capacitor branch lags the current in the inductor branch by one-fourth
of a cycle.
ans: B
64. The rms value of an ac current is:
A. its peak value
B. its average value
C. that steady current that produces the same rate of heating in a resistor as the actual
current
D. that steady current that will charge a battery at the same rate as the actual current
E. zero
ans: C
√
65. The rms value of a sinusoidal voltage is V0 / 2, where V0 is the amplitude. What is the rms
value of its fully rectified wave? Recall that Vrect (t) = |V (t)|.
V0
A.
B.
C.
D.
E.
..................
...
....
.
.
.
...
..
..
...
....
...
.
.
...... ......
......
V0
t
.................. ...................
...
....
... ...
.
.
.
.....
..
..
t
√
V02 / 2
V02 /2
√
2V√0
V0 / 2√
V0 /(2 2)
ans: D
Chapter 31:
ELECTROMAGNETIC OSCILLATIONS & ALTERNATING CURRENT
469
66. A sinusoidal voltage V (t) has an rms value of 100 V. Its maximum value is:
A. 100 V
B. 707 V
C. 70.7 V
D. 141 V
E. 200 V
ans: D
67. An ac generator produces 10 V (rms) at 400 rad/s. It is connected to a series RL circuit
(R = 17.3 Ω, L = 0.025 H). The rms current is:
A. 0.50 A and leads the emf by 30◦
B. 0.71 A and lags the emf by 30◦
C. 1.40 A and lags the emf by 60◦
D. 0.50 A and lags the emf by 30◦
E. 0.58 A and leads the emf by 90◦
ans: D
68. An ac generator producing 10 V (rms) at 200 rad/s is connected in series with a 50-Ω resistor,
a 400-mH inductor, and a 200-µF capacitor. The rms current in amperes is:
A. 0.125
B. 0.135
C. 0.18
D. 0.20
E. 0.40
ans: B
69. An ac generator producing 10 V (rms) at 200 rad/s is connected in series with a 50-Ω resistor,
a 400-mH inductor, and a 200-µF capacitor. The rms voltage (in volts) across the resistor is:
A. 2.5
B. 3.4
C. 6.7
D. 10.0
E. 10.8
ans: C
70. An ac generator producing 10 V (rms) at 200 rad/s is connected in series with a 50-Ω resistor,
a 400-mH inductor, and a 200-µF capacitor. The rms voltage (in volts) across the capacitor is:
A. 2.5
B. 3.4
C. 6.7
D. 10.0
E. 10.8
ans: B
470
Chapter 31:
ELECTROMAGNETIC OSCILLATIONS & ALTERNATING CURRENT
71. An ac generator producing 10 V (rms) at 200 rad/s is connected in series with a 50-Ω resistor,
a 400-mH inductor, and a 200-µF capacitor. The rms voltage (in volts) across the inductor is:
A. 2.5
B. 3.4
C. 6.7
D. 10.0
E. 10.8
ans: E
72. The ideal meters shown read rms current and voltage. The average power delivered to the load
is:
..........
..... .......
..
.
............................................................................................... ....
..........................................................
...
...
.
.
....
..................
.
....
....
...
..
..
..
..........
..........
..... ......
..... .......
..
............. ....
....
.
... ....... .
...
.
..
...
...
....................
....................
.
.
.....
....
...
...
..
...
..
..
.........................................................................................................................................................................
I
V
A.
B.
C.
D.
E.
unknown
load
definitely equal to V I
definitely more than V I
possibly equal to V I even if the load contains an inductor and a capacitor
definitely less than V I
zero, as is the average of any sine wave
ans: C
73. The average power supplied to the circuit shown passes through a maximum when which one
of the following is increased continuously from a very low to a very high value?
R
E, f
A.
B.
C.
D.
E.
.
.
.....
.......
.......
.. ..
.......................................... .. .... ..... .... ..... .... ........................................... ..
... ..
... ..
... ..
...
...
....
....
....
...
...
...
...
...
...
...
...
...
.....
.
.................
.
.
.
....
.
.
...
.
.... .......
.
... .. .... ... ...
...... ...
...
.
.
....
..
.
.
.
.
.
..................
.....
..
...
...
...
...
...
...
...
.....
..
...
.................................................................................................................................................................................
C
Source emf E
R
C
Source frequency f
None of these
ans: B
Chapter 31:
ELECTROMAGNETIC OSCILLATIONS & ALTERNATING CURRENT
471
74. In a series RLC circuit the rms value of the generator emf is E and the rms value of the current
is i. The current lags the emf by φ. The average power supplied by the generator is given by:
A. (iE/2) cos φ
B. iE
C. i2 /Z
D. i2 Z
E. i2 R
ans: E
75. The units of the power factor are:
A. ohm
B. watt
C. radian
D. ohm1/2
E. none of these
ans: E
76. A series circuit consists of a 15-Ω resistor, a 25-mH inductor, and a 35-µF capacitor. If the
frequency is 100 Hz the power factor is:
A. 0
B. 0.20
C. 0.45
D. 0.89
E. 1.0
ans: C
77. The main reason that alternating current replaced direct current for general use is:
A. ac generators do not need slip rings
B. ac voltages may be conveniently transformed
C. electric clocks do not work on dc
D. a given ac current does not heat a power line as much as the same dc current
E. ac minimizes magnetic effects
ans: B
78. A step-down transformer is used to:
A. increase the power
B. decrease the power
C. increase the voltage
D. decrease the voltage
E. change ac to dc
ans: D
472
Chapter 31:
ELECTROMAGNETIC OSCILLATIONS & ALTERNATING CURRENT
79. Iron, rather than copper, is used in the core of transformers because iron:
A. can withstand a higher temperature
B. has a greater resistivity
C. has a very high permeability
D. makes a good permanent magnet
E. insulates the primary from the secondary
ans: C
80. The core of a transformer is made in a laminated form to:
A. facilitate easy assembly
B. reduce i2 R losses in the coils
C. increase the magnetic flux
D. save weight
E. prevent eddy currents
ans: E
81. A generator supplies 100 V to the primary coil of a transformer. The primary has 50 turns and
the secondary has 500 turns. The secondary voltage is:
A. 1000 V
B. 500 V
C. 250 V
D. 100 V
E. 10 V
ans: A
82. The resistance of the primary coil of a well-designed, 1 : 10 step-down transformer is 1 Ω. With
the secondary circuit open, the primary is connected to a 12 V ac generator. The primary
current is:
A. essentially zero
B. about 12 A
C. about 120 A
D. depends on the actual number of turns in the primary coil
E. depends on the core material
ans: A
83. The primary of an ideal transformer has 100 turns and the secondary has 600 turns. Then:
A. the power in the primary circuit is less than that in the secondary circuit
B. the currents in the two circuits are the same
C. the voltages in the two circuits are the same
D. the primary current is six times the secondary current
E. the frequency in the secondary circuit is six times that in the primary circuit
ans: D
Chapter 31:
ELECTROMAGNETIC OSCILLATIONS & ALTERNATING CURRENT
473
84. The primary of a 3 : 1 step-up transformer is connected to a source and the secondary is
connected to a resistor R. The power dissipated by R in this situation is P . If R is connected
directly to the source it will dissipate a power of:
A. P/9
B. P/3
C. P
D. 3P
E. 9P
ans: A
85. In an ideal 1 : 8 step-down transformer, the primary power is 10 kW and the secondary current
is 25 A. The primary voltage is:
A. 25, 600 V
B. 3200 V
C. 400 V
D. 50 V
E. 6.25 V
ans: B
86. A source with an impedance of 100 Ω is connected to the primary coil of a transformer and a
resistance R is connected to the secondary coil. If the transformer has 500 turns in its primary
coil and 100 turns in its secondary coil the greatest power will be dissipated in the resistor if
R =:
A. 0
B. 0.25 Ω
C. 4.0 Ω
D. 50 Ω
E. 100 Ω
ans: C
474
Chapter 31:
ELECTROMAGNETIC OSCILLATIONS & ALTERNATING CURRENT
Chapter 32:
MAXWELL’S EQUATIONS; MAGNETISM AND MATTER
1. Gauss’ law for magnetism:
A. can be used to find B due to given currents provided there is enough symmetry
B. is false because there are no magnetic poles
C. can be used with open surfaces because there are no magnetic poles
D. contradicts Faraday’s law because one says ΦB = 0 and the other says E = −dΦB /dt
E. none of the above
ans: E
2. Gauss’ law for magnetism tells us:
A. the net charge in any given volume
B. that the line integral of a magnetic field around any closed loop must vanish
C. the magnetic field of a current element
D. that magnetic monopoles do not exist
E. charges must be moving to produce magnetic fields
ans: D
3. The statement that magnetic field lines form closed loops is a direct consequence of:
A. Faraday’s law
B. Ampere’s law
C. Gauss’ law for electricity
D. Gauss’ law for magnetism
E. the Lorentz force
ans: D
4. A magnetic field parallel to the x axis with a magnitude that decreases with increasing x but
does not change with y and z is impossible according to:
A. Faraday’s law
B. Ampere’s law
C. Gauss’ law for electricity
D. Gauss’ law for magnetism
E. Newton’s second law
ans: D
5. According to Gauss’ law for magnetism, magnetic field lines:
A. form closed loops
B. start at south poles and end at north poles
C. start at north poles and end at south poles
D. start at both north and south poles and end at infinity
E. do not exist
ans: A
Chapter 32:
MAXWELL’S EQUATIONS; MAGNETISM AND MATTER
475
6. The magnetic field lines due to an ordinary bar magnet:
A. form closed curves
B. cross one another near the poles
C. are more numerous near the N pole than near the S pole
D. do not exist inside the magnet
E. none of the above
ans: A
7. Four closed surfaces are shown. The areas Atop and Abot of the top and bottom faces and the
magnitudes Btop and Bbot of the uniform magnetic fields through the top and bottom faces
are given. The fields are perpendicular to the faces and are either inward or outward. Rank
the surfaces according to the magnitude of the magnetic flux through the curved sides, least
to greatest.
Atop = 2 cm2
Btop = 2 mT, inward
Atop = 2 cm2
Btop = 2 mT, inward
.................................
.......
.
...............................................
...
...
...
....
...
...
...
...
...
...
...
.
.
...
....
...
...
...
...
...
...
...
...
.
.
.
...
...
...
...
..
...
......
....
.
.
.
.
...........
...................................................
................................
.......
....
...
...........................................
..
...
....
...
...
...
...
..
...
....
...
.
.
...
....
...
...
...
...
..
...
...
...
...
...
...
...
...
..
..
......
....
.
.
.
..........
.
.....................................................
1
Abot = 4 cm2
Bbot = 2 mT, outward
Abot = 4 cm2
Bbot = 6 mT, outward
Atop = 2 cm2
Btop = 3 mT, inward
Atop = 2 cm2
Btop = 3 mT, inward
....................................
......
..
..........
.........
.. ....................... .....
.
...
...
...
....
...
...
...
..
...
...
..
..
....
..
..
.
.
...
.
.
...
.
.
.
...
...
...
...
...
...
...
...
..
.
.
...........
.........................
....................................
......
..
..........
.........
.. ........................ .....
.
...
...
...
....
...
..
...
..
...
...
..
..
...
..
..
.
.
...
.
.
..
...
....
...
..
...
...
...
...
...
..
.
.
...........
..........................
3
Abot = 2 cm2
Bbot = 3 mT, outward
A.
B.
C.
D.
E.
476
1, 2, 3,
3, 4, 1,
1, 2, 4,
4, 3, 2,
2, 1, 4,
ans: B
2
4
Abot = 2 cm2
Bbot = 2 mT, outward
4
2
3
1
3
Chapter 32:
MAXWELL’S EQUATIONS; MAGNETISM AND MATTER
8. Consider the four Maxwell equations:
−
→
1. E · d A = q/ 0
2. B · dA = 0
3. E · ds = −dΦB /dt
4. B · ds = µ0 i + µ0 0 dΦE /dt
Which of these must be modified if magnetic poles are discovered?
A. Only 1
B. Only 2
C. Only 2 and 3
D. Only 3 and 4
E. Only 2, 3, and 4
ans: C
9. One of the Maxwell equations begins with B · ds = . . .. The symbol “ds” means:
A. an infinitesimal displacement of a charge
B. an infinitesimal displacement of a magnetic pole
C. an infinitesimal inductance
D. an infinitesimal surface area
E. none of the above
ans: E
10. One of the Maxwell equations begins with E · ds = . . .. The “◦” symbol in the integral sign
means:
A. the same as the subscript in µ0
B. integrate clockwise around the path
C. integrate counterclockwise around the path
D. integrate around a closed path
E. integrate over a closed surface
ans: D
11. One of the Maxwell equations begins with B · dA = . . .. The “◦” symbol in the integral sign
means:
A. the same as the subscript in µ0
B. integrate clockwise around the path
C. integrate counterclockwise around the path
D. integrate around a closed path
E. integrate over a closed surface
ans: E
12. One of the crucial facts upon which the Maxwell equations are based is:
A. the numerical value of the electron charge
B. charge is quantized
C. the numerical value of the charge/mass ratio of the electron
D. there are three types of magnetic materials
E. none of the above
ans: E
Chapter 32:
MAXWELL’S EQUATIONS; MAGNETISM AND MATTER
477
13. Two of Maxwell’s equations contain a path integral on the left side and an area integral on the
right. For them:
A. the path must pierce the area
B. the path must be well-separated from the area
C. the path must be along a field line and the area must be perpendicular to the field line
D. the path must be the boundary of the area
E. the path must lie in the area, away from its boundary
ans: D
14. Two of Maxwell’s equations contain an integral over a closed surface. For them the infinitesimal
vector area dA is always:
A. tangent to the surface
B. perpendicular to the surface and pointing outward
C. perpendicular to the surface and pointing inward
D. tangent to a field line
E. perpendicular to a field line
ans: B
15. Two of Maxwell’s equations contain a path integral on the left side and an area integral on the
right. The directions of the infinitesimal path element ds and infinitesimal area element dA
are:
A. always in the same direction
B. always in opposite directions
C. always perpendicular to each other
D. never perpendicular to each other
E. none of the above
ans: E
16. Two of Maxwell’s equations contain a path integral on the left side and an area integral on the
right. Suppose the area is the surface of a piece of paper at which you are looking and dA is
chosen to point toward you. Then, the path integral is:
A. clockwise around the circumference of the paper
B. counterclockwise around the circumference of the paper
C. from left to right
D. from right to left
E. from top to bottom
ans: B
17. Which of the following equations can be used, along with a symmetry argument, to calculate
the electric field of a point charge?
A.
E · dA = q/ 0
B.
B · dA = 0
C.
E · ds = −dΦB /dt
D.
B · ds = µ0 i + µ0 0 dΦE /dt
E. None of these
ans: A
478
Chapter 32:
MAXWELL’S EQUATIONS; MAGNETISM AND MATTER
18. Which of the following equations can be used, along with a symmetry argument, to calculate
the magnetic field of a long straight wire carrying current?
A.
E · dA = q/ 0
B.
B · dA = 0
C.
E · ds = −dΦB /dt
D.
B · ds = µ0 i + µ0 0 dΦE /dt
E. None of these
ans: D
19. Which of the following equations can be used to show that magnetic field lines form closed
loops?
A.
E · dA = q/ 0
B.
B · dA = 0
C.
E · ds = −dΦB /dt
D.
B · ds = µ0 i + µ0 0 dΦE /dt
E. None of these
ans: B
20. Which of the following equations, along with a symmetry argument, can be used to calculate
the magnetic field produced by a uniform time-varying electric field?
A.
E · dA = q/ 0
B.
B · dA = 0
C.
E · ds = −dΦB /dt
D.
B · ds = µ0 i + µ0 0 dΦE /dt
E. None of these
ans: D
21. Which of the following equations, along with a symmetry argument, can be used to calculate
the electric field produced by a uniform time-varying magnetic field?
A.
E · dA = q/ 0
B.
B · dA = 0
C.
E · ds = −dΦB /dt
D.
B · ds = µ0 i + µ0 0 dΦE /dt
E. None of these
ans: C
22. Which of the following equations, along with a symmetry argument, can be used to calculate
the magnetic field between the plates of a charging parallel plate capacitor with circular plates?
A.
E · dA = q/ 0
B.
B · dA = 0
C.
E · ds = −dΦB /dt
D.
B · ds = µ0 i + µ0 0 dΦE /dt
E. None of these
ans: D
Chapter 32:
MAXWELL’S EQUATIONS; MAGNETISM AND MATTER
479
23. Maxwell’s equations, along with an appropriate symmetry argument, can be used to calculate:
A. the electric force on a given charge
B. the magnetic force on a given moving charge
C. the flux of a given electric field
D. the flux of a given magnetic field
E. none of these
ans: E
24. The polarity of an unmarked magnet can be determined using:
A. a charged glass rod
B. a compass
C. an electroscope
D. another unmarked magnet
E. iron filings
ans: B
25. A bar magnet is placed vertically with its S pole up and its N pole down. Its B field at its
center is:
A. zero
B. down
C. up due to the weight of the magnet
D. horizontal
E. slightly below the horizontal
ans: B
26. A bar magnet is broken in half. Each half is broken in half again, etc. The observation is that
each piece has both a north and south pole. This is usually explained by:
A. Ampere’s theory that all magnetic phenomena result from electric currents
B. our inability to divide the magnet into small enough pieces
C. Coulomb’s law
D. Lenz’ law
E. conservation of charge.
ans: A
27. A small bar magnet is suspended horizontally by a string. When placed in a uniform horizontal
magnetic field, it will:
A. translate in the direction of B
B. translate in the opposite direction of B
C. rotate so as to be at right angles to B
D. rotate so as to be vertical
E. none of the above
ans: E
480
Chapter 32:
MAXWELL’S EQUATIONS; MAGNETISM AND MATTER
28. Magnetic dipole X is fixed and dipole Y is free to move. Dipole Y will initially:
X
Y
....
.....................................................................................................................................
....
A.
B.
C.
D.
E.
....
.....................................................................................................................................
....
move toward X but not rotate
move away from X but not rotate
move toward X and rotate
move away from X and rotate
rotate but not translate
ans: A
29. Magnetic dipole X is fixed and dipole Y is free to move. Dipole Y will initially:
...
......
.......
... .... ..
....
...
..
...
....
..
...
...
...
...
....
..
...
....
.
X
.....
...................................................................................................................................
....
A.
B.
C.
D.
E.
Y
move toward X but not rotate
move away from X but not rotate
move toward X and rotate
move away from X and rotate
rotate but not move toward or away from X
ans: E
30. The diagram shows the angular momentum vectors of two electrons and two protons in the
same external magnetic field. The field points upward in the diagram. Rank the situations
according to the potential energy, least to greatest.
....
..........
... .... ...
...
....
..
...
...
...
....
..
...
...
...
..
A.
B.
C.
D.
E.
1 and 3
2 and 3
1 and 2
3 and 4
all tie
ans: B
tie,
tie,
tie,
tie,
then
then
then
then
Chapter 32:
2
1
3
1
and
and
and
and
4
4
4
2
B
...
.......
.........
....
...
...
...
..
...
.......
.........
....
...
...
...
..
e•
e •.......
p•
p •......
.
1
2
3
4
...
...
...
.
...... ..
.........
...
..
...
...
.
....... ..
.........
...
tie
tie
tie
tie
MAXWELL’S EQUATIONS; MAGNETISM AND MATTER
481
31. The energy of a magnetic dipole in an external magnetic field is least when:
A. the dipole moment is parallel to the field
B. the dipole moment is antiparallel to the field
C. the dipole moment is perpendicular to the field
D. none of the above (the same energy is associated with all orientations)
E. none of the above (no energy is associated with the dipole-field interaction)
ans: A
32. The magnetic properties of materials stem chiefly from:
A. particles with north poles
B. particles with south poles
C. motions of protons within nuclei
D. proton spin angular momentum
E. electron magnetic dipole moments
ans: E
33. Magnetization is:
A. the current density in an object
B. the charge density of moving charges in an object
C. the magnetic dipole moment of an object
D. the magnetic dipole moment per unit volume of an object
E. the magnetic field per unit volume produced by an object
ans: D
34. The units of magnetization are:
A. ampere
B. ampere·meter
C. ampere·meter2
D. ampere/meter
E. ampere/meter2
ans: D
35. If L is the orbital angular momentum of an electron, the magnetic dipole moment associated
with its orbital motion:
A. is in the direction of L and has magnitude proportional to L
B. is opposite to the direction of L and has magnitude proportional to L
C. is in the direction of L and has magnitude proportional to L2
D. is opposite to the direction of L and has magnitude proportional to L2
E. does not depend on L
ans: B
482
Chapter 32:
MAXWELL’S EQUATIONS; MAGNETISM AND MATTER
36. If an electron has an orbital angular momentum with magnitude L the magnitude of the orbital
contribution to its magnetic dipole moment is given by:
A. eL/m
B. eL/2m
C. 2eL/m
D. mL/e
E. mL/2
ans: B
37. An
A.
B.
C.
D.
E.
electron traveling with speed v around a circle of radius r is equivalent to a current of:
evr/2
ev/r
ev/2πr
2πer/v
2πev/r
ans: C
38. The intrinsic magnetic dipole moments of protons and neutrons are much less than that of an
electron because:
A. their masses are greater
B. their angular momenta are much less
C. their angular momenta are much greater
D. their charges are much less
E. their radii are much less
ans: A
39. The spin magnetic dipole moment of an electron:
A. is in the same direction as the spin angular momentum
B. is zero
C. has a magnitude that depends on the orbital angular momentum
D. has a magnitude that depends on the applied magnetic field
E. none of the above
ans: E
40. If an electron has zero orbital angular momentum, the magnitude of its magnetic dipole moment
equals:
A. zero
B. half the Bohr magneton
C. a Bohr magneton
D. twice a Bohr magneton
E. none of these
ans: C
Chapter 32:
MAXWELL’S EQUATIONS; MAGNETISM AND MATTER
483
41. The magnetic dipole moment of an atomic electron is typically:
A. much less than a Bohr magneton
B. a few Bohr magnetons
C. much greater than a Bohr magneton
D. much greater or much less than a Bohr magneton, depending on the atom
E. not related to the value of the Bohr magneton
ans: B
42. The magnitude of the Bohr magneton in J/T is about:
A. 10−15
B. 10−19
C. 10−23
D. 10−27
E. 10−31
ans: C
43. The molecular theory of magnetism can explain each of the following EXCEPT:
A. an N pole attracts a S pole
B. stroking an iron bar with a magnet will magnetize the bar
C. when a bar magnet is broken in two, each piece is a bar magnet
D. heating tends to destroy magnetization
E. hammering tends to destroy magnetization
ans: A
44. Lenz’ law can explain:
A. paramagnetism only
B. diamagnetism only
C. ferromagnetism only
D. only two of the three types of magnetism
E. all three of the types of magnetism
ans: B
45. The diagram shows two small diamagnetic spheres, one near each end of a bar magnet. Which
of the following statements is true?
..................
...
..
....
.
.... .....
.........
1
A.
B.
C.
D.
E.
484
The
The
The
The
The
ans:
N
S
...........
.... ......
.
....
..
...
................
2
force on 1 is toward the magnet and the force on 2 is away from the magnet
force on 1 is away from the magnet and the force on 2 is away from the magnet
forces on 1 and 2 are both toward the magnet
forces on 1 and 2 are both away from the magnet
magnet does not exert a force on either sphere
D
Chapter 32:
MAXWELL’S EQUATIONS; MAGNETISM AND MATTER
46. Paramagnetism is closely associated with:
A. the tendency of electron dipole moments to align with an applied magnetic field
B. the tendency of electron dipole moments to align opposite to an applied magnetic field
C. the exchange force between electrons
D. the force exerted by electron dipole moments on each other
E. the torque exerted by electron dipole moments on each other
ans: A
47. The diagram shows two small paramagnetic spheres, one near each end of a bar magnet. Which
of the following statements is true?
...........
.... ......
...
..
...
.................
1
A.
B.
C.
D.
E.
The
The
The
The
The
ans:
N
S
...............
...
...
....
..
...
.................
2
force on 1 is toward the magnet and the force on 2 is away from the magnet
force on 1 is away from the magnet and the force on 2 is away from the magnet
forces on 1 and 2 are both toward the magnet
forces on 1 and 2 are both away from the magnet
magnet does not exert a force on either sphere
C
48. A paramagnetic substance is placed in a weak magnetic field and its absolute temperature T
is increased. As a result, its magnetization:
A. increases in proportion to T
B. increases in proportion to T 2
C. remains the same
D. decreases in proportion to 1/T
E. decreases in proportion to 1/T 2
ans: D
49. A magnetic field B0 is applied to a paramagnetic substance. In the interior the magnetic field
produced by the magnetic dipoles of the substance is:
A. greater than B0 and in the opposite direction
B. less than B0 and in the opposite direction
C. greater than B0 and in the same direction
D. less than B0 and in the same direction
E. the same as B0
ans: D
50. A paramagnetic substance, in an external magnetic field, is thermally isolated. The field is
then removed. As a result:
A. the magnetic energy of the magnetic dipoles decreases
B. the temperature of the substance increases
C. the magnetization decreases, but only slightly
D. the magnetization reverses direction
E. none of the above
ans: E
Chapter 32:
MAXWELL’S EQUATIONS; MAGNETISM AND MATTER
485
51. A magnetic field B0 is applied to a diamagnetic substance. In the interior the magnetic field
produced by the magnetic dipoles of the substance is:
A. greater than B0 and in the opposite direction
B. less than B0 and in the opposite direction
C. greater than B0 and in the same direction
D. less than B0 and in the same direction
E. the same as B0
ans: B
52. Ferromagnetism is closely associated with:
A. the tendency of electron dipole moments to align with an applied magnetic field
B. the tendency of electron dipole moments to align opposite to an applied magnetic field
C. the tendency of electron dipole moments to change magnitude in an applied magnetic field
D. the tendency of electron dipole moments to align with each other
E. the force exerted by electron dipole moments on each other
ans: D
53. Of the three chief kinds of magnetic materials (diamagnetic, paramagnetic, and ferromagnetic),
which are used to make permanent magnets?
A. Only diamagnetic
B. Only ferromagnetic
C. Only paramagnetic
D. Only paramagnetic and ferromagnetic
E. All three
ans: B
54. When a permanent magnet is strongly heated:
A. nothing happens
B. it becomes an induced magnet
C. it loses its magnetism
D. its magnetism increases
E. its polarity reverses
ans: C
55. Magnetization vectors in neighboring ferromagnetic domains are:
A. always in opposite directions
B. always in the same direction
C. always in different directions
D. sometimes in different directions and sometimes in the same direction
E. sometimes in opposite directions and sometimes in the same direction
ans: C
486
Chapter 32:
MAXWELL’S EQUATIONS; MAGNETISM AND MATTER
56. The behavior of ferromagnetic domains in an applied magnetic field gives rise to:
A. hysteresis
B. ferromagnetism
C. the Curie law
D. a lowering of the Curie temperature
E. Gauss’ law for magnetism
ans: A
57. Because ferromagnets have ferromagnetic domains, the net magnetization:
A. can never be in the same direction as an applied field
B. may not vanish when an applied field is reduced to zero
C. can never vanish
D. is proportional to any applied magnetic field
E. is always opposite to the direction of any applied magnetic field
ans: B
58. The soft iron core in the solenoid shown is removable. Then:
.. .. ..
.............................. .. ........ ........ ...........................................................
.............................................
.. .. ..
...
...
....
...
..
...
...
...
...
...
.
...
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.
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..
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.............................................................................................................................................................................................................................................................................................
....
....
....
....
....
iron core
A.
B.
C.
D.
E.
.....
...
...
...
.
...
..
..
.
.
.
.
....
the current will be larger without the core
the current will be larger with the core
one must do work to remove the core
the circuit will do work in expelling the core
the stored energy is the same with or without the core
ans: C
59. An unmagnetized steel bar is placed inside a solenoid. As the current in the solenoid is slowly
increased from zero to some large value, the magnetization of the bar:
A. increases proportionally with the current
B. remains zero for awhile and then increases linearly with any further increase in current
C. increases with increasing current at first but later is much less affected by it
D. is unaffected by the current
E. increases quadratically with the current
ans: C
Chapter 32:
MAXWELL’S EQUATIONS; MAGNETISM AND MATTER
487
60. The magnetic field of Earth is roughly the same as that of a magnetic dipole with a dipole
moment of about:
A. 1017 J/T
B. 1019 J/T
C. 1021 J/T
D. 1023 J/T
E. 1025 J/T
ans: D
61. Of the following places, one would expect that the horizontal component of Earth’s magnetic
field is largest in:
A. Maine
B. Florida
C. Maryland
D. New York
E. Iowa
ans: B
62. A positively charged ion, due to a cosmic ray, is headed through Earth’s atmosphere toward
the center of Earth. Due to Earth’s magnetic field, the ion will be deflected:
A. south
B. north
C. west
D. east
E. not at all since it is a charge and not a pole
ans: D
63. Maxwell’s great contribution to electromagnetic theory was his hypothesis that:
A. work is required to move a magnetic pole through a closed path surrounding a current
B. a time-varying electric flux acts as a current for purposes of producing a magnetic field
C. the speed of light could be determined from simple electrostatic and magnetostatic experiments (finding the values of µ0 and 0 )
D. the magnetic force on a moving charge particle is perpendicular to both v and B
E. magnetism could be explained in terms of circulating currents in atoms
ans: B
64. Displacement current is:
A. dΦE /dt
B. 0 dΦE /dt
C. µ0 dΦE /dt
D. µ0 0 dΦE /dt
E. −dΦB /dt
ans: B
488
Chapter 32:
MAXWELL’S EQUATIONS; MAGNETISM AND MATTER
65. Displacement current exists wherever there is:
A. a magnetic field
B. moving charge
C. a changing magnetic field
D. an electric field
E. a changing electric field
ans: E
66. Displacement current exists in the region between the plates of a parallel plate capacitor if:
A. the capacitor leaks charge across the plates
B. the capacitor is being discharged
C. the capacitor is fully charged
D. the capacitor is fully discharged
E. none of the above are true
ans: B
67. An electric field exists in the cylindrical region shown and is parallel to the cylinder axis. The
magnitude of the field might vary with time according to any of the four graphs shown. Rank
the four variations according to the magnitudes of the magnetic field induced at the edge of
the region, least to greatest.
...
E
.......
......1
.
............... ..................... E
.
.
.......
......
.
.
.
.
.
.
.
.
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.....
× ..............
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× ×
.
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.
.
× × .....
... × ×
..............................................................................................
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..
× ×
...
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×
×
.
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.
×
×
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...... 3
.
.
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.
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.
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...
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×
×
.
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.
....
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.
.........
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..... ×
×..............
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............................................... 4
.
.
........
.
.
.
.
.......................................
.
.
.
.... .......
.......................
t
A.
B.
C.
D.
E.
2, 4, 3, 1
3 and 4 tie, then 1, 2
4, 3, 2, 1
4, 3, 1, 2
2, 1, 3, 4
ans: A
Chapter 32:
MAXWELL’S EQUATIONS; MAGNETISM AND MATTER
489
68. The diagram shows one plate of a parallel-plate capacitor from within the capacitor. The plate
is circular and has radius R. The dashed circles are four integration paths and have radii of
r1 = R/4, r2 = R/2, r3 = 3R/2, and r4 = 2R. Rank the paths according to the magnitude of
B · ds around the paths during the discharging of the capacitor, least to greatest.
...... ........ ........ ....... .......
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2 ...
...
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A.
B.
C.
D.
E.
3
4
1, 2 and 3 tie, then 4
1, 2, 3, 4
1, 2, 3 and 4 tie
4, 3, 1, 2
all tie
ans: C
69. A 1.2-m radius cylindrical region contains a uniform electric field along the cylinder axis. It is
increasing uniformly with time. To obtain a total displacement current of 2.0 × 10−9 A through
a cross section of the region, the magnitude of the electric field should change at a rate of:
A. 5.0 V/m · s
B. 12 V/m · s
C. 37 V/m · s
D. 50 V/m · s
E. 4.0 × 107 V/m · s
ans: D
70. A current of 1 A is used to charge a parallel plate capacitor with square plates. If the area
of each plate is 0.6 m2 the displacement current through a 0.3 m2 area wholly between the
capacitor plates and parallel to them is:
A. 1 A
B. 2 A
C. 0.7 A
D. 0.5 A
E. 0.25 A
ans: D
490
Chapter 32:
MAXWELL’S EQUATIONS; MAGNETISM AND MATTER
71. A 1-µF capacitor is connected to an emf that is increasing uniformly with time at a rate of
100 V/s. The displacement current between the plates is:
A. 0
B. 1 × 10−8 A
C. 1 × 10−6 A
D. 1 × 10−4 A
E. 100 A
ans: D
72. A magnetic field exists between the plates of a capacitor:
A. always
B. never
C. when the capacitor is fully charged
D. while the capacitor is being charged
E. only when the capacitor is starting to be charged
ans: D
73. Suppose you are looking into one end of a long cylindrical tube in which there is a uniform
electric field, pointing away from you. If the magnitude of the field is decreasing with time the
direction of the induced magnetic field is:
A. toward you
B. away from you
C. clockwise
D. counterclockwise
E. to your right
ans: D
74. Suppose you are looking into one end of a long cylindrical tube in which there is a uniform
electric field, pointing away from you. If the magnitude of the field is decreasing with time the
field lines of the induced magnetic field are:
A. circles
B. ellipses
C. straight lines parallel to the electric field
D. straight lines perpendicular to the electric field
E. none of the above
ans: A
75. A cylindrical region contains a uniform electric field that is along the cylinder axis and is
changing with time. If r is distance from the cylinder axis the magnitude of the magnetic field
within the region is:
A. uniform
B. proportional to 1/r
C. proportional to r2
D. proportional to 1/r2
E. proportional to r
ans: E
Chapter 32:
MAXWELL’S EQUATIONS; MAGNETISM AND MATTER
491
76. A cylindrical region contains a uniform electric field that is parallel to the axis and is changing
with time. If r is distance from the cylinder axis the magnitude of the magnetic field outside
the region is:
A. 0
B. proportional to 1/r
C. proportional to r2
D. proportional to 1/r2
E. proportional to r
ans: B
77. A 0.70-m radius cylindrical region contains a uniform electric field that is parallel to the axis
and is decreasing at the rate 5.0 × 1012 V/m · s. The magnetic field at a point 0.25 m from the
axis has a magnitude of:
A. 0
B. 7.0 × 10−6 T
C. 2.8 × 10−5 T
D. 5.4 × 10−5 T
E. 7.0 × 10−5 T
ans: B
78. A 0.70-m radius cylindrical region contains a uniform electric field that is parallel to the axis
and is decreasing at the rate 5.0 × 1012 V/m · s. The magnetic field at a point 1.2 m from the
axis has a magnitude of:
A. 0
B. 7.0 × 10−6 T
C. 1.1 × 10−5 T
D. 2.3 × 10−5 T
E. 2.8 × 10−5 T
ans: C
79. A 1-A current is used to charge a parallel plate capacitor. A large square piece of paper is
placed between
the plates and parallel to them so it sticks out on all sides. The value of the
integral B · ds around the perimeter of the paper is:
A. 2 T · m
B. 4π × 10−7 T · m
C. 8.85 × 10−12 T · m
D. 10−7 T · m
E. not determined from the given quantities
ans: B
80. A sinusoidal emf is connected to a parallel plate capacitor. The magnetic field between the
plates is:
A. 0
B. constant
C. sinusoidal and its amplitude does not depend on the frequency of the source
D. sinusoidal and its amplitude is proportional to the frequency of the source
E. sinusoidal and its amplitude is inversely proportional to the frequency of the source
ans: D
492
Chapter 32:
MAXWELL’S EQUATIONS; MAGNETISM AND MATTER
81. An electron is on the z axis moving toward the xy plane but it has not reached that plane yet.
At that instant:
A. there is only a true current through the xy plane
B. there is only a displacement current through the xy plane
C. there are both true and displacement currents through the xy plane
D. there is neither a true nor a displacement current through the xy plane
E. none of the above are true
ans: B
Chapter 32:
MAXWELL’S EQUATIONS; MAGNETISM AND MATTER
493
Chapter 33:
ELECTROMAGNETIC WAVES
1. Select the correct statement:
A. ultraviolet light has a longer wavelength than infrared
B. blue light has a higher frequency than x rays
C. radio waves have higher frequency than gamma rays
D. gamma rays have higher frequency than infrared waves
E. electrons are a type of electromagnetic wave
ans: D
2. Consider: radio waves (r), visible light (v), infrared light (i), x-rays (x), and ultraviolet light
(u). In order of increasing frequency, they are:
A. r, v, i, x, u
B. r, i, v, u, x
C. i, r, v, u, x
D. i, v, r, u, x
E. r, i, v, x, u
ans: B
3. The order of increasing wavelength for blue (b), green (g), red (r), and yellow (y) light is:
A. r, y, g, b
B. r, g, y, b
C. g, y, b, r
D. b, g, y, r
E. b, y, g, r
ans: D
4. Of
A.
B.
C.
D.
E.
the following human eyes are most sensitive to:
red light
violet light
blue light
green light
none of these (they are equally sensitive to all colors)
ans: D
5. Which of the following is NOT true for electromagnetic waves?
A. they consist of changing electric and magnetic fields
B. they travel at different speeds in vacuum, depending on their frequency
C. they transport energy
D. they transport momentum
E. they can be reflected
ans: B
494
Chapter 33:
ELECTROMAGNETIC WAVES
6. The product µ0 0 has the same units as:
A. (velocity)2
B. (velocity)1/2
C. 1/velocity
D. 1/velocity2
E. 1/velocity1/2
ans: D
7. Maxwell’s equations predict that the speed of electromagnetic waves in free space is given by:
A. µ0 0
B. (µ0 0 )1/2
C. 1/µ0 0
D. 1/(µ0 0 )1/2
E. 1/(µ0 0 )2
ans: D
8. Maxwell’s equations predict that the speed of light in free space is
A. an increasing function of frequency
B. a decreasing function of frequency
C. independent of frequency
D. a function of the distance from the source
E. a function of the size of the source
ans: C
9. The speed of light in vacuum is about:
A. 1100 ft/s
B. 93 × 106 m/s
C. 6 × 1023 m/s
D. 3 × 1010 cm/s
E. 186, 000 mph
ans: D
10. The Sun is about 1.5 × 1011 m away. The time for light to travel this distance is about:
A. 4.5 × 1018 s
B. 8 s
C. 8 min
D. 8 hr
E. 8 yr
ans: C
Chapter 33:
ELECTROMAGNETIC WAVES
495
11. The time for a radar signal to travel to the Moon and back, a one-way distance of about
3.8 × 108 m, is:
A. 1.3 s
B. 2.5 s
C. 8 s
D. 8 min
E. 1 × 106 s
ans: B
12. Which of the following types of electromagnetic radiation travels at the greatest speed in
vacuum?
A. Radio waves
B. Visible light
C. X rays
D. Gamma rays
E. All of these travel at the same speed
ans: E
13. Radio waves differ from visible light waves in that radio waves:
A. travel slower
B. have a higher frequency
C. travel faster
D. have a lower frequency
E. require a material medium
ans: D
14. Visible light has a frequency of about:
A. 5 × 1018 Hz
B. 5 × 1016 Hz
C. 5 × 1014 Hz
D. 5 × 1012 Hz
E. 5 × 1010 Hz
ans: C
15. The theoretical upper limit for the frequency of electromagnetic waves is:
A. just slightly greater than that of red light
B. just slightly less than that of blue light
C. the greatest x-ray frequency
D. none of the above (there is no upper limit)
E. none of the above (but there is an upper limit)
ans: D
496
Chapter 33:
ELECTROMAGNETIC WAVES
16. Radio waves of wavelength 3 cm have a frequency of:
A. 1 MHz
B. 9 MHz
C. 100 MHz
D. 10, 000 MHz
E. 900 MHz
ans: D
17. Radio waves of wavelength 300 m have a frequency of:
A. 10−3 kHz
B. 500 kHz
C. 1 MHz
D. 9 MHz
E. 108 kHz
ans: C
18. If the electric field in a plane electromagnetic wave is given by Em sin[(3 × 106 m−1 )x − ωt], the
value of ω is:
A. 0.01 rad/s
B. 10 rad/s
C. 100 rad/s
D. 9 × 1014 rad/s
E. 9 × 1016 rad/s
ans: D
19. An
A.
B.
C.
D.
E.
electromagnetic wave is generated by:
any moving charge
any accelerating charge
only a charge with changing acceleration
only a charge moving in a circle
only a charge moving in a straight line
ans: B
Chapter 33:
ELECTROMAGNETIC WAVES
497
20. The electric field for a plane electromagnetic wave traveling in the +y direction is shown.
Consider a point where E is in the +z direction. The B field is:
...
...
..
...
...
...
...
...
...
...
...
...
..
....................................................................................................................................................................................................................................................................................................
.
.
...
.
.
...
.
.
.
....
...
...
....
...
.
.
....
z
...
........
..
..
.
..
........
..
..
E
.
........
.
.
.........
...
x
A.
B.
C.
D.
E.
...
...
..........
..
...
...
..
..........
..
...
...
..........
..
.
........
.
.
.........
...
..
........
..
..
...
........
..
..
.
y
in the +x direction and in phase with the E field
in the−x direction and in phase with the E field
in the +x direction and one-fourth of a cycle out of phase with the E field
in the +z direction and in phase with the E field
in the +z direction and one-fourth of a cycle out of phase with the E field
ans: A
21. A plane electromagnetic wave is traveling in the positive x direction. At the instant shown the
electric field at the extremely narrow dashed rectangle is in the negative z direction and its
magnitude is decreasing. Which diagram correctly shows the directions and relative magnitudes
of the magnetic field at the edges of the rectangle?
y
...
...
..
...
...
...
...
...
...
...
...
...
..
.................................................................................................................................
.
.
...
.
.
....
.
.
..
....
...
....
....
.
.
...
....
...
E
..........
.
.
.
..
.....
x
dx
z
..
........
.. ......
....
...
....
..
..
E
⊗
A
...
........
...... ..
...
.
...
........
.........
...
.
E
⊗
B
..
........
.........
....
...
....
..
..
...
...
...
...
...
.
.........
........
...
E
⊗
...
.
....... ..
.........
...
C
...
.
....... ..
.........
..
E
⊗
D
...
...
...
...
...
.
.........
........
...
...
...
...
...
...
.
....... ..
........
...
E
⊗
...
........
.........
...
.
E
ans: B
22. In a plane electromagnetic wave in vacuum, the ratio E/B of the amplitudes in SI units of the
two fields is:
A. the speed of light
B. an increasing function of frequency
C. a√decreasing function of frequency
2√
D.
E. 1/ 2
ans: A
498
Chapter 33:
ELECTROMAGNETIC WAVES
23. If the magnetic field in a plane electromagnetic wave is along the y axis and its component
is given by Bm sin(kx − ωt), in SI units, then the electric field is along the z axis and its
component is given by:
A. (cBm ) cos(kx − ωt)
B. −(cBm /c) cos(kx − ωt)
C. −(cBm /c) sin(kx − ωt)
D. Bm cos(kx − ωt)
E. (cBm /c) sin(kx − ωt)
ans: E
24. If the electric field in a plane electromagnetic wave is along the y axis and its component is given
by Em sin(kx + ωt), in SI units, then the magnetic field is along the z axis and its component
is given by:
A. (Em /c) cos(kx + ωt)
B. −(Em /c) cos(kx + ωt)
C. −(Em /c) sin(kx + ωt)
D. Em cos(kx + ωt)
E. (Em /c) sin(kx + ωt)
ans: C
25. An electromagnetic wave is traveling in the positive x direction with its electric field along the
z axis and its magnetic field along the y axis. The fields are related by:
A. ∂E/∂x = µ0 0 ∂B/∂x
B. ∂E/∂x = µ0 0 ∂B/∂t
C. ∂B/∂x = µ0 0 ∂E/∂x
D. ∂B/∂x = µ0 0 ∂E/∂t
E. ∂B/∂x = −µ0 0 ∂E/∂t
ans: E
26. If the amplitude of the electric field in a plane electromagnetic wave is 100 V/m then the
amplitude of the magnetic field is:
A. 3.3 × 10−7 T
B. 6.7 × 10−7 T
C. 0.27 T
D. 8.0 × 107 T
E. 3.0 × 109 T
ans: A
27. For
A.
B.
C.
D.
E.
an electromagnetic wave the direction of the vector E × B gives:
the direction of the electric field
the direction of the magnetic field
the direction of wave propagation
the direction of the electromagnetic force on a proton
the direction of the emf induced by the wave
ans: C
Chapter 33:
ELECTROMAGNETIC WAVES
499
28. The dimensions of S = (1/µ0 )E × B are:
A. J/m2
B. J/s
C. W/s
D. W/m2
E. J/m3
ans: D
29. The time-averaged energy in a sinusoidal electromagnetic wave is:
A. overwhelmingly electrical
B. slightly more electrical than magnetic
C. equally divided between the electric and magnetic fields
D. slightly more magnetic than electrical
E. overwhelmingly magnetic
ans: C
30. At a certain point and a certain time the electric field of an electromagnetic wave is in the
negative z direction and the magnetic field is in the positive y direction. Which of the following
statements is true?
A. Energy is being transported in the positive x direction but half a cycle later, when the
electric field is in the opposite direction, it will be transported in the negative x direction
B. Energy is being transported in the positive x direction and half a cycle later, when the
electric field is in the opposite direction, it will still be transported in the positive x direction
C. Energy is being transported in the negative x direction but half a cycle later, when the
electric field is in the opposite direction, it will be transported in the positive x direction
D. Energy is being transported in the negative x direction and half a cycle later, when the
electric field is in the opposite direction, it will still be transported in the negative x
direction
E. None of the above are true
ans: B
31. An electromagnetic wave is transporting energy in the negative y direction. At one point and
one instant the magnetic field is in the positive x direction. The electric field at that point and
instant is:
A. positive y direction
B. negative y direction
C. positive z direction
D. negative z direction
E. negative x direction
ans: D
500
Chapter 33:
ELECTROMAGNETIC WAVES
32. A point source emits electromagnetic energy at a rate of 100 W. The intensity 10 m from the
source is:
2
A. 10 W/m
2
B. 1.6 W/m
C. 1 W/m2
2
D. 0.024 W/m
2
E. 0.080 W/m
ans: E
2
33. The light intensity 10 m from a point source is 1000 W/m . The intensity 100 m from the same
source is:
2
A. 1000 W/m
2
B. 100 W/m
2
C. 10 W/m
2
D. 1 W/m
2
E. 0.1 W/m
ans: C
34. When the distance between a point source of light and a light meter is reduced from 6.0 m to
2.0 m, the intensity of illumination at the meter will be the original value multiplied by:
A. 3
B. 9
C. 1/3
D. 1/9
E. 1
ans: A
35. The magnetic field in a sinusoidal light wave has an amplitude of 3.3 × 10−7 T. The intensity
of the wave is:
2
A. 1.7 × 10−4 W/m
2
B. 13 W/m
C. 27 W/m2
2
D. 1.0 × 105 W/m
2
E. 4.0 × 1010 W/m
ans: B
36. A sinusoidal electromagnetic wave with an electric field amplitude of 100 V/m is incident normally on a surface with an area of 1 cm2 and is completely absorbed. The energy absorbed in
10 s is:
A. 1.3 mJ
B. 13 mJ
C. 27 mJ
D. 130 mJ
E. 270 mJ
ans: B
Chapter 33:
ELECTROMAGNETIC WAVES
501
37. Evidence that electromagnetic waves carry momentum is:
A. the tail of a comet points away from the Sun
B. electron flow through a wire generates heat
C. a charged particle in a magnetic field moves in a circular orbit
D. heat can be generated by rubbing two sticks together
E. the Doppler effect
ans: A
38. Light of uniform intensity shines perpendicularly on a totally absorbing surface, fully illuminating the surface. If the area of the surface is decreased:
A. the radiation pressure increases and the radiation force increases
B. the radiation pressure increases and the radiation force decreases
C. the radiation pressure stays the same and the radiation force increases
D. the radiation pressure stays the same and the radiation force decreases
E. the radiation pressure decreases and the radiation force decreases
ans: D
2
39. Light with an intensity of 1 kW/m falls normally on a surface and is completely absorbed.
The radiation pressure is:
A. 1 kPa
B. 3 × 1011 Pa
C. 1.7 × 10−6 Pa
D. 3.3 × 10−6 Pa
E. 6.7 × 10−6 Pa
ans: D
2
40. Light with an intensity of 1 kW/m falls normally on a surface and is completely reflected. The
radiation pressure is:
A. 1 kPa
B. 3 × 1011 Pa
C. 1.7 × 10−6 Pa
D. 3.3 × 10−6 Pa
E. 6.7 × 10−6 Pa
ans: E
2
41. Light with an intensity of 1 kW/m falls normally on a surface with an area of 1 cm2 and is
completely absorbed. The force of the radiation on the surface is:
A. 1.0 × 10−4 N
B. 3.3 × 10−11 N
C. 1.7 × 10−10 N
D. 3.3 × 10−10 N
E. 6.7 × 10−10 N
ans: D
502
Chapter 33:
ELECTROMAGNETIC WAVES
2
42. Light with an intensity of 1 kW/m falls normally on a surface with an area of 1 cm2 and is
completely reflected. The force of the radiation on the surface is:
A. 1.0 × 10−4 N
B. 3.3 × 10−11 N
C. 1.7 × 10−10 N
D. 3.3 × 10−10 N
E. 6.7 × 10−10 N
ans: E
43. A company claims to have developed material that absorbs light energy without a transfer of
momentum. Such material is:
A. impossible
B. possible, but very expensive
C. inexpensive and already in common use
D. in use by NASA but is not commercially available
E. a breakthrough in high technology
ans: A
44. Polarization experiments provide evidence that light is:
A. a longitudinal wave
B. a stream of particles
C. a transverse wave
D. some type of wave
E. nearly monochromatic
ans: C
45. A vertical automobile radio antenna is sensitive to electric fields that are polarized:
A. horizontally
B. in circles around the antenna
C. vertically
D. normal to the antenna in the forward direction
E. none of the above
ans: C
46. For
A.
B.
C.
D.
E.
linearly polarized light the plane of polarization is:
perpendicular to both the direction of polarization and the direction of propagation
perpendicular to the direction of polarization and parallel to the direction of propagation
parallel to the direction of polarization and perpendicular to the direction of propagation
parallel to both the direction of polarization and the direction of propagation
none of the above
ans: D
Chapter 33:
ELECTROMAGNETIC WAVES
503
47. Light from any ordinary source (such as a flame) is usually:
A. unpolarized
B. plane polarized
C. circularly polarized
D. elliptically polarized
E. monochromatic
ans: A
48. The electric field in unpolarized light:
A. has no direction at any time
B. rotates rapidly
C. is always parallel to the direction of propagation
D. changes direction randomly and often
E. remains along the same line but reverses direction randomly and often
ans: D
49. The diagrams show four pairs of polarizing sheets, with the polarizing directions indicated by
dashed lines. The two sheets of each pair are placed one behind the other and the front sheet
is illuminated by unpolarized light. The incident intensity is the same for all pairs of sheets.
Rank the pairs according to the intensity of the transmitted light, least to greatest.
........
........
........
.........
............. .............
......... .............
............. .............
............. .............
.... . .....
.... ..... ..
.... .....
.... . .....
...
...
...
...
.
.
.
.
.
...
...
...
...
.. 45◦... ....
.. 75◦ .....
.. 60◦ .....
.... 60◦ ..... ..
.
.
.
.
.
.
...
...
.
...
...
...
..
.
.
...
...
...
.
.
.
.
.
.
..
.
...
...
..
...
.
.
.
.
...
...
...
...
...
.
..
.
.
.
.
.
.
.
..
....
..
....
....
.
..
..
.....
... ...
.
. ..
. .
.......
.......
....... ..... .........
.................................
.......................
......................
................
A.
B.
C.
D.
E.
504
........
......... .................
....
..
..
.
...
.
◦ ....
..
.. 60
....
..
.
...
...
..
... .....
.
..
..... ....
.............................
........
......... .................
.
....
..
.
..
.
...
◦ ....
45
.
....
.
..
..
...
.
..
... .... ...
.
..
..... .
.............................
........
......... ..................
....
..
...
.
.
◦ ....
..
.. 75
....
..
..
...
..
..
...
.
.
...
..
..... ...
...............................
........
......... ..................
....
..
.
..
.
.... ◦ .
...
.
...
.... 45
..
..
...
...
..
... .. ......
.
.
.......
........ ...........
............
1
2
3
4
1, 2, 3,
4, 2, 1,
2, 4, 3,
2, 4, 1,
3, 1, 4,
ans: D
4
3
1
3
2
Chapter 33:
ELECTROMAGNETIC WAVES
50. A clear sheet of polaroid is placed on top of a similar sheet so that their polarizing axes make an
angle of 30◦ with each other. The ratio of the intensity of emerging light to incident unpolarized
light is:
A. 1 : 4
B. 1 : 3
C. 1 : 2
D. 3 : 4
E. 3 : 8
ans: E
51. An unpolarized beam of light has intensity I0 . It is incident on two ideal polarizing sheets.
The angle between the axes of polarization of these sheets is θ. Find θ if the emerging light
has intensity I0 /4:
A. sin−1 (1/2)
√
B. sin−1 (1/ 5)
C. cos−1 (1/2)
√
D. cos−1 (1/ 2)
E. tan−1 (1/4)
ans: D
52. In a stack of three polarizing sheets the first and third are crossed while the middle one has its
axis at 45◦ to the axes of the other two. The fraction of the intensity of an incident unpolarized
beam of light that is transmitted by the stack is:
A. 1/2
B. 1/3
C. 1/4
D. 1/8
E. 0
ans: D
53. Three polarizing sheets are placed in a stack with the polarizing directions of the first and third
perpendicular to each other. What angle should the polarizing direction of the middle sheet
make with the polarizing direction of the first sheet to obtain maximum transmitted intensity
when unpolarized light is incident on the stack?
A. 0
B. 30◦
C. 45◦
D. 60◦
E. 90◦
ans: C
Chapter 33:
ELECTROMAGNETIC WAVES
505
54. Three polarizing sheets are placed in a stack with the polarizing directions of the first and third
perpendicular to each other. What angle should the polarizing direction of the middle sheet
make with the polarizing direction of the first sheet to obtain zero transmitted intensity when
unpolarized light is incident on the stack?
A. 0
B. 30◦
C. 45◦
D. 60◦
E. All angles allow light to pass through
ans: A
55. The relation θincident = θreflected , which applies as a ray of light strikes an interface between
two media, is known as:
A. Faraday’s law
B. Snell’s law
C. Ampere’s law
D. Cole’s law
E. none of these
ans: E
56. The relation n1 sin θ1 = n2 sin θ2 , which applies as a ray of light strikes an interface between
two media, is known as:
A. Gauss’ law
B. Snell’s law
C. Faraday’s law
D. Cole’s law
E. law of sines
ans: B
57. As
A.
B.
C.
D.
E.
used in the laws of reflection and refraction, the “normal” direction is:
any convenient direction
tangent to the interface
along the incident ray
perpendicular to the electric field vector of the light
perpendicular to the interface
ans: E
58. When an electromagnetic wave meets a reflecting surface, the direction taken by the reflected
wave is determined by:
A. the material of the reflecting surface
B. the angle of incidence
C. the index of the medium
D. the intensity of the wave
E. the wavelength
ans: B
506
Chapter 33:
ELECTROMAGNETIC WAVES
59. The index of refraction of a substance is:
A. the speed of light in the substance
B. the angle of refraction
C. the angle of incidence
D. the speed of light in vacuum divided by the speed of light in the substance
E. measured in radians
ans: D
60. The units of index of refraction are:
A. m/s
B. s/m
C. radian
D. m/s2
E. none of these
ans: E
61. The diagram shows the passage of a ray of light from air into a substance X. The index of
refraction of X is:
....
....
.... .
............ 40◦
.......
◦ ....... ......................
50 .... ....
.
.... .
..
...
... ....
... ........ ◦
.......... 70
...
...
...
..
....................
...
.
20◦..........
.
A.
B.
C.
D.
E.
air
X
0.53
0.88
1.9
2.2
3.0
ans: C
Chapter 33:
ELECTROMAGNETIC WAVES
507
62. If nwater = 1.33, what is the angle of refraction for the ray shown?
air
water
..........
60 ..... .
............
... ...........
.
.. ◦
.. 30
.
.
.
..
◦
A.
B.
C.
D.
E.
...
...
...
....
.....
19◦
22◦
36◦
42◦
48◦
ans: D
63. Which diagram below illustrates the path of a light ray as it travels from a given point X in
air to another given point Y in glass?
Y
•..
.
....
.
....
..............
.....
.......
.
.
.
.
.
X•
X
A
Y
...•
.
.
...
..........
...
...
.
.
...
.•.
X
B
C
Y
..•.
.
.
...
..........
.
...
..........
..
X •.
Y
•.
...
.
........
.
...........
.
..
.....
X •..
D
E
ans: E
508
Chapter 33:
Y
....•.
.
.
.
...
............
.
..
.....
.......
.
•..
ELECTROMAGNETIC WAVES
64. The index of refraction for diamond is 2.5. Which of the following is correct for the situation
shown?
...
...
...
...
...
... a
......
.
b .......... ..................
...
diamond
............
..
..
..
....... ....
.......... d
.........
air
.. ......
.....
....... .
.
.
.
.
.
....
.
.
.
.
.
.
.
.
.
.
.
.
.
.......
c
..............
A.
B.
C.
D.
E.
(sin a)/(sin b) = 2.5
(sin b)/(sin d) = 2.5
(cos a)/(cos c) = 2.5
(sin c)/(sin a) = 2.5
a/c = 2.5
ans: D
65. When light travels from medium X to medium Y as shown:
.......
.......
..........
..............
X
.......
...
...
Y
...
...
...
...
..
.............
.
A.
B.
C.
D.
E.
both the
both the
both the
both the
both the
ans: C
speed and the frequency decrease
speed and the frequency increase
speed and the wavelength decrease
speed and the wavelength increase
wavelength and the frequency are unchanged
66. A ray of light passes obliquely through a plate of glass having parallel faces. The emerging ray:
A. is totally internally reflected
B. is bent more toward the normal than the incident ray
C. is bent further away from the normal than the incident ray
D. is parallel to the incident ray but displaced sideways
E. lies on the same straight line as the incident ray
ans: D
Chapter 33:
ELECTROMAGNETIC WAVES
509
67. When light passes from air to glass, it bends:
A. toward the normal without changing speed
B. toward the normal and slows down
C. toward the normal and speeds up
D. away from the normal and slows down
E. away from the normal and speeds up
ans: B
68. A ray of light passes through three media as shown. The speed of light in these media obey:
.....
.....
.....
................
.....
.....
medium 1
....
...
...
medium 2
..........
.......
.......
....... medium 3
.......
....... .
............
.
A.
B.
C.
D.
E.
69. As
A.
B.
C.
D.
E.
v1 > v2
v3 > v2
v3 > v 1
v2 > v1
v1 > v3
ans: C
> v3
> v1
> v2
> v3
> v2
light goes from one medium to another, it is bent away from the normal. Then:
the speed of the light has increased
dispersion must occur
the second medium has a higher index of refraction than the first
no change in speed has occurred
refraction has not occurred because refraction means a bending toward the normal
ans: A
70. A pole stands in a river, half in and half out of the water. Another pole of the same length
stands vertically on the shore at a place where the ground is level. The shadow cast by the
pole in the river on the river bottom is:
A. slightly longer than the shadow of the pole on land
B. much longer than the shadow of the pole on land
C. shorter than the shadow of the pole on land
D. shorter than the shadow of the pole on land if the Sun is high and longer if the sun is low
E. the same length as the shadow of the pole on land
ans: C
510
Chapter 33:
ELECTROMAGNETIC WAVES
71. The rectangular metal tank shown is filled with an unknown liquid. The observer, whose eye
is level with the top of the tank, can just see corner E. The index of refraction of this liquid is:
....
........
............. ...
........
...
eye
3 ft
E
4 ft
A.
B.
C.
D.
E.
1.75
1.67
1.50
1.33
1.25
ans: E
72. The index of refraction of benzene is 1.80. The critical angle for total internal reflection, at a
benzene-air interface, is about:
A. 56◦
B. 47◦
C. 34◦
D. 22◦
E. 18◦
ans: C
73. The index of refraction of a certain glass is 1.50. The sine of the critical angle for total internal
reflection at a glass-air interface is:
A. 0.50
B. 0.67
C. 0.75
D. 1.00
E. 1.50
ans: B
Chapter 33:
ELECTROMAGNETIC WAVES
511
74. The illustration shows total internal reflection taking place in a piece of glass. The index of
refraction of this glass:
.........
.. .................
..................... ..........
.......
.. 60◦
.......
.
.. ...
........
.
.
.
....... ....... .......... . ....... ....... ....... ....... ....... ....... ....... ....... ............
..
..
.. ...... air
.......
..
..
.......
...
.......
..
.
..
.
.......
.. glass ....
.......
.....
.
..
.
...
...
..
.
..
.
...
..
........
..
..........
.
A.
B.
C.
D.
E.
is at least 2.0
is at most 2.0
is at least 1.15
is at most 1.15
cannot be calculated from the given data
ans: C
75. The critical angle for total internal reflection at a diamond-air interface is 25◦ . Suppose light
is incident at an angle of θ with the normal. Total internal reflection will occur if the incident
medium is:
A. air and θ = 25◦
B. air and θ > 25◦
C. air and θ < 25◦
D. diamond and θ < 25◦
E. diamond and θ > 25◦
ans: E
76. If nwater = 1.50 and nglass = 1.33, then total internal reflection at an interface between this
glass and water:
A. occurs whenever the light goes from glass to water
B. occurs whenever the light goes from water to glass
C. may occur when the light goes from glass to water
D. may occur when the light goes from water to glass
E. can never occur at this interface
ans: D
77. The separation of white light into colors by a prism is associated with:
A. total internal reflection
B. partial reflection from each surface
C. variation of index of refraction with wavelength
D. a decrease in the speed of light in the glass
E. selective absorption of various colors
ans: C
512
Chapter 33:
ELECTROMAGNETIC WAVES
78. The diagram shows total internal reflection. Which of the following statements is NOT true?
A ..
B
.....
.............
N
.....
.
.
.
......
....
.....
.
.............
.
.
.....
...
..... .......
medium I
.
.......
.. .. .. .. .. .. .. .. .. .. .. .. ..
.. .. .. .. .. .. .. .. .. .
.. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. ..
... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
O
A.
B.
C.
D.
E.
medium II
Angle AON is the angle of incidence
Angle AON = angle BON
Angle AON must be the critical angle
The speed of light in medium II is greater than that in medium I
if angle AON were increased, there would still be total internal reflection
ans: C
79. A ray of light in water (index n1 ) is incident on its surface (with air) at the critical angle for
total internal reflection. Some oil (index n2 ) is now floated on the water. The angle between
the ray in the oil and the normal is:
A. sin−1 (1.00)
B. sin−1 (1/n1 )
C. sin−1 (1/n2 )
D. sin−1 (n1 /n2 )
E. sin−1 (n2 /n1 )
ans: C
Chapter 33:
ELECTROMAGNETIC WAVES
513
Chapter 34:
IMAGES
1. A virtual image is one:
A. toward which light rays converge but do not pass through
B. from which light rays diverge but do not pass through
C. from which light rays diverge as they pass through
D. toward which light rays converge and pass through
E. with a ray normal to a mirror passing through it
ans: B
2. Which of the following is true of all virtual images?
A. They can be seen but not photographed
B. They are ephemeral
C. They are smaller than the objects
D. They are larger than the objects
E. None of the above
ans: E
3. When you stand in front of a plane mirror, your image is:
A. real, erect, and smaller than you
B. real, erect, and the same size as you
C. virtual, erect, and smaller than you
D. virtual, erect, and the same size as you
E. real, inverted, and the same size as you
ans: D
4. An
A.
B.
C.
D.
E.
object is 2 m in front of a plane mirror. Its image is:
virtual, inverted, and 2 m behind the mirror
virtual, inverted, and 2 m in front of the mirror
virtual, erect, and 2 m in front of the mirror
real, erect, and 2 m behind the mirror
none of the above
ans: E
5. A ball is held 50 cm in front of a plane mirror. The distance between the ball and its image is:
A. 100 cm
B. 150 cm
C. 200 cm
D. 0
E. 50 cm
ans: A
514
Chapter 34:
IMAGES
6. A card marked IAHIO8 is standing upright in front of a plane mirror. Which of the following
is NOT true?
A. The image is virtual
B. The image shifts its position as the observer shifts his position
C. The image appears as 8OIHAI to a person looking in the mirror
D. The image is caused mostly by specular rather than diffuse reflection
E. The image is the same size as the object
ans: B
7. The angle between a horizontal ruler and a vertical plane mirror is 30◦ . The angle between the
ruler and its image is:
A. 15◦
B. 30◦
C. 60◦
D. 90◦
E. 180◦
ans: C
8. A 5.0-ft woman wishes to see a full length image of herself in a plane mirror. The minimum
length mirror required is:
A. 5 ft
B. 10 ft
C. 2.5 ft
D. 3.54 ft
E. variable: the farther away she stands the smaller the required mirror length
ans: C
9. A man holds a rectangular card in front of and parallel to a plane mirror. In order for him to
see the entire image of the card, the least mirror area needed is:
A. that of the whole mirror, regardless of its size
B. that of the pupil of his eye
C. one-half that of the card
D. one-fourth that of the card
E. an amount which decreases with his distance from the mirror
ans: D
10. A light bulb burns in front of the center of a 40-cm wide plane mirror that is hung vertically
on a wall. A man walks in front of the mirror along a line that is parallel to the mirror and
twice as far from it as the bulb. The greatest distance he can walk and still see the image of
the bulb is:
A. 20 cm
B. 40 cm
C. 60 cm
D. 80 cm
E. 120 cm
ans: E
Chapter 34:
IMAGES
515
11. A plane mirror is in a vertical plane and is rotating about a vertical axis at 100 rpm. A
horizontal beam of light is incident on the mirror. The reflected beam will rotate at:
A. 100 rpm
B. 141 rpm
C. 0 rpm
D. 200 rpm
E. 10, 000 rpm
ans: D
12. A candle C sits between two parallel mirrors, a distance 0.2d from mirror 1. Here d is the
distance between the mirrors. Multiple images of the candle appear in both mirrors. How far
behind mirror 1 are the nearest three images of the candle in that mirror?
1
2
0.2d
←→
•C
A.
B.
C.
D.
E.
0.2d, 1.8d,
0.2d, 2.2d,
0.2d, 1.8d,
0.2d, 0.8d,
0.2d, 1.8d,
ans: A
2.2d
4.2d
3.8d
1.4d
3.4d
←−−−− d −−−−→
13. Two plane mirrors make an angle of 120◦ with each other. The maximum number of images
of an object placed between them is:
A. one
B. two
C. three
D. four
E. more than four
ans: B
14. A parallel beam of monochromatic light in air is incident on a plane glass surface. In the glass,
the beam:
A. remains parallel
D. undergoes dispersion
B. becomes diverging
E. follows a parabolic path
C. becomes converging
ans: A
516
Chapter 34:
IMAGES
15. The focal length of a spherical mirror is N times its radius of curvature where N is:
A. 1/4
B. 1/2
C. 1
D. 2
E. 4
ans: B
16. Real images formed by a spherical mirror are always:
A. on the side of the mirror opposite the source
B. on the same side of the mirror as the source but closer to the mirror than the source
C. on the same side of the mirror as the source but closer to the mirror than the focal point
D. on the same side of the mirror as the source but further from the mirror than the focal
point
E. none of the above
ans: E
17. The image produced by a convex mirror of an erect object in front of the mirror is always:
A. virtual, erect, and larger than the object
B. virtual, erect, and smaller than the object
C. real, erect, and larger than the object
D. real, erect, and smaller than the object
E. none of the above
ans: B
18. An
A.
B.
C.
D.
E.
erect object is located between a concave mirror and its focal point. Its image is:
real, erect, and larger than the object
real, inverted, and larger than the object
virtual, erect, and larger than the object
virtual, inverted, and larger than the object
virtual, erect, and smaller than the object
ans: C
19. An erect object is in front of a convex mirror a distance greater than the focal length. The
image is:
A. real, inverted, and smaller than the object
B. virtual, inverted, and larger than the object
C. real, inverted, and larger than the object
D. virtual, erect, and smaller than the object
E. real, erect, and larger than the object
ans: D
Chapter 34:
IMAGES
517
20. As an object is moved from the center of curvature of a concave mirror toward its focal point
its image:
A. remains virtual and becomes larger
B. remains virtual and becomes smaller
C. remains real and becomes larger
D. remains real and becomes smaller
E. remains real and approaches the same size as the object
ans: C
21. As an object is moved from a distant location toward the center of curvature of a concave
mirror its image:
A. remains virtual and becomes smaller
B. remains virtual and becomes larger
C. remains real and becomes smaller
D. remains real and becomes larger
E. changes from real to virtual
ans: D
22. The image of an erect candle, formed using a convex mirror, is always:
A. virtual, inverted, and smaller than the candle
B. virtual, inverted, and larger than the candle
C. virtual, erect, and larger than the candle
D. virtual, erect, and smaller than the candle
E. real, erect, and smaller than the candle
ans: D
23. At what distance in front of a concave mirror must an object be placed so that the image and
object are the same size?
A. a focal length
B. half a focal length
C. twice a focal length
D. less than half focal length
E. more than twice a focal length
ans: B
24. A point source is to be used with a concave mirror to produce a beam of parallel light. The
source should be placed:
A. as close to the mirror as possible
B. at the center of curvature
C. midway between the center of curvature and the focal point
D. midway between the center of curvature and the mirror
E. midway between the focal point and the mirror
ans: D
518
Chapter 34:
IMAGES
25. A concave mirror forms a real image that is twice the size of the object. If the object is 20 cm
from the mirror, the radius of curvature of the mirror must be about:
A. 13 cm
B. 20 cm
C. 27 cm
D. 40 cm
E. 80 cm
ans: C
26. A man stands with his nose 8 cm from a concave shaving mirror of radius 32 cm The distance
from the mirror to the image of his nose is:
A. 8 cm
B. 12 cm
C. 16 cm
D. 24 cm
E. 32 cm
ans: C
27. The figure shows a concave mirror with a small object located at the point marked 6. If the
image is also at this point, then the center of curvature of the mirror is at the point marked:
................
.................
...............
..............
..............
..............
.................
....................
.......................................
....
...
...
...
...
...
...
....
...
..
...
...
...
...
....
...
....
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
.
.............................................
A.
B.
C.
D.
E.
2
4
•
6
8
10
12
3
4
6
9
12
ans: C
28. A concave spherical mirror has a focal length of 12 cm. If an object is placed 6 cm in front of
it the image position is:
A. 4 cm behind the mirror
B. 4 cm in front of the mirror
C. 12 cm behind the mirror
D. 12 cm in front of the mirror
E. at infinity
ans: C
Chapter 34:
IMAGES
519
29. A concave spherical mirror has a focal length of 12 cm. If an object is placed 18 cm in front of
it the image position is:
A. 7.2 cm behind the mirror
B. 7.2 cm in front of the mirror
C. 36 cm behind the mirror
D. 36 cm in front of the mirror
E. at infinity
ans: D
30. A convex spherical mirror has a focal length of 12 cm. If an object is placed 6 cm in front of it
the image position is:
A. 4 cm behind the mirror
B. 4 cm in front of the mirror
C. 12 cm behind the mirror
D. 12 cm in front of the mirror
E. at infinity
ans: A
31. A concave spherical mirror has a focal length of 12 cm. If an erect object is placed 6 cm in front
of it:
A. the magnification is 2 and the image is erect
B. the magnification is 2 and the image is inverted
C. the magnification is 0.67 and the image is erect
D. the magnification is 0.67 and the image is inverted
E. the magnification is 0.5 and the image is erect
ans: A
32. An erect object is located on the central axis of a spherical mirror. The magnification is −3.
This means:
A. its image is real, inverted, and on the same side of the mirror
B. its image is virtual, erect, and on the opposite side of the mirror
C. its image is real, erect, and on the same side of the mirror
D. its image is real, inverted, and on the opposite side of the mirror
E. its image is virtual, inverted, and on the opposite side of the mirror
ans: A
520
Chapter 34:
IMAGES
33. An object O, in air, is in front of the concave spherical refracting surface of a piece of glass.
Which of the general situations depicted below is like this situation?
...........................
n1 ... n2
..
• .....
O ....
...
..........................
n2 > n 1
A
..................................
...........................
n1 ... n2
n1 ..... n2
...
..
• .....
• ....
O ....
O ....
...
..................................
..........................
n2 < n 1
n2 > n 1
B
C
..................................
..................................
n1 ..... n2
n1 ..... n2
...
...
• .....
• .....
O ...
O ...
...................................
...................................
n2 = n 1
n2 < n 1
D
E
ans: C
34. A concave refracting surface is one with a center of curvature:
A. to the left of the surface
B. to the right of the surface
C. on the side of the incident light
D. on the side of the refracted light
E. on the side with the higher index of refraction
ans: C
35. A convex refracting surface has a radius of 12 cm. Light is incident in air (n = 1) and is
refracted into a medium with an index of refraction of 2. Light incident parallel to the central
axis is focused at a point:
A. 3 cm from the surface
B. 6 cm from the surface
C. 12 cm from the surface
D. 18 cm from the surface
E. 24 cm from the surface
ans: E
36. A convex refracting surface has a radius of 12 cm. Light is incident in air (n = 1) and refracted
into a medium with an index of refraction of 2. To obtain light with rays parallel to the central
axis after refraction a point source should be placed on the axis:
A. 3 cm from the surface
B. 6 cm from the surface
C. 12 cm from the surface
D. 18 cm from the surface
E. 24 cm from the surface
ans: C
Chapter 34:
IMAGES
521
37. A concave refracting surface of a medium with index of refraction n produces a real image no
matter where an object is placed outside:
A. always
B. only if the index of refraction of the surrounding medium is less than n
C. only if the index of refraction of the surrounding medium is greater than n
D. never
E. none of the above
ans: E
38. A convex spherical refracting surface separates a medium with index of refraction 2 from air.
The image of an object outside the surface is real:
A. always
B. never
C. only if it is close to the surface
D. only if it is far from the surface
E. only if the radius of curvature is small
ans: D
39. A convex spherical surface with radius r separates a medium with index of refraction 2 from
air. As an object is moved toward the surface from far away along the central axis, its image:
A. changes from virtual to real when it is r/2 from the surface
B. changes from virtual to real when it is r from the surface
C. changes from real to virtual when it is r/2 from the surface
D. changes from real to virtual when it is r from the surface
E. remains real
ans: D
40. A concave spherical surface with radius r separates a medium with index of refraction 2 from
air. As an object is moved toward the surface from far away along the central axis, its image:
A. changes from virtual to real when it is r/2 from the surface
B. changes from virtual to real when it is 2r from the surface
C. changes from real to virtual when it is r/2 from the surface
D. changes from real to virtual when it is 2r from the surface
E. remains virtual
ans: E
41. An erect object is placed on the central axis of a thin lens, further from the lens than the
magnitude of its focal length. The magnification is +0.4. This means:
A. the image is real and erect and the lens is a converging lens
B. the image is real and inverted and the lens is a converging lens
C. the image is virtual and erect, and the lens is a diverging lens
D. the image is virtual and erect, and the lens is a converging lens
E. the image is virtual and inverted and the lens is a diverging lens
ans: C
522
Chapter 34:
IMAGES
42. Where must an object be placed in front of a converging lens in order to obtain a virtual image?
A. At the focal point
B. At twice the focal length
C. Greater than the focal length
D. Between the focal point and the lens
E. Between the focal length and twice the focal length
ans: D
43. An
is:
A.
B.
C.
D.
E.
erect object placed outside the focal point of a converging lens will produce an image that
44. An
A.
B.
C.
D.
E.
object is 30 cm in front of a converging lens of focal length 10 cm. The image is:
real and larger than the object
real and the same size than the object
real and smaller than the object
virtual and the same size than the object
virtual and smaller than the object
ans: C
erect and virtual
inverted and virtual
erect and real
inverted and real
impossible to locate
ans: D
45. Let p denote the object-lens distance and i the image-lens distance. The image produced by a
lens of focal length f has a height that can be obtained from the object height by multiplying
it by:
A. p/i
B. i/p
C. f /p
D. f /i
E. i/f
ans: B
46. A camera with a lens of focal length 6.0 cm takes a picture of a 1.4-m tall man standing 11 m
away. The height of the image is about:
A. 0.39 cm
B. 0.77 cm
C. 1.5 cm
D. 3.0 cm
E. 6.0 cm
ans: B
Chapter 34:
IMAGES
523
47. A hollow lens is made of thin glass, as shown. It can be filled with air, water (n = 1.3) or CS2
(n = 1.6). The lens will diverge a beam of parallel light if it is filled with:
.....................
....................
............
...........
..............
..............
.....................
...........
.....................
.............................................................
...
...
...
...
...
...
...
...
....
...
..
..
...
..
...
...
....
.
....
..
...
..
...
..
...
....
...
...
...
.
.
...
..
.
...
..
..
.
.
.
.
..........................................................
A.
B.
C.
D.
E.
air and immersed in air
air and immersed in water
water and immersed in CS2
CS2 and immersed in water
CS2 and immersed in CS2
ans: D
48. The object-lens distance for a certain converging lens is 400 mm. The image is three times the
size of the object. To make the image five times the size of the object-lens distance must be
changed to:
A. 360 mm
B. 540 mm
C. 600 mm
D. 720 mm
E. 960 mm
ans: A
49. An
A.
B.
C.
D.
E.
erect object is 2f in front of a converging lens of focal length f . The image is:
real, inverted, magnified
real, erect, same size
real, inverted, same size
virtual, inverted, reduced
real, inverted, reduced
ans: C
50. An
A.
B.
C.
D.
E.
ordinary magnifying glass in front of an erect object produces an image that is:
real and erect
real and inverted
virtual and inverted
virtual and erect
none of these
ans: D
524
Chapter 34:
IMAGES
51. The Sun subtends 0.5◦ as seen from Earth. The diameter of its image, using a 1.0-m focal
length lens, is about:
A. 10 cm
B. 2 cm
C. 1 cm
D. 5 mm
E. 1 mm
ans: C
52. An object is in front of a converging lens, at a distance less than the focal length from the lens.
Its image is:
A. virtual and larger than the object
B. real and smaller than the object
C. virtual and smaller than the object
D. real and larger than the object
E. virtual and the same size as the object
ans: A
53. A plano-convex glass (n = 1.5) lens has a curved side whose radius is 50 cm. If the image size
is to be the same as the object size, the object should be placed at a distance from the lens of:
A. 50 cm
B. 100 cm
C. 200 cm
D. 400 cm
E. 340 cm
ans: C
54. Which of the following five glass lenses is a diverging lens?
...............
.........................
........................
....................
....................
..............
....................
...............
..............................................
...
...
...
...
....
...
...
....
..
..
...
...
..
....
..
....
....
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
..
.
...............................................
A
.......
...........
......................
........................
....................
..............
.................
...........
.......
........................
....
...
...
...
...
....
...
...
...
...
...
....
..
...
...
....
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
..
....................
B
..................
..................
..................
..................
..................
..................
..................
.............
........
... ....
... ....
... ...
...
...
...
...
...
...
...
...
...
...
..
...
..
...
..
...
....
.
...
.
...
...
... .....
... ....
........
..
..
.......
..........
............
............
.........
......
.
....
... ....
... .....
...
...
...
...
.
...
...
...
...
...
....
...
...
...
....
...
...
...
...
...
..
.
...
...
...
...
...
..
...
...
.
...
.
... ....
........
C
D
E
........
.....................
.................
.............................
.................
..............
.........
......
ans: A
55. The bellows of an adjustable camera can be extended so that the largest film to lens distance
is one and one-half times the focal length. If the focal length is 12 cm, the nearest object that
can be sharply focused on the film must be what distance from the lens?
A. 12 cm
B. 24 cm
C. 36 cm
D. 48 cm
E. 72 cm
ans: C
Chapter 34:
IMAGES
525
56. A 3-cm high object is in front of a thin lens. The object distance is 4 cm and the image distance
is −8 cm. The image height is:
A. 0.5 cm
B. 1 cm
C. 1.5 cm
D. 6 cm
E. 24 cm
ans: D
57. When a single-lens camera is focused on a distant object, the lens-to-film distance is found to
be 40.0 mm. To focus on an object 0.54 m in front of the lens, the film-to-lens distance should
be:
A. 40.0 mm
B. 37.3 mm
C. 36.8 mm
D. 42.7 mm
E. 43.2 mm
ans: E
58. In a cinema, a picture 2.5 cm wide on the film is projected to an image 3.0 m wide on a screen
that is 18 m away. The focal length of the lens is about:
A. 7.5 cm
B. 10 cm
C. 12.5 cm
D. 15 cm
E. 20 cm
ans: D
59. The term “virtual” as applied to an image made by a mirror means that the image:
A. is on the mirror surface
B. cannot be photographed by a camera
C. is in front of the mirror
D. is the same size as the object
E. cannot be shown directly on a screen
ans: E
60. Which instrument uses a single converging lens with the object placed just inside the focal
point?
A. Camera
B. Compound microscope
C. Magnifying glass
D. Overhead projector
E. Telescope
ans: C
526
Chapter 34:
IMAGES
61. Let fo and fe be the focal lengths of the objective and eyepiece of a compound microscope. In
ordinary use, the object:
A. is less than fo from the objective lens
B. is more that fo from the objective
C. produces an intermediate image that is slightly more than fe from the eyepiece
D. produces an intermediate image that is 2fe away from the eyepiece
E. produces an intermediate image that is less than fo from the objective lens
ans: B
62. Consider the following four statements concerning a compound microscope:
1. Each lens produces an image that is virtual and inverted.
2. The objective lens has a very short focal length.
3. The eyepiece is used as a simple magnifying glass.
4. The objective lens is convex and the eyepiece is concave.
Which two of the four statements are correct?
A. 1, 2
B. 1, 3
C. 1, 4
D. 2, 3
E. 2, 4
ans: D
63. What type of eyeglasses should a nearsighted person wear?
A. diverging lenses
D. bifocal lenses
B. converging lenses
E. plano-convex lenses
C. double convex lenses
ans: A
64. Which of the following is NOT correct for a simple magnifying glass?
A. The image is virtual
B. The image is erect
C. The image is larger than the object
D. The object is inside the focal point
E. The lens is diverging
ans: E
65. A nearsighted person can see clearly only objects within 1.4 m of her eye. To see distant objects,
she should wear eyeglasses of what type and focal length?
A. diverging, 2.8 m
B. diverging, 1.4 m
C. converging, 2.8 m
D. converging, 1.4 m
E. diverging, 0.72 m
ans: B
Chapter 34:
IMAGES
527
66. A magnifying glass has a focal length of 15 cm. If the near point of the eye is 25 cm from the
eye the angular magnification of the glass is about:
A. 0.067
B. 0.33
C. 0.67
D. 1.7
E. 15
ans: D
67. An object is 20 cm to the left of a lens of focal length +10 cm. A second lens, of focal length
+12.5 cm, is 30 cm to the right of the first lens. The distance between the original object and
the final image is:
A. 28 cm
B. 50 cm
C. 100 cm
D. 0
E. infinity
ans: D
68. A converging lens of focal length 20 cm is placed in contact with a converging lens of focal
length 30 cm. The focal length of this combination is:
A. +10 cm
B. −10 cm
C. +60 cm
D. −60 cm
E. +25 cm
ans: A
69. A student sets the cross-hairs of an eyepiece in line with an image that he is measuring. He
then notes that when he moves his head slightly to the right, the image moves slightly to the
left (with respect to the cross-hairs). Therefore the image is:
A. infinitely far away
B. farther away from him that the cross-hairs
C. nearer to him than the cross-hairs
D. in the focal plane of the eyepiece
E. in the plane of the cross-hairs
ans: C
70. In a two lens microscope, the intermediate image is:
A. virtual, erect, and magnified
B. real, erect, and magnified
C. real, inverted, and magnified
D. virtual, inverted, and reduced
E. virtual, inverted, and magnified
ans: C
528
Chapter 34:
IMAGES
71. Two thin lenses (focal lengths f1 and f2 ) are in contact. Their equivalent focal length is:
A. f1 + f2
B. f1 f2 /(f1 + f2 )
C. 1/f1 + 1/f2
D. f1 − f2
E. f1 (f1 − f2 )/f2
ans: B
72. The two lenses shown are illuminated by a beam of parallel light from the left. Lens B is then
moved slowly toward lens A. The beam emerging from lens B is:
f = −25 cm
............................................. ..
... . . . . . ...
..
.
.............
... . . . . ...
.......................
... . . ...
... . ...
....................
.......................... B
...........................
.......................................
. . . ..
.... . . . .....
.................
................................................
←−−−−−−− 25 cm −−−−−−−→
f = 50 cm
.....
.......
...........
..
.
. ...
.
..
............
...........................................
..
... ..... ...
..............
.. . . ..
.. . . . ..
..
.... .... ....... ..
........................................
............. A
.. .
.... . . ...
.............
... ..... ...
..
.... . ....
..........................................
..........
..
.... ....
... . ..
.......
..
....
........................................
..
...........................................
..
.....
A.
B.
C.
D.
E.
initially parallel and then diverging
always diverging
initially converging and finally parallel
always parallel
initially converging and finally diverging
ans: A
Chapter 34:
IMAGES
529
Chapter 35:
INTERFERENCE
1. A “wave front” is a surface of constant:
A. phase
B. frequency
C. wavelength
D. amplitude
E. speed
ans: A
2. Huygens’ construction can be used only:
A. for light
B. for an electromagnetic wave
C. if one of the media is vacuum (or air)
D. for transverse waves
E. for all of the above and other situations
ans: E
3. Consider (I) the law of reflection and (II) the law of refraction. Huygens’ principle can be used
to derive:
A. only I
B. only II
C. both I and II
D. neither I nor II
E. the question is meaningless because Huygens’ principle is for wave fronts whereas both I
and II concern rays
ans: C
4. Units of “optical path length” are:
A. m−1
B. m
C. m/s
D. Hz/m
E. m/Hz
ans: B
530
Chapter 35:
INTERFERENCE
5. The light waves represented by the three rays shown in the diagram all have the same frequency.
4.7 wavelengths fit into layer 1, 3.2 wavelengths fit into layer 2, and 5.3 wavelengths fit into
layer 3. Rank the layers according to the speeds of the waves, least to greatest.
..
..
..
............................................................................................................................................................................................................................................................
..
..
..
layer 1
..
..
..
............................................................................................................................................................................................................................................................
..
..
..
layer 2
..
..
..
............................................................................................................................................................................................................................................................
..
..
..
layer 3
A.
B.
C.
D.
E.
1, 2, 3
2, 1, 3
3, 1, 2
3, 1, 2
1, 3, 2
ans: D
6. Interference of light is evidence that:
A. the speed of light is very large
B. light is a transverse wave
C. light is electromagnetic in character
D. light is a wave phenomenon
E. light does not obey conservation of energy
ans: D
7. The reason there are two slits, rather than one, in a Young’s experiment is:
A. to increase the intensity
B. one slit is for frequency, the other for wavelength
C. to create a path length difference
D. one slit is for E fields, the other is for B fields
E. two slits in parallel offer less resistance
ans: C
8. In a Young’s double-slit experiment the center of a bright fringe occurs wherever waves from
the slits differ in the distance they travel by a multiple of:
A. a fourth of a wavelength
B. a half a wavelength
C. a wavelength
D. three-fourths of a wavelength
E. none of the above
ans: E
Chapter 35:
INTERFERENCE
531
9. In a Young’s double-slit experiment the center of a bright fringe occurs wherever waves from
the slits differ in phase by a multiple of:
A. π/4
B. π/2
C. π
D. 3π/4
E. 2π
ans: E
10. Waves from two slits are in phase at the slits and travel to a distant screen to produce the
third side maximum of the interference pattern. The difference in the distance traveled by the
waves is:
A. half a wavelength
B. a wavelength
C. three halves of a wavelength
D. two wavelengths
E. three wavelengths
ans: E
11. Waves from two slits are in phase at the slits and travel to a distant screen to produce the
second minimum of the interference pattern. The difference in the distance traveled by the
waves is:
A. half a wavelength
B. a wavelength
C. three halves of a wavelength
D. two wavelengths
E. five halves of a wavelength
ans: C
12. A monochromatic light source illuminates a double slit and the resulting interference pattern
is observed on a distant screen. Let d = center-to-center slit spacing, a = individual slit width,
D = screen-to-slit distance, and = adjacent dark line spacing in the interference pattern. The
wavelength of the light is then:
A. d /D
B. Ld/a
C. da/D
D. D/a
E. Dd/
ans: A
532
Chapter 35:
INTERFERENCE
13. Light from a small region of an ordinary incandescent bulb is passed through a yellow filter and
then serves as the source for a Young’s double-slit experiment. Which of the following changes
would cause the interference pattern to be more closely spaced?
A. Use slits that are closer together
B. Use a light source of lower intensity
C. Use a light source of higher intensity
D. Use a blue filter instead of a yellow filter
E. Move the light source further away from the slits.
ans: D
14. In a Young’s double-slit experiment, the slit separation is doubled. To maintain the same fringe
spacing on the screen, the screen-to-slit distance D must be changed to:
A. D/2
√
B. D/
√ 2
C. D 2
D. 2D
E. 4D
ans: D
15. In a Young’s double-slit experiment, light of wavelength 500 nm illuminates two slits that are
separated by 1 mm. The separation between adjacent bright fringes on a screen 5 m from the
slits is:
A. 0.10 cm
B. 0.25 cm
C. 0.50 cm
D. 1.0 cm
E. none of the above
ans: B
16. In a Young’s double-slit experiment, the separation between slits is d and the screen is a distance
D from the slits. D is much greater than d and λ is the wavelength of the light. The number
of bright fringes per unit width on the screen is:
A. Dd/λ
B. Dλ/d
C. D/dλ
D. λ/Dd
E. d/Dλ
ans: E
17. In a Young’s double-slit experiment, the slit separation is doubled. This results in:
A. an increase in fringe intensity
B. a decrease in fringe intensity
C. a halving of the wavelength
D. a halving of the fringe spacing
E. a doubling of the fringe spacing
ans: D
Chapter 35:
INTERFERENCE
533
18. In an experiment to measure the wavelength of light using a double slit, it is found that the
fringes are too close together to easily count them. To spread out the fringe pattern, one could:
A. decrease the slit separation
B. increase the slit separation
C. increase the width of each slit
D. decrease the width of each slit
E. none of these
ans: A
19. The phase difference between the two waves that give rise to a dark spot in a Young’s double-slit
experiment is (where m = integer):
A. zero
B. 2πm + π/8
C. 2πm + π/4
D. 2πm + π/2
E. 2πm + π
ans: E
20. In a Young’s experiment, it is essential that the two beams:
A. have exactly equal intensity
B. be exactly parallel
C. travel equal distances
D. come originally from the same source
E. be composed of a broad band of frequencies
ans: D
21. A light wave with an electric field amplitude of E0 and a phase constant of zero is to be
combined with one of the following waves:
wave A has an amplitude of E0 and a phase constant of zero
wave B has an amplitude of E0 and a phase constant of π
wave C has an amplitude of 2E0 and a phase constant of zero
wave D has an amplitude of 2E0 and a phase constant of π
wave E has an amplitude of 3E0 and a phase constant of π
Which of these combinations produces the greatest intensity?
ans: C
22. A light wave with an electric field amplitude of 2E0 and a phase constant of zero is to be
combined with one of the following waves:
wave A has an amplitude of E0 and a phase constant of zero
wave B has an amplitude of E0 and a phase constant of π
wave C has an amplitude of 2E0 and a phase constant of zero
wave D has an amplitude of 2E0 and a phase constant of π
wave E has an amplitude of 3E0 and a phase constant of π
Which of these combinations produces the least intensity?
ans: D
534
Chapter 35:
INTERFERENCE
23. One of the two slits in a Young’s experiment is painted over so that it transmits only one-half
the intensity of the other slit. As a result:
A. the fringe system disappears
B. the bright fringes get brighter and the dark ones get darker
C. the fringes just get dimmer
D. the dark fringes just get brighter
E. the dark fringes get brighter and the bright ones get darker
ans: E
24. In a Young’s double-slit experiment, a thin sheet of mica is placed over one of the two slits. As
a result, the center of the fringe pattern (on the screen) shifts by an amount corresponding to
30 dark bands. The wavelength of the light in this experiment is 480 nm and the index of the
mica is 1.60. The mica thickness is:
A. 0.090 mm
B. 0.012 mm
C. 0.014 mm
D. 0.024 mm
E. 0.062 mm
ans: D
25. Light from a point source X contains only blue and red components. After passing through a
mysterious box, the light falls on a screen. Bright red and blue hands are observed as shown.
The box must contain:
screen
X.
.
................... ...............................................................
•.....
....
red & blue
mysterious box
A.
B.
C.
D.
E.
blue
red
blue
a lens
a mirror
a prism
a double slit
a blue and red filter
ans: D
Chapter 35:
INTERFERENCE
535
26. Binoculars and microscopes are frequently made with coated optics by adding a thin layer of
transparent material to the lens surface as shown. One wants:
incident light
1 2
...
.
.
......
.......
...
............. .............
...
...
..
..
...
..
..
.
.
...
...
...
...
...
...
...
...
...
.
..
..
............
.
.
........
...
...
...
...
...
...
...
...
...
..
...
.
....
...
...
..
...
..
...
...
..
...
... ....
....
... ..
... ...
..
......
...
...
...
... ........
... .. ...
... ... ...
...... ...
...
....
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
........... ...........
........ ......
.
.
air
coating
lens
3 4
A.
B.
C.
D.
E.
constructive interference between waves 1 and 2
destructive interference between waves 3 and 4
constructive interference between 3 and 4
the coating to be more transparent than the lens
the speed of light in the coating to be less than that in the lens
ans: C
27. Monochromatic light, at normal incidence, strikes a thin film in air. If λ denotes the wavelength
in the film, what is the thinnest film in which the reflected light will be a maximum?
A. Much less than λ
B. λ/4
C. λ/2
D. 3λ/4
E. λ
ans: B
28. A soap film is illuminated by white light normal to its surface. The index of refraction of the
film is 1.50. Wavelengths of 480 nm and 800 nm and no wavelengths between are be intensified
in the reflected beam. The thickness of the film is:
A. 1.5 × 10−5 cm
B. 2.4 × 10−5 cm
C. 3.6 × 10−5 cm
D. 4.0 × 10−5 cm
E. 6.0 × 10−5 cm
ans: D
536
Chapter 35:
INTERFERENCE
29. Red light is viewed through a thin vertical soap film. At the third dark area shown, the
thickness of the film, in terms of the wavelength within the film, is:
.............................................
.............
.........
........
.......
.......
......
......
.
......
.
.
.
.
.....
...
.
.
.
....
.
....
....
.
.
...
..
.
.
...
..
.
...
.
...
...
.
...
..
.
...
..
.
...
..
....
...
....
...
..
..
...
...
...
...
...
...
...
..
..
.
...
.
.
.
...
...
...
...
...
...
...
...
..
.
...
.
...
...
...
...
...
...
....
..
.
.
.
....
.....
.....
......
.....
.....
......
......
.......
.......
.........
.
.
.
.
.
.
.
.............
..
............................................
large red area
......................................................................................
.......................................................................................
........................................................................................
.......................................................................................
........................................................................................
.......................................................................................
........................................................................................
.......................................................................................
........................................................................................
.......................................................................................
first dark area
........................................................................................
.......................................................................................
........................................................................................
.......................................................................................
......................................................................................
.......................................................................................
red area
............................................................................
.............................................................................
...........................................................................
..........................................................................
.........................................................................
........................................................................
....................................................................... second dark area
.........................................................
........................................................
.......................................................
...................................................... third dark area
.......................................
......................................
...................................
A.
B.
C.
D.
E.
λ
3λ/4
λ/2
λ/4
5λ/4
ans: E
30. Yellow light is viewed by reflection from a thin vertical soap film. Let λ be the wavelength of
the light within the film. Why is there a large dark space at the top of the film?
..................................................................................................................
.
.
.
.
.
.
..
.
.
................... .........
......................................................
.......................................................
........................................................
.........................................................
..........................................................
...........................................................
............................................................
.............................................................
..............................................................
...............................................................
................................................................
.................................................................
..................................................................
...................................................................
....................................................................
.....................................................................
...................................................................... large dark area
.......................................................................
........................................................................
.........................................................................
..........................................................................
...........................................................................
............................................................................
.............................................................................
..............................................................................
...............................................................................
................................................................................
.................................................................................
..................................................................................
...................................................................................
....................................................................................
...................................................................................
.....................................................................................
....................................................................................
.....................................................
...........
........
........
.......
.......
......
......
.....
.
.
.
.
.
.....
....
.
....
.
.
....
...
.
.
...
..
.
.
...
...
...
.
...
..
.
...
..
.
...
..
.
...
....
..
...
....
..
..
..
..
...
..
...
..
...
...
...
...
..
.
...
..
.
...
...
...
...
...
..
...
..
...
.
.
...
..
...
...
...
...
..
....
....
....
.
.
.
.....
.....
......
.....
......
......
.......
......
........
.......
.
.
.
...........
.
.
.
.
.
.
............................................
yellow area
.......................................................................................
......................................................................................
.....................................................................................
....................................................................................
.....................................................................................
....................................................................................
...................................................................................
..................................................................................
...................................................................................
................................................................................. dark area
yellow area
.......................................................................
......................................................................
.....................................................................
....................................................................
...................................................................
..................................................................
.................................................................
................................................................
...............................................................
..............................................................
.............................................................
............................................................
.................................................
................................................
...............................................
............................................
...........................................
A.
B.
C.
D.
E.
no light is transmitted through this part of the film
the film thickness there is λ/4
the film thickness there is much less than λ
the film is too thick in this region for thin film formulas to apply
the reflected light is in the infrared
ans: C
Chapter 35:
INTERFERENCE
537
31. Three experiments involving a thin film (in air) are shown. If t denotes the film thickness and
λ denotes the wavelength of the light in the film, which experiments will produce constructive
interference as seen by the observer? The incident light is nearly normal to the surface.
incident light
incident light
↑|
t
↓|
...
...
...
...
...
...
...
...
..
..............
......
...
...
...
...
...
...
...
...
...
...
..
.
...
...
...
...
...
...
...
...
..
..............
.....
...
...
...
...
...
...
...
...
...
...
..
eye
...
........
............. ....
.......
.
incident light
eye
..
........
............. ....
........
.................
.................
.................
.................
.................
.................
.................
.................
.................
.................
.................
.................
.........
t = 5λ/4
...
...
...
...
...
...
...
...
..
..............
.....
...
...
...
...
...
...
...
...
...
...
..
.................
.................
.........
t = λ/2
.
......
............. ....
........
....
t = 3λ/2
II
I
A.
B.
C.
D.
E.
eye
III
I only
II only
III only
I and III only
II and III only
ans: D
32. A liquid of refractive index n = 4/3 replaces the air between a fixed wedge formed from two
glass plates as shown. As a result, the spacing between adjacent dark bands in the interference
pattern:
.......................
....................
..
...................
..
.....................
..
.....................
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.............
....................
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.............
............
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
............
.
.................
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.......
...
....................
...
....................
... ......................................
........................................................................................................................................................................................
...
..
.
.....
....
.
.
.............................................................................................................................................................................................................................................
glass
............
.
.
.
.
.
.
.
.
.
.
............
. . ..................................................... liquid
. . . ..............................................................................
glass
A.
B.
C.
D.
E.
538
increases by a factor of 4/3
increases by a factor of 3
remains the same
decreases to 3/4 of its original value
decreases to 1/3 of its original value
ans: D
Chapter 35:
INTERFERENCE
33. A lens with a refractive index of 1.5 is coated with a material of refractive index 1.2 in order
to minimize reflection. If λ denotes the wavelength of the incident light in air, what is the
thinnest possible such coating?
incident light
...
...
...
...
...
...
...
...
...
..
..............
.....
...
...
...
...
...
...
...
...
...
...
...
..
.. ... ... ... ... ... ... ... .... ... ... ... ... ... ... ... ... ...
.
.. ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
.
.. ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
.
... ..... ..... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... ..
.. .. ... ... ... .. .. .. .. .. .. .. .. .. .. .. .. ..
... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
.. .. .. .. .. ... ... ... ... ... ... ... ... ... ... ... ... ...
..... ..... ..... ..... ..... ..... ..... ..... .... .... .... .... .... .... .... .... .... ....
... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
.. .. .. .. .. .. .. .. .. .. .. .. .. .. .. ... ... ...
... ..... ..... ..... ..... ..... ..... ..... ..... ..... ..... ..... ..... ..... ..... ..... .... .... ..
... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
... .. .. ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
... ... ... .. .. .. .. .. .. .. .. .. .. .. .. .. ... ...
... .... ..... ..... ..... ..... ..... ..... ..... ..... ..... ..... ..... ..... ..... ..... ..... ..... ..
... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ..
... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
... ... .. .. .. .. .. ... ... ... ... ... ... ... ... ... ... ...
... .... ..... ..... ..... ..... ..... ..... .... .... .... .... .... .... .... .... .... .... ...
... ... .. ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
......................................................................................................................................................................................... ... ...
air
A.
B.
C.
D.
E.
coating
glass lens
0.5λ
0.416λ
0.3λ
0.208λ
0.25λ
ans: D
34. In a thin film experiment, a wedge of air is used between two glass plates. If the wavelength
of the incident light in air is 480 nm, how much thicker is the air wedge at the 16th dark fringe
than it is at the 6th ?
A. 2400 nm
B. 4800 nm
C. 240 nm
D. 480 nm
E. None of these
ans: A
35. An air wedge is formed from two glass plates that are in contact at their left edges. There are
ten dark bands when viewed by reflection using monochromatic light. The left edge of the top
plate is now slowly lifted until the plates are parallel. During this process:
A. the dark bands crowd toward the right edge
B. the dark bands remain stationary
C. the dark bands crowd toward the left edge
D. the dark bands spread out, disappearing off the right edge
E. the dark bands spread out, disappearing off the left edge
ans: E
Chapter 35:
INTERFERENCE
539
36. An air wedge is formed using two glass plates that are in contact along their left edge. When
viewed by highly monochromatic light, there are exactly 4001 dark bands in the reflected light.
The air is now evacuated (with the glass plates remaining rigidly fixed) and the number of dark
bands decreases to exactly 4000. The index of refraction of the air is:
A. 0.00025
B. 0.00050
C. 1.00025
D. 1.00050
E. 1.00000, by definition
ans: C
37. A glass (n = 1.6) lens is coated with a thin film (n = 1.3) to reduce reflection of certain incident
light. If λ is the wavelength of the light in the film, the least film thickness is:
A. less than λ/4
B. λ/4
C. λ/2
D. λ
E. more than λ
ans: B
38. Two point sources, vibrating in phase, produce an interference pattern in a ripple tank. If the
frequency is increased by 20%, the number of nodal lines:
A. is increased by 20%
B. is increased by 40%
C. remains the same
D. is decreased by 20%
E. is decreased by 40%
ans: A
39. If two light waves are coherent:
A. their amplitudes are the same
B. their frequencies are the same
C. their wavelengths are the same
D. their phase difference is constant
E. the difference in their frequencies is constant
ans: D
40. To
A.
B.
C.
D.
E.
540
obtain an observable double-slit interference pattern:
the light must be incident normally on the slits
the light must be monochromatic
the light must consist of plane waves
the light must be coherent
the screen must be far away from the slits
ans: D
Chapter 35:
INTERFERENCE
Chapter 36:
DIFFRACTION
1. Sound differs from light in that sound:
A. is not subject to diffraction
B. is a torsional wave rather than a longitudinal wave
C. does not require energy for its origin
D. is a longitudinal wave rather than a transverse wave
E. is always monochromatic
ans: D
2. Radio waves are readily diffracted around buildings whereas light waves are negligibly diffracted
around buildings. This is because radio waves:
A. are plane polarized
B. have much longer wavelengths than light waves
C. have much shorter wavelengths than light waves
D. are nearly monochromatic (single frequency)
E. are amplitude modulated (AM).
ans: B
3. Diffraction plays an important role in which of the following phenomena?
A. The sun appears as a disk rather than a point to the naked eye
B. Light is bent as it passes through a glass prism
C. A cheerleader yells through a megaphone
D. A farsighted person uses eyeglasses of positive focal length
E. A thin soap film exhibits colors when illuminated with white light
ans: C
4. The rainbow seen after a rain shower is caused by:
A. diffraction
B. interference
C. refraction
D. polarization
E. absorption
ans: C
5. When a highly coherent beam of light is directed against a very fine wire, the shadow formed
behind it is not just that of a single wire but rather looks like the shadow of several parallel
wires. The explanation of this involves:
A. refraction
B. diffraction
C. reflection
D. the Doppler effect
E. an optical illusion
ans: B
Chapter 36:
DIFFRACTION
541
6. When the atmosphere is not quite clear, one may sometimes see colored circles concentric with
the Sun or the Moon. These are generally not more than a few diameters of the Sun or Moon
and invariably the innermost ring is blue. The explanation for this phenomena involves:
A. reflection
B. refraction
C. interference
D. diffraction
E. the Doppler effect
ans: D
7. The shimmering or wavy lines that can often be seen near the ground on a hot day are due to:
A. Brownian movement
B. reflection
C. refraction
D. diffraction
E. dispersion
ans: C
8. A point source of monochromatic light is placed in front of a soccer ball and a screen is placed
behind the ball. The light intensity pattern on the screen is best described as:
A. a dark disk on a bright background
B. a dark disk with bright rings outside
C. a dark disk with a bright spot at its center
D. a dark disk with a bright spot at its center and bright rings outside
E. a bright disk with bright rings outside
ans: D
9. In the equation sin θ = λ/a for single-slit diffraction, θ is:
A. the angle to the first minimum
B. the angle to the second maximum
C. the phase angle between the extreme rays
D. N π where N is an integer
E. (N + 1/2)π where N is an integer
ans: A
10. In the equation φ = (2πa/λ) sin θ for single-slit diffraction, φ is:
A. the angle to the first minimum
B. the angle to the second maximum
C. the phase angle between the extreme rays
D. N π where N is an integer
E. (N + 1/2)π where N is an integer
ans: C
542
Chapter 36:
DIFFRACTION
11. No
A.
B.
C.
D.
E.
fringes are seen in a single-slit diffraction pattern if:
the screen is far away
the wavelength is less than the slit width
the wavelength is greater than the slit width
the wavelength is less than the distance to the screen
the distance to the screen is greater than the slit width
ans: C
12. A student wishes to produce a single-slit diffraction pattern in a ripple tank experiment. He
considers the following parameters:
1. frequency
2. wavelength
3. water depth
4. slit width
Which two of the above should be decreased to produce more bending?
A. 1, 3
B. 1, 4
C. 2, 3
D. 2, 4
E. 3, 4
ans: B
13. A parallel beam of monochromatic light is incident on a slit of width 2 cm. The light passing
through the slit falls on a screen 2 m away. As the slit width is decreased:
A. the width of the pattern on the screen continuously decreases
B. the width of the pattern on the screen at first decreases but then increases
C. the width of the pattern on the screen increases and then decreases
D. the width of the pattern on the screen remains the same
E. the pattern on the screen changes color going from red to blue
ans: B
14. Monochromatic plane waves of light are incident normally on a single slit. Which one of the
five figures below correctly shows the diffraction pattern observed on a distant screen?
A
B
C
D
E
ans: B
Chapter 36:
DIFFRACTION
543
15. The diagram shows a single slit with the direction to a point P on a distant screen shown. At
P, the pattern has its second minimum (from its central maximum). If X and Y are the edges
of the slit, what is the path length difference (PX) - (PY)?
incident
light
A.
B.
C.
D.
E.
...................................................
...................................................
...................................................
..................................................
...................................................
...................................................
...................................................
...................................................
..................................................
..........
.................................
..........................
..........................
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
..........................
..........................
..........................
.........
...............................
..........................
...........................
...........................
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
..........................
..........................
Y
to P
X
λ/2
λ
3λ/2
2λ
5λ/2
ans: D
16. The diagram shows a single slit with the direction to a point P on a distant screen shown. At
P, the pattern has its maximum nearest the central maximum. If X and Y are the edges of the
slit, what is the path length difference (PX) - (PY)?
incident
light
A.
B.
C.
D.
E.
...................................................
...................................................
...................................................
...................................................
..................................................
...................................................
...................................................
...................................................
...................................................
.....
............................
........................
...........................
Y .........................................................................................
..........................
to P
.......
................................
..........................
...........................
.........................
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
...
...........................
..........................
X
λ/2
λ
3λ/2
2λ
5λ/2
ans: C
17. At the first minimum adjacent to the central maximum of a single-slit diffraction pattern the
phase difference between the Huygens wavelet from the top of the slit and the wavelet from
the midpoint of the slit is:
A. π/8 rad
B. π/4 rad
C. π/2 rad
D. π rad
E. 3π/2 rad
ans: D
544
Chapter 36:
DIFFRACTION
18. At the second minimum adjacent to the central maximum of a single-slit diffraction pattern
the Huygens wavelet from the top of the slit is 180◦ out of phase with the wavelet from:
A. a point one-fourth of the slit width from the top
B. the midpoint of the slit
C. a point one-fourth of the slit width from the bottom of the slit
D. the bottom of the slit
E. none of these
ans: A
19. A plane wave with a wavelength of 500 nm is incident normally on a single slit with a width of
5.0 × 10−6 m. Consider waves that reach a point on a far-away screen such that rays from the
slit make an angle of 1.0◦ with the normal. The difference in phase for waves from the top and
bottom of the slit is:
A. 0
B. 0.55 rad
C. 1.1 rad
D. 1.6 rad
E. 2.2 rad
ans: C
20. A diffraction pattern is produced on a viewing screen by illuminating a long narrow slit with
light of wavelength λ. If λ is increased and no other changes are made:
A. the intensity at the center of the pattern decreases and the pattern expands away from the
bright center
B. the intensity at the center of the pattern increases and the pattern contracts toward the
bright center
C. the intensity at the center of the pattern does not change and the pattern expands away
from the bright center
D. the intensity at the center of the pattern does not change and the pattern contracts toward
the bright center
E. neither the intensity at the center of the pattern nor the pattern itself change
ans: C
21. A diffraction pattern is produced on a viewing screen by illuminating a long narrow slit with
light of wavelength λ. If the slit width is decreased and no other changes are made:
A. the intensity at the center of the pattern decreases and the pattern expands away from the
bright center
B. the intensity at the center of the pattern increases and the pattern contracts toward the
bright center
C. the intensity at the center of the pattern does not change and the pattern expands away
from the bright center
D. the intensity at the center of the pattern does not change and the pattern contracts toward
the bright center
E. neither the intensity at the center of the pattern nor the pattern itself change
ans: A
Chapter 36:
DIFFRACTION
545
22. In order to obtain a good single-slit diffraction pattern, the slit width could be:
A. λ
B. λ/10
C. 10λ
D. 104 λ
E. λ/104
ans: C
23. Consider a single-slit diffraction pattern caused by a slit of width a. There is a maximum if
sin θ is equal to:
A. slightly more than 3λ/2a
B. slightly less than 3λ/2a
C. exactly 3λ/2a
D. exactly λ/2a
E. very nearly λ/2a
ans: B
24. Consider a single-slit diffraction pattern caused by a slit of width a. There is a minimum if
sin θ is equal to:
A. exactly λ/a
B. slightly more than λ/a
C. slightly less than λ/a
D. exactly λ/2a
E. very nearly λ/2a
ans: A
25. In a single-slit diffraction pattern, the central maximum is about twice as wide as the other
maxima. This is because:
A. half the light is diffracted up and half is diffracted down
B. the central maximum has both electric and magnetic fields present
C. the small angle approximation applies only near the central maximum
D. the screen is flat instead of spherical
E. none of the above
ans: E
26. The intensity at a secondary maximum of a single-slit diffraction pattern is less than the
intensity at the central maximum chiefly because:
A. some Huygens wavelets sum to zero at the secondary maximum but not at the central
maximum
B. the secondary maximum is further from the slits than the central maximum and intensity
decreases as the square of the distance
C. the Huygens construction is not valid for a secondary maximum
D. the amplitude of every Huygens wavelet is smaller when it travels to a secondary maximum
than when it travels to the central maximum
E. none of the above
ans: A
546
Chapter 36:
DIFFRACTION
27. Figure (i) shows a double-slit pattern obtained using monochromatic light. Consider the following five possible changes in conditions:
1. decrease the frequency
2. increase the frequency
3. increase the width of each slit
4. increase the separation between the slits
5. decrease the separation between the slits
Which of the above would change Figure (i) into Figure (ii)?
i
ii
A.
B.
C.
D.
E.
3 only
5 only
1 and 3 only
1 and 5 only
2 and 4 only
ans: E
28. Two wavelengths, 800 nm and 600 nm, are used separately in single-slit diffraction experiments.
The diagram shows the intensities on a far-away viewing screen as function of the angle made by
the rays with the straight-ahead direction. If both wavelengths are then used simultaneously,
at which angle is the light on the screen purely 800-nm light?
I
..........
.......
.......
......
... ...
... ...
... ...
... ...
... ...
... ...
... ...
... ....
... ....
... .....
.... .....
......... ......................................................................................................................................
....
...
........
A
B
C
D
E
θ
ans: C
Chapter 36:
DIFFRACTION
547
29. If we increase the wavelength of the light used to form a double-slit diffraction pattern:
A. the width of the central diffraction peak increases and the number of bright fringes within
the peak increases
B. the width of the central diffraction peak increases and the number of bright fringes within
the peak decreases
C. the width of the central diffraction peak decreases and the number of bright fringes within
the peak increases
D. the width of the central diffraction peak decreases and the number of bright fringes within
the peak decreases
E. the width of the central diffraction peak increases and the number of bright fringes within
the peak stays the same
ans: E
30. Two slits of width a and separation d are illuminated by a beam of light of wavelength λ. The
separation of the interference fringes on a screen a distance D away is:
A. λa/D
B. λd/D
C. λD/d
D. dD/λ
E. λD/a
ans: C
31. Two slits in an opaque barrier each have a width of 0.020 mm and are separated by 0.050 mm.
When coherent monochromatic light passes through the slits the number of interference maxima
within the central diffraction maximum:
A. is 1
B. is 2
C. is 4
D. is 5
E. cannot be determined unless the wavelength is given
ans: D
32. When 450-nm light is incident normally on a certain double-slit system the number of interference maxima within the central diffraction maximum is 5. When 900-nm light is incident on
the same slit system the number is:
A. 2
B. 3
C. 5
D. 9
E. 10
ans: C
548
Chapter 36:
DIFFRACTION
33. In a double-slit diffraction experiment the number of interference fringes within the central
diffraction maximum can be increased by:
A. increasing the wavelength
B. decreasing the wavelength
C. decreasing the slit separation
D. increasing the slit width
E. decreasing the slit width
ans: E
34. A diffraction-limited laser of length and aperture diameter d generates light of wavelength
λ. If the beam is directed at the surface of the Moon a distance D away, the radius of the
illuminated area on the Moon is approximately:
A. dD/
B. dD/λ
C. Dλ/
D. Dλ/d
E. λ/d
ans: D
35. Two stars that are close together are photographed through a telescope. The black and white
film is equally sensitive to all colors. Which situation would result in the most clearly separated
images of the stars?
A. Small lens, red stars
B. Small lens, blue stars
C. Large lens, red stars
D. Large lens, blue stars
E. Large lens, one star red and the other blue
ans: D
36. The resolving power of a telescope can be increased by:
A. increasing the objective focal length and decreasing the eyepiece focal length
B. increasing the lens diameters
C. decreasing the lens diameters
D. inserting a correction lens between objective and eyepiece
E. none of the above
ans: B
37. In the equation d sin θ = mλ for the lines of a diffraction grating m is:
A. the number of slits
B. the slit width
C. the slit separation
D. the order of the line
E. the index of refraction
ans: D
Chapter 36:
DIFFRACTION
549
38. In the equation d sin θ = mλ for the lines of a diffraction grating d is:
A. the number of slits
B. the slit width
C. the slit separation
D. the order of the line
E. the index of refraction
ans: C
39. As
A.
B.
C.
D.
E.
more slits with the same spacing are added to a diffraction grating the lines:
spread farther apart
move closer together
become wider
becomes narrower
do not change in position or width
ans: D
40. An N -slit system has slit separation d and slit width a. Plane waves with intensity I and
wavelength λ are incident normally on it. The angular separation of the lines depends only on:
A. a and N
B. a and λ
C. N and λ
D. d and λ
E. I and N
ans: D
41. 600-nm light is incident on a diffraction grating with a ruling separation of 1.7 × 10−6 m. The
second order line occurs at a diffraction angle of:
A. 0
B. 10◦
C. 21◦
D. 42◦
E. 45◦
ans: E
42. The widths of the lines produced by monochromatic light falling on a diffraction grating can
be reduced by:
A. increasing the wavelength of the light
B. increasing the number of rulings without changing their spacing
C. decreasing the spacing between adjacent rulings without changing the number of rulings
D. decreasing both the wavelength and the spacing between rulings by the same factor
E. increasing the number of rulings and decreasing their spacing so the length of the grating
remains the same
ans: B
550
Chapter 36:
DIFFRACTION
43. Monochromatic light is normally incident on a diffraction grating that is 1 cm wide and has
10, 000 slits. The first order line is deviated at a 30◦ angle. What is the wavelength, in nm, of
the incident light?
A. 300
B. 400
C. 500
D. 600
E. 1000
ans: C
44. A light spectrum is formed on a screen using a diffraction grating. The entire apparatus (source,
grating and screen) is now immersed in a liquid of refractive index 1.33. As a result, the pattern
on the screen:
A. remains the same
B. spreads out
C. crowds together
D. becomes reversed, with the previously blue end becoming red
E. disappears because the refractive index isn’t an integer
ans: C
45. The spacing between adjacent slits on a diffraction grating is 3λ. The deviation θ of the first
order diffracted beam is given by:
A. sin(θ/2) = 1/3
B. sin(θ/3) = 2/3
C. sin(θ) = 1/3
D. tan(θ/2) = 1/3
E. tan(θ) = 2/3
ans: C
46. When light of a certain wavelength is incident normally on a certain diffraction grating the line
of order 1 is at a diffraction angle of 25◦ . The diffraction angle for the second order line is:
A. 25◦
B. 42◦
C. 50◦
D. 58◦
E. 75◦
ans D
47. A diffraction grating of width W produces a deviation θ in second order for light of wavelength
λ. The total number N of slits in the grating is given by:
A. 2W λ/ sin θ
B. (W/λ) sin θ
C. λW/2 sin θ
D. (W/2λ) sin θ
E. 2λ/ sin θ
ans: D
Chapter 36:
DIFFRACTION
551
48. Light of wavelength λ is normally incident on a diffraction grating G. On the screen S, the
central line is at P and the first order line is at Q, as shown. The distance between adjacent
slits in the grating is:
•Q
incident
light ....
3m
...........................................................
..
G
A.
B.
C.
D.
E.
•P
4m
S
3λ/5
3λ/4
4λ/5
5λ/4
5λ/3
ans: E
49. 550-nm light is incident normally on a diffraction grating and exactly 6 lines are produced.
The ruling separation must be:
A. between 2.75 × 10−7 m and 5.50 × 10−7 m
B. between 5.50 × 10−7 m and 1.10 × 10−6 m
C. between 3.30 × 10−6 m and 3.85 × 10−6 m
D. between 3.85 × 10−6 m and 4.40 × 10−6 m
E. greater than 4.40 × 10−6 m
ans: E
50. A mixture of 450-nm and 900-nm light is incident on a diffraction grating. Which of the
following is true?
A. all lines of the 900-nm light coincide with even order lines of the 450-nm light
B. all lines of the 450-nm light coincide with even order lines of the 900-nm light
C. all lines of the 900-nm light coincide with odd order lines of the 450-nm light
D. None of the lines of the 450-nm light coincide with lines of the 900-nm light
E. All of the lines of the 450-nm light coincide with lines of the 900-nm light
ans: A
552
Chapter 36:
DIFFRACTION
51. A beam of white light (from 400 nm for violet to 700 nm for red) is normally incident on a
diffraction grating. It produces two orders on a distant screen. Which diagram below (R =
red, V = violet) correctly shows the pattern on the screen?
V
R V
R
R R V
V
V R
V
V V R
R
V R
V
white
R
V R
V
A
V
V R R
B
R
V
R V
R
C
R
R V V
D
R
R
V R
V
E
ans: C
52. If white light is incident on a diffraction grating:
A. the first order lines for all visible wavelengths occur at smaller diffraction angles than any
of the second order lines
B. some first order lines overlap the second order lines if the ruling separation is small but do
not if it is large
C. some first order lines overlap second order lines if the ruling separation is large but do not
if it is small
D. some first order lines overlap second order lines no matter what the ruling separation
E. first and second order lines have the same range of diffraction angles
ans: A
Chapter 36:
DIFFRACTION
553
53. Light of wavelength is normally incident on some plane optical device. The intensity pattern
shown is observed on a distant screen (θ is the angle measured from the normal of the device).
The device could be:
intensity
.......
... ....
.
.. ...
... .....
...
..
...
...
...
..
...
...
..
...
..
...
...
...
..
...
...
..
...
..
... ........
.
.
.
.
.
.
.
.
.
.
.
........... ......................................
...................................... ..........
−3
A.
B.
C.
D.
E.
−2
−1
0
1
2
(W/λ) sin θ
3
a single slit of width W
a single slit of width 2W
two narrow slits with separation W
two narrow slits with separation 2W
a diffraction grating with slit separation W
ans: A
54. A person with her eye relaxed looks through a diffraction grating at a distant monochromatic
point source of light. The slits of the grating are vertical. She sees:
A. one point of light
B. a hazy horizontal strip of light of the same color as the source
C. a hazy strip of light varying from violet to red
D. a sequence of horizontal points of light
E. a sequence of closely spaced vertical lines
ans: D
55. Monochromatic light is normally incident on a diffraction grating. The mth order line is at a
diffraction angle θ and has width w. A wide single slit is now placed in front of the grating
and its width is then slowly reduced. As a result:
A. both θ and w increase
B. both θ and w decrease
C. θ remains the same and w increases
D. θ remains the same and w decreases
E. θ decreases and w increases
ans: C
554
Chapter 36:
DIFFRACTION
56. At
A.
B.
C.
D.
E.
a diffraction line phasors associated with waves from the slits of a multiple-slit barrier:
are aligned
form a closed polygon
form a polygon with several sides missing
are parallel but adjacent phasors point in opposite directions
form the arc of a circle
ans: A
57. For
A.
B.
C.
D.
E.
a certain multiple-slit barrier the slit separation is 4 times the slit width. For this system:
the orders of the lines that appear are all multiples of 4
the orders of lines that appear are all multiples of 2
the orders of the missing lines are all multiples of 4
the orders of the missing lines are all multiples of 2
none of the above are true
ans: C
58. The dispersion D of a grating can have units:
A. cm
B. 1/nm
C. nm/cm
D. radian
E. none of these
ans: B
59. The resolving power R of a grating can have units:
A. cm
B. degree/nm
C. watt
D. nm/cm
E. watt/nm
ans: D
60. The dispersion of a diffraction grating indicates:
A. the resolution of the grating
B. the separation of lines of the same order
C. the number of rulings in the grating
D. the width of the lines
E. the separation of lines of different order for the same wavelength
ans: B
Chapter 36:
DIFFRACTION
555
61. The resolving power of a diffraction grating is defined by R = λ/∆λ. Here λ and λ + ∆λ are:
A. any two wavelengths
B. any two wavelengths that are nearly the same
C. two wavelengths for which lines of the same order are separated by π radians
D. two wavelengths for which lines of the same order are separated by 2π radians
E. two wavelengths for which lines of the same order are separated by half the width of a
maximum
ans: E
62. A light beam incident on a diffraction grating consists of waves with two different wavelengths.
The separation of the two first order lines is great if:
A. the dispersion is great
B. the resolution is great
C. the dispersion is small
D. the resolution is small
E. none of the above (line separation does not depend on either dispersion or resolution)
ans: A
63. To
A.
B.
C.
D.
E.
obtain greater dispersion by a diffraction grating:
the slit width should be increased
the slit width should be decreased
the slit separation should be increased
the slit separation should be decreased
more slits with the same width and separation should be added to the system
ans: D
64. Two nearly equal wavelengths of light are incident on an N -slit grating. The two wavelengths
are not resolvable. When N is increased they become resolvable. This is because:
A. more light gets through the grating
B. the lines get more intense
C. the entire pattern spreads out
D. there are more orders present
E. the lines become more narrow
ans: E
65. A diffraction grating just resolves the wavelengths 400.0 nm and 400.1 nm in first order. The
number of slits in the grating is:
A. 400
B. 1000
C. 2500
D. 4000
E. not enough information is given
ans: D
556
Chapter 36:
DIFFRACTION
66. What is the minimum number of slits required in a diffraction grating to just resolve light with
wavelengths of 471.0 nm and 471.6 nm?
A. 99
B. 197
C. 393
D. 786
E. 1179
ans: C
67. X rays are:
A. electromagnetic waves
B. negatively charged ions
C. rapidly moving electrons
D. rapidly moving protons
E. rapidly moving neutrons
ans: A
68. Bragg’s law for x-ray diffraction is 2d sin θ = mλ, where θ is the angle between the incident
beam and:
A. a reflecting plane of atoms
B. the normal to a reflecting plane of atoms
C. the scattered beam
D. the normal to the scattered beam
E. the refracted beam
ans: A
69. Bragg’s law for x-ray diffraction is 2d sin θ = mλ, where the quantity d is:
A. the height of a unit cell
B. the smallest interatomic distance
C. the distance from detector to sample
D. the distance between planes of atoms
E. the usual calculus symbol for a differential
ans: D
70. Which of the following is true for Bragg diffraction but not for diffraction from a grating?
A. Two different wavelengths may be used
B. For a given wavelength, a maximum may exist in several directions
C. Long waves are deviated more than short ones
D. There is only one grating spacing
E. Maxima occur only for particular angles of incidence
ans: E
Chapter 36:
DIFFRACTION
557
71. The longest x-ray wavelength that can be diffracted by crystal planes with a separation of
0.316 nm is:
A. 0.158 nm
B. 0.316 nm
C. 0.474 nm
D. 0.632 nm
E. 1.26 nm
ans: D
72. A beam of x rays of wavelength 0.20 nm is diffracted by a set of planes in a crystal whose
separation is 3.1 × 10−8 cm. The smallest angle between the beam and the crystal planes for
which a reflection occurs is:
A. 0.70 rad
B. 0.33 rad
C. 0.033 rad
D. 0.066 rad
E. no such angle exists
ans: C
73. An x-ray beam of wavelength 3 × 10−11 m is incident on a calcite crystal of lattice spacing
0.3 nm. The smallest angle between crystal planes and the x-ray beam that will result in
constructive interference is:
A. 2.87◦
B. 5.73◦
C. 11.63◦
D. 23.27◦
E. none of these
ans: A
74. A beam of x rays of wavelength 0.10 nm is found to diffract in second order from the face of a
LiF crystal at a Bragg angle of 30◦ . The distance between adjacent crystal planes, in nm, is
about:
A. 0.15
B. 0.20
C. 0.25
D. 0.30
E. 0.40
ans: B
558
Chapter 36:
DIFFRACTION
Chapter 37:
SPECIAL THEORY OF RELATIVITY
1. A basic postulate of Einstein’s theory of relativity is:
A. moving clocks run more slowly than when they are at rest
B. moving rods are shorter than when they are at rest
C. light has both wave and particle properties
D. the laws of physics must be the same for observers moving with uniform velocity relative
to each other
E. everything is relative
ans: D
2. A consequence of Einstein’s theory of relativity is:
A. moving clocks run more slowly than when they are at rest
B. moving rods are longer than when they are at rest
C. light has both wave and particle properties
D. the laws of physics must appear the same to all observers moving with uniform velocity
relative to each other
E. everything is relative
ans: A
3. A consequence of Einstein’s theory of relativity is:
A. moving clocks run faster than when they are at rest
B. moving rods are shorter than when they are at rest
C. light has both wave and particle properties
D. the laws of physics must appear the same to all observers moving with uniform velocity
relative to each other
E. everything is relative
ans: B
4. According to the theory of relativity:
A. moving clocks run fast
B. energy is not conserved in high speed collisions
C. the speed of light must be measured relative to the ether
D. momentum is not conserved in high speed collisions
E. none of the above are true
ans: E
5. Two events occur simultaneously on the x axis of reference frame S, one at x = −a and the
other at x = +a. According to an observer moving in the positive x direction:
A. the event at x = +a occurs first
B. the event at x = −a occurs first
C. either event might occur first, depending on the value of a and the observer’s speed
D. the events are simultaneous
E. none of the above
ans: A
Chapter 37:
SPECIAL THEORY OF RELATIVITY
559
6. Two events occur simultaneously at separated points on the y axis of reference frame S. According to an observer moving in the positive x direction:
A. the event with the greater y coordinate occurs first
B. the event with the greater y coordinate occurs last
C. either event might occur first, depending on the observer’s speed
D. the events are simultaneous
E. none of the above
ans: D
7. A train traveling very fast (v = 0.6c) has an engineer (E) at the front, a guard (G) at the
rear, and an observer (S ) exactly half way between them. Both E and G are equipped with
yellow signaling lamps. The train passes a station, closely observed by the station master (S).
Both E and G use their lamps to send signals. According to both S and S these signals arrive
simultaneously at the instant S is passing S. According to S :
A. E and G sent their signals simultaneously from different distances
B. G sent his signal before E and from farther away
C. G sent his signal before E but was the same distance away
D. E sent his signal before G and from farther away
E. none of the above
ans: E
8. The proper time between two events is measured by clocks at rest in a reference frame in which
the two events:
A. occur at the same time
B. occur at the same coordinates
C. are separated by the distance a light signal can travel during the time interval
D. occur in Boston
E. satisfy none of the above
ans: B
9. The spaceship U.S.S. Enterprise, traveling through the galaxy, sends out a smaller explorer
craft that travels to a nearby planet and signals its findings back. The proper time for the trip
to the planet is measured by clocks:
A. on board the Enterprise
B. on board the explorer craft
C. on Earth
D. at the center of the galaxy
E. none of the above
ans: B
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10. Spaceship A, traveling past us at 0.7c, sends a message capsule to spaceship B, which is in front
of A and is traveling in the same direction as A at 0.8c relative to us. The capsule travels at
0.95c relative to us. A clock that measures the proper time between the sending and receiving
of the capsule travels:
A. in the same direction as the spaceships at 0.7c relative to us
B. in the opposite direction from the spaceships at 0.7c relative to us
C. in the same direction as the spaceships at 0.8c relative to us
D. in the same direction as the spaceships at 0.95c relative to us
E. in the opposite direction from the spaceships at 0.95c relative to us
ans: D
11. Two events occur on the x axis separated in time by ∆t and in space by ∆x. A reference frame,
traveling at less than the speed of light, in which the two events occur at the same time:
A. exists no matter what the values of ∆x and ∆t
B. exists only if ∆x/∆t < c
C. exists only if ∆x/∆t > c
D. exists only if ∆x/∆t = c
E. does not exist under any condition
ans: C
12. Two events occur on the x axis separated in time by ∆t and in space by ∆x. A reference frame,
traveling at less than the speed of light, in which the two events occur at the same coordinate:
A. exists no matter what the values of ∆x and ∆t
B. exists only if ∆x/∆t < c
C. exists only if ∆x/∆t > c
D. exists only if ∆x/∆t = c
E. does not exist under any condition
ans: B
13. As we watch, a spaceship passes us in time ∆t. The crew of the spaceship measures the passage
time and finds it to be ∆t . Which of the following statements is true?
A. ∆t is the proper time for the passage and it is smaller than ∆t
B. ∆t is the proper time for the passage and it is greater than ∆t
C. ∆t is the proper time for the passage and it is smaller than ∆t
D. ∆t is the proper time for the passage and it is greater than ∆t
E. None of the above statements are true.
ans: C
14. A millionairess was told in 1992 that she had exactly 15 years to live. However, if she travels
away from the Earth at 0.8c and then returns at the same speed, the last New Year’s day the
doctors expect her to celebrate is:
A. 2001
B. 2003
C. 2007
D. 2010
E. 2017
ans: E
Chapter 37:
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561
15. Two events occur 100 m apart with an intervening time interval of 0.60 µs. The speed of a
reference frame in which they occur at the same coordinate is:
A. 0
B. 0.25c
C. 0.56c
D. 1.1c
E. 1.8c
ans: C
16. Two independent events occur 100 m apart with an intervening time interval of 0.42 µs. The
proper time in µs between the events is:
A. 0
B. 0.16
C. 0.26
D. 0.42
E. 0.69
ans: C
17. Two events occur 100 m apart with an intervening time interval of 0.37 µs. The speed of a clock
that measures the proper time between the events is:
A. 0
B. 0.45c
C. 0.56c
D. 0.90c
E. 1.8c
ans: D
18. A rocket traveling with constant velocity makes a 8.4 × 1015 m trip in exactly one year. The
proper time in years between events that mark the beginning and end of the trip is:
A. 0.21
B. 0.46
C. 1.0
D. 2.2
E. 4.7
ans: B
19. An observer notices that a moving clock runs slow by a factor of exactly 10. The speed of the
clock is:
A. 0.100c
B. 0.0100c
C. 0.990c
D. 0.900c
E. 0.995c
ans: E
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Chapter 37:
SPECIAL THEORY OF RELATIVITY
20. A meson when at rest decays 2 µs after it is created. If moving in the laboratory at 0.99c, its
lifetime according to laboratory clocks would be:
A. the same
B. 0.28 si
C. 14 µs
D. 4.6 s
E. none of these
ans: C
21. Pi mesons at rest have a half-life of T . If a beam of pi mesons is traveling at a speed of v = βc,
the distance in which the intensity of the beam is halved is:
A. cβT (1 − β 2 )−1/2
B. cβT [(1 + β)/(1 − β)]1/2
C. βvT
D. (1 − β 2 )1/2 vT
E. none of the above
ans: A
22. A meson moving through a laboratory of length x at a speed v decays after a lifetime T as
measured by an observer at rest in the laboratory. If the meson were at rest in the laboratory
its lifetime would be:
A. T (1 − v/c)
B. T (1 − v/c)−1
C. T (1 − v2 /c2 )−1/2
D. T (1 − v2 /c2 )1/2
E. (T − vx/c2 )(1 − v2 /c2 )−1/2
ans: D
23. A measurement of the length of an object that is moving relative to the laboratory consists of
noting the coordinates of the front and back:
A. at different times according to clocks at rest in the laboratory
B. at the same time according to clocks that move with the object
C. at the same time according to clocks at rest in the laboratory
D. at the same time according to clocks at rest with respect to the fixed stars
E. none of the above
ans: C
24. A meter stick moves in the direction of its length through a laboratory. According to measurements taken in the laboratory, its length is 0.31 m The speed of the meter stick relative to the
laboratory is:
A. 0.096c
B. 0.31c
C. 0.69c
D. 0.83c
E. 0.95c
ans: E
Chapter 37:
SPECIAL THEORY OF RELATIVITY
563
25. A meter stick moves sideways at 0.95c. According to measurements taken in the laboratory,
its length is:
A. 0
B. 0.098 m
C. 0.31 m
D. 3.2 m
E. 1.0 m
ans: E
26. A rocket ship of rest length 100 m is moving at speed 0.8c past a timing device that records the
time interval between the passage of the front and back ends of the ship. This time interval is:
A. 0.20 µs
B. 0.25 µs
C. 0.33 µs
D. 0.52 µs
E. 0.69 µs
ans: B
27. The length of a meter stick moving at 0.95c in the direction of its length is measured by
simultaneously marking its ends on a stationary axis. As measured by clocks moving with the
stick, the time interval between the making of the back mark and the making of the front mark
is:
A. 0
B. 3.1 × 10−10 s
C. 1.0 × 10−9 s
D. 3.2 × 10−9 s
E. 1.0 × 10−8 s
ans: D
28. A certain automobile is 6 m long if at rest. If it is measured to be 4/5 as long, its speed is:
A. 0.1c
B. 0.3c
C. 0.6c
D. 0.8c
E. > 0.95c
ans: C
29. As a rocket ship moves by at 0.95c a mark is made on a stationary axis at the front end of the
rocket and 9 × 10−8 s later a mark is made on the axis at the back end. The marks are found
to be 100 m apart. The rest length of the rocket is:
A. 31 m
B. 78 m
C. 100 m
D. 240 m
E. 320 m
ans: D
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Chapter 37:
SPECIAL THEORY OF RELATIVITY
30. A clock is moving along the x axis at 0.6c. It reads zero as it passes the origin (x = 0). When
it passes the x = 180 m mark on the x axis the clock reads:
A. 0.60 µs
B. 0.80 µs
C. 1.00 µs
D. 1.25 µs
E. 1.67 µs
ans: B
31. Relative to reference frame 1, reference frame 2 moves with speed v in the negative x direction.
When the origins of the two frames coincide the clocks in both frames are set to zero. An event
in reference frame 1 and at coordinate x2 and
occurs at coordinate x1 and time t1 as measured
0
time t2 as measured in frame 2. If γ = 1/ 1 − v 2 /c2 , then the coordinates and times of the
event are related by:
A. x2 = γ[x1 − vt1 ] and t2 = γ[t1 − vx1 /c2 ]
B. x2 = γ[x1 − vt1 ] and t2 = γ[t1 + vx1 /c2 ]
C. x2 = γ[x1 + vt1 ] and t2 = γ[t1 − vx1 /c2 ]
D. x2 = γ[x1 + vt1 ] and t2 = γ[t1 + vx1 /c2 ]
E. none of the above are correct
ans: D
32. An event occurs at x = 500 m, t = 0.90 µs in one frame of reference. Another frame is moving
at 0.90c in the positive x direction. The origins coincide at t = 0 and clocks in the second
frame are zeroed when the origins coincide. The coordinate and time of the event in the second
frame are:
A. 500 m, 0.90 µs
B. 1700 m, 5.5 µs
C. 740 m, 2.4 µs
D. 260 m, −0.60 µs
E. 590 m, −1.4 µs
ans: E
33. An event occurs at x = 500 m, t = 0.90 µs in one frame of reference. Another frame is moving
at 0.90c in the negative x direction. The origins coincide at t = 0 and clocks in the second
frame are zeroed when the origins coincide. The coordinate and time of the event in the second
frame are:
A. 500 m, 0.90 µs
B. 1700 m, 5.5 µs
C. 740 m, 2.4 µs
D. 260 m, −0.60 µs
E. 590 m, −1.4 µs
ans: B
Chapter 37:
SPECIAL THEORY OF RELATIVITY
565
34. Two flashes of light occur simultaneously at t = 0 in reference frame S, one at x = 0 and the
other at x = 600 m. They are observed in reference frame S , which is moving at 0.95c in the
positive x direction. The origins of the two frames coincide at t = 0 and the clocks of S are
zeroed when the origins coincide. In S the coordinate where the leading edges of the two light
flashes meet and the time when they meet are:
A. 300 m, 1.0 µs
B. 15 m, 0.050 µs
C. 585 m, 1.95 µs
D. 49 m, 0.16 µs
E. 1900 m, 0.16 µs
ans: D
35. Frame S moves in the positive x direction at 0.6c with respect to frame S. A particle moves in
the positive x direction at 0.4c as measured by an observer in S . The speed of the particle as
measured by an observer in S is:
A. c/5
B. 5c/19
C. 8c/25
D. 25c/31
E. c
ans: D
36. Star S1 is moving away from us at a speed of 0.8c. Star S2 is moving away from us in the
opposite direction at a speed of 0.5c. The speed of S1 as measured by an observer on S2 is:
A. 0.21c
B. 0.5c
C. 0.93c
D. 1.3c
E. 2.17c
ans: C
37. Observer A measures the velocity of a rocket as v and a comet as u. Here u and v are parallel
and in the direction of the observer’s positive x axis. The speed of the comet as measured by
observer B on the rocket is:
A. (u − v)/(1 − uv/c2 )
B. (u − v)/(1 − v2 /c2 )
C. (u − v)/(1 − v2 /c2 )1/2
D. (u − v)/(1 + uv/c2 )
E. (u + v)/(1 − uv/c2 )
ans: A
566
Chapter 37:
SPECIAL THEORY OF RELATIVITY
38. Two electrons move in opposite directions at 0.70c as measured in the laboratory. The speed
of one electron as measured from the other is:
A. 0.35c
B. 0.70c
C. 0.94c
D. 1.00c
E. 1.40c
ans: C
39. Light from some stars shows an apparent change in frequency because of:
A. interference
B. refraction by layers of air
C. diffraction
D. reflection
E. relative motion
ans: E
40. While emitting light of proper frequency f0 , a source moves to the right with speed c/4 relative
to reference frame S. A detector, to the left of the source, measures the frequency to be f ,
which is greater than f0 . This means:
S
detector
.......................
..
..
......................
......
......
......
......
......
...
source
..............
.. .......
..
.. ....................................... c/4
..................................... .
...
.
.
.
......
...... .
.
.
.
.
.
.
......
.
.
.
.
.
.
.
.
.
.
...
.....
......
A.
B.
C.
D.
E.
the detector
the detector
the detector
the detector
the detector
ans: A
is
is
is
is
is
moving to the
moving to the
moving to the
moving to the
not moving
right with a speed that is greater than c/4 relative to S
right with a speed that is less than c/4 relative to S
left with a speed that is greater than c/4 relative to S
left with a speed that is less than c/4 relative to S
41. Light from a stationary spaceship is observed, then the spaceship moves directly away from the
observer at high speed while still emitting the light. As a result, the light seen by the observer
has:
A. a higher frequency and a longer wavelength than before
B. a lower frequency and a shorter wavelength than before
C. a higher frequency and a shorter wavelength than before
D. a lower frequency and a longer wavelength than before
E. the same frequency and wavelength as before
ans: D
Chapter 37:
SPECIAL THEORY OF RELATIVITY
567
42. A train traveling very fast (v = 0.6c) has an engineer (E) at the front, a guard (G) at the
rear, and a passenger (S ) exactly halfway between them. Both E and G are equipped with
yellow signaling lamps. The train passes a station, closely observed by the station master (S).
Both E and G use their lamps to send signals. According to both S and S these signals arrive
simultaneously at the instant S is passing S. According to S, the signal from E will look
and that from G will look
.
A. red, blue
B. yellow, yellow
C. blue, red
D. blue, blue
E. red, red
ans: A
43. A console lamp in the cabin of a spaceship appears green when the ship and observer are both
at rest on Earth. When the ship is moving at 0.90c away from Earth, passengers on board see:
A. nothing (the frequency is too high to be seen)
B. nothing (the frequency is too low to be seen)
C. a red lamp
D. a violet lamp
E. a green lamp
ans: E
44. A spectral line of a certain star is observed to be “red shifted” from a wavelength of 500 nm to
a wavelength of 1500 nm. Interpreting this as a Doppler effect, the speed of recession of this
star is:
A. 0.33c
B. 0.50c
C. 0.71c
D. 0.8c
E. c
ans: D
45. A source at rest emits light of wavelength 500 nm. When it is moving at 0.90c toward an
observer, the observer detects light of wavelength:
A. 26 nm
B. 115 nm
C. 500 nm
D. 2200 nm
E. 9500 nm
ans: B
568
Chapter 37:
SPECIAL THEORY OF RELATIVITY
46. A source at rest emits light of wavelength 500 nm. When it is moving at 0.90c away from an
observer, the observer detects light of wavelength:
A. 26 nm
B. 115 nm
C. 500 nm
D. 2200 nm
E. 9500 nm
ans: D
47. Visible light, with a frequency of 6.0 × 1014 Hz, is reflected from a spaceship moving directly
away at a speed of 0.90c. The frequency of the reflected waves observed at the source is:
A. 3.2 × 1013 Hz
B. 1.4 × 1014 Hz
C. 6.0 × 1014 Hz
D. 2.6 × 1015 Hz
E. 1.1 × 1016 Hz
ans: A
48. How fast should you move away from a 6.0 × 1014 Hz light source to observe waves with a
frequency of 4.0 × 1014 Hz?
A. 0.20c
B. 0.38c
C. 0.45c
D. 0.51c
E. 0.76c
ans: B
49. A particle with rest mass m moves with speed 0.6c. Its kinetic energy is:
A. 0.18mc2
B. 0.22mc2
C. 0.25mc2
D. mc2
E. 1.25mc2
ans: C
50. An electron is moving at 0.6c. If we calculate its kinetic energy using (1/2)mv2 , we get a result
that is:
A. just right
B. just half enough
C. twice the correct value
D. about 1% too low
E. about 28% too low
ans: E
Chapter 37:
SPECIAL THEORY OF RELATIVITY
569
51. The velocity of an electron is changed from c/2 in the −x direction to c/2 in the +x direction.
As a result, its kinetic energy changes by:
A. mc2
B. √
0.5mc2
C.
2mc2
D. 2mc2
E. zero
ans: E
52. The work that must be done to increase the speed of an electron (m = 9.11 × 10−31 kg) from
0.90c to 0.95c is:
A. 2.6 × 10−13 J
B. 8.2 × 10−13 J
C. 3.2 × 10−13 J
D. 7.4 × 10−14 J
E. 3.8 × 10−15 J
ans: D
53. An
A.
B.
C.
D.
E.
electron (m = 9.11 × 10−31 kg) has a speed of 0.95c. Its kinetic energy is:
8.2 × 10−14 J
1.8 × 10−13 J
2.0 × 10−13 J
2.2 × 10−13 J
2.6 × 10−13 J
ans: B
54. An
A.
B.
C.
D.
E.
electron (m = 9.11 × 10−31 kg) has a speed of 0.95c. The magnitude of its momentum is:
2.6 × 10−22 kg · m/s
2.9 × 10−22 kg · m/s
6.0 × 10−22 kg · m/s
8.3 × 10−22 kg · m/s
8.8 × 10−22 kg · m/s
ans: D
55. According to the special theory of relativity:
A. all forms of energy have mass-like properties
B. moving particles lose mass
C. momentum is not conserved in high speed collisions
D. a rod moving rapidly sideways is shorter along its length
E. a rod moving rapidly sideways is longer along its length
ans: A
570
Chapter 37:
SPECIAL THEORY OF RELATIVITY
56. The mass of a particle is m. In order for its total energy to be twice its rest energy, its
momentum must be:
A. mc/2
√
B. mc/ 2
C. mc
√
3mc
D.
E. 2mc
ans: D
57. If the kinetic energy of a particle is equal to its rest energy then its speed must be:
A. 0.25c
B. 0.50c
C. 0.87c
D. c
E. unknown unless its mass is given
ans: C
58. If the mass of a particle is zero its speed must be:
A. c
B. infinite
C. 0
D. any speed less than c
E. any speed greater than c
ans: A
59. A particle with zero mass and energy E carries momentum:
A. Ec
B. √
Ec2
C.
Ec
D. E/c
E. E/c2
ans: D
60. According to relativity theory a particle of mass m with a momentum of 2mc has a speed of:
A. 2c
B. 4c
C. c
D. c/2
E. 0.89c
ans: E
Chapter 37:
SPECIAL THEORY OF RELATIVITY
571
61. If the kinetic energy of a free particle is much greater than its rest energy then its kinetic
energy is proportional to:
A. the magnitude of its momentum
B. the square of the magnitude of its momentum
C. the square root of the magnitude of its momentum
D. the reciprocal of the magnitude of its momentum
E. none of the above
ans: A
62. If the kinetic energy of a free particle is much less than its rest energy then its kinetic energy
is proportional to:
A. the magnitude of its momentum
B. the square of the magnitude of its momentum
C. the square root of the magnitude of its momentum
D. the reciprocal of the magnitude of its momentum
E. none of the above
ans: B
63. The magnitude of the momentum of a particle can never exceed:
A. mc, where m is its mass
B. E/c, where E is its total energy
C. K/c, where K is its kinetic energy
D. none of the above, but there is an upper limit
E. none of the above; there is no upper limit
ans: B
64. An
is:
A.
B.
C.
D.
E.
electron (m = 9.11 × 10−31 kg) has a momentum of 4.0 × 10−22 kg · m/s. Its kinetic energy
6.3 × 10−14 J
8.2 × 10−14 J
1.2 × 10−13 J
1.5 × 10−13 J
2.7 × 10−13 J
ans: A
65. A certain particle has a kinetic energy of 3.2 × 10−10 J and a momentum of 1.7 × 10−18 kg · m/s.
Its mass is:
A. 9.11 × 10−31 kg
B. 2.7 × 10−27 kg
C. 4.5 × 10−27 kg
D. 6.3 × 10−27 kg
E. 8.6 × 10−27 kg
ans: B
572
Chapter 37:
SPECIAL THEORY OF RELATIVITY
66. An electron (m = 9.11 × 10−31 kg, q = 1.60 × 10−19 C) travels at 0.95c around a circular orbit
perpendicular to a uniform 1.8-T magnetic field. The radius of its orbit is:
A. 0.28 mm
B. 0.90 mm
C. 1.1 mm
D. 2.9 mm
E. 4.7 mm
ans: D
67. An electron (m = 9.11 × 10−31 kg, q = 1.60 × 10−19 C) travels around a 1.7-mm radius circular
orbit perpendicular to a 2.8-T magnetic field. Its speed is:
A. 0.16c
B. 0.36c
C. 0.94c
D. c
E. 2.8c
ans: C
Chapter 37:
SPECIAL THEORY OF RELATIVITY
573
Chapter 38:
PHOTONS AND MATTER WAVES
1. The units of the Planck constant h are those of:
A. energy
B. power
C. momentum
D. angular momentum
E. frequency
ans: D
2. If h is the Planck constant, then h̄ is:
A. 2πh
B. 2h
C. h/2
D. h/2π
E. 2h/π
ans: D
3. The quantization of energy, E = nhf , is not important for an ordinary pendulum because:
A. the formula applies only to mass-spring oscillators
B. the allowed energy levels are too closely spaced
C. the allowed energy levels are too widely spaced
D. the formula applies only to atoms
E. the value of h for a pendulum is too large
ans: B
4. The frequency of light beam A is twice that of light beam B. The ratio EA /EB of photon
energies is:
A. 1/2
B. 1/4
C. 1
D. 2
E. 4
ans: D
5. The wavelength of light beam B is twice the wavelength of light beam B. The energy of a
photon in beam A is:
A. half the energy of a photon in beam B
B. one-fourth the energy of a photon in beam B
C. equal to the energy of a photon in beam B
D. twice the energy of a photon in beam B
E. four times the energy of a photon in beam B
ans: A
574
Chapter 38:
PHOTONS AND MATTER WAVES
6. A photon in light beam A has twice the energy of a photon in light beam B. The ratio pA /pB
of their momenta is:
A. 1/2
B. 1/4
C. 1
D. 2
E. 4
ans: D
7. Which of the following electromagnetic radiations has photons with the greatest energy?
A. blue light
B. yellow light
C. x rays
D. radio waves
E. microwaves
ans: C
8. Which of the following electromagnetic radiations has photons with the greatest momentum?
A. blue light
B. yellow light
C. x rays
D. radio waves
E. microwaves
ans: C
9. Rank following electromagnetic radiations according to the energies of their photons, from least
to greatest.
1. blue light
2. yellow light
3. x rays
4. radio waves
A. 1, 2, 3, 4
B. 4, 2, 1, 3
C. 4, 1, 2, 3
D. 3, 2, 1, 4
E. 3, 1, 2, 4
ans: B
10. The intensity of a uniform light beam with a wavelength of 500 nm is 2000 W/m2 . The photon
flux (in number/m 2 · s) is about:
A. 5 × 1017
B. 5 × 1019
C. 5 × 1021
D. 5 × 1023
E. 5 × 1025
ans: C
Chapter 38:
PHOTONS AND MATTER WAVES
575
11. The concentration of photons in a uniform light beam with a wavelength of 500 nm is 1.7 ×
1013 m−3 . The intensity of the beam is:
2
A. 6.7 × 10−6 W/m
2
B. 1.0 × 103 W/m
C. 2.0 × 103 W/m2
2
D. 4.0 × 103 W/m
2
E. 3.2 × 102 W/m
ans: C
12. Light beams A and B have the same intensity but the wavelength associated with beam A is
longer than that associated with beam B. The photon flux (number crossing a unit area per
unit time) is:
A. greater for A than for B
B. greater for B than for A
C. the same for A and B
D. greater for A than for B only if both have short wavelengths
E. greater for B than for A only if both have short wavelengths
ans: A
13. In a photoelectric effect experiment the stopping potential is:
A. the energy required to remove an electron from the sample
B. the kinetic energy of the most energetic electron ejected
C. the potential energy of the most energetic electron ejected
D. the photon energy
E. the electric potential that causes the electron current to vanish
ans: E
14. In a photoelectric effect experiment at a frequency above cut off, the stopping potential is
proportional to:
A. the energy of the least energetic electron before it is ejected
B. the energy of the least energetic electron after it is ejected
C. the energy of the most energetic electron before it is ejected
D. the energy of the most energetic electron after it is ejected
E. the electron potential energy at the surface of the sample
ans: D
15. In a photoelectric effect experiment at a frequency above cut off, the number of electrons ejected
is proportional to:
A. their kinetic energy
B. their potential energy
C. the work function
D. the frequency of the incident light
E. the number of photons that hit the sample
ans: E
576
Chapter 38:
PHOTONS AND MATTER WAVES
16. In a photoelectric effect experiment no electrons are ejected if the frequency of the incident
light is less than A/h, where h is the Planck constant and A is:
A. the maximum energy needed to eject the least energetic electron
B. the minimum energy needed to eject the least energetic electron
C. the maximum energy needed to eject the most energetic electron
D. the minimum energy needed to eject the most energetic electron
E. the intensity of the incident light
ans: D
17. The diagram shows the graphs of the stopping potential as a function of the frequency of the
incident light for photoelectric experiments performed on three different materials. Rank the
materials according to the values of their work functions, from least to greatest.
.
.
.
3 ...
2 ...
1 ...
Vstop
..
..
..
..
..
..
...
...
...
..
..
..
...
...
...
.
.
.
..
..
..
f
A.
B.
C.
D.
E.
1, 2, 3
3, 2, 1
2, 3, 1
2, 1, 3
1, 3, 2
ans: A
18. The work function for a certain sample is 2.3 eV. The stopping potential for electrons ejected
from the sample by 7.0 × 1014 -Hz electromagnetic radiation is:
A. 0
B. 0.60 V
C. 2.3 V
D. 2.9 V
E. 5.2 V
ans: B
19. The stopping potential for electrons ejected by 6.8×1014 -Hz electromagnetic radiation incident
on a certain sample is 1.8 V. The kinetic energy of the most energetic electrons ejected and
the work function of the sample, respectively, are:
A. 1.8 eV, 2.8 eV
B. 1.8 eV, 1.0 eV
C. 1.8 eV, 4.6 eV
D. 2.8 eV, 1.0 eV
E. 1.0 eV, 4.6 eV
ans: B
Chapter 38:
PHOTONS AND MATTER WAVES
577
20. Separate Compton effect experiments are carried out using visible light and x rays. The
scattered radiation is observed at the same scattering angle. For these experiments:
A. the x rays have the greater shift in wavelength and the greater change in photon energy
B. the two radiations have the same shift in wavelength and the x rays have the greater change
in photon energy
C. the two radiations have the same shift in wavelength and the visible light has the greater
change in photon energy
D. the two radiations have the same shift in wavelength and the same change in photon energy
E. the visible light has the greater shift in wavelength and the greater shift in photon energy
ans: B
21. In Compton scattering from stationary particles the maximum change in wavelength can be
made smaller by using:
A. higher frequency radiation
B. lower frequency radiation
C. more massive particles
D. less massive particles
E. particles with greater charge
ans: C
22. Of
A.
B.
C.
D.
E.
the following, Compton scattering from electrons is most easily observed for:
microwaves
infrared light
visible light
ultraviolet light
x rays
ans: E
23. In Compton scattering from stationary electrons the largest change in wavelength occurs when
the photon is scattered through:
A. 0◦
B. 22.5◦
C. 45◦
D. 90◦
E. 180◦
ans: E
24. In Compton scattering from stationary electrons the frequency of the emitted light is independent of:
A. the frequency of the incident light
B. the speed of the electron
C. the scattering angle
D. the electron recoil energy
E. none of the above
ans: E
578
Chapter 38:
PHOTONS AND MATTER WAVES
25. In Compton scattering from stationary electrons the largest change in wavelength that can
occur is:
A. 2.43 × 10−15 m
B. 2.43 × 10−12 m
C. 2.43 × 10−9 m
D. dependent on the frequency of the incident light
E. dependent on the work function
ans: B
26. Electromagnetic radiation with a wavelength of 5.7×10−12 m is incident on stationary electrons.
Radiation that has a wavelength of 6.57 × 10−12 m is detected at a scattering angle of:
A. 10◦
B. 121◦
C. 40◦
D. 50◦
E. 69◦
ans: D
27. Electromagnetic radiation with a wavelength of 3.5 × 10−12 m is scattered from stationary
electrons and photons that have been scattered through 50◦ are detected. An electron from
which one of these photons was scattered receives an energy of:
A. 0
B. 1.1 × 10−14 J
C. 1.9 × 10−14 J
D. 2.3 × 10−14 J
E. 1.3 × 10−13 J
ans: B
28. Electromagnetic radiation with a wavelength of 3.5 × 10−12 m is scattered from stationary
electrons and photons that have been scattered through 50◦ are detected. After a scattering
event the magnitude of the electron’s momentum is:
A. 0
B. 1.5 × 10−22 kg · m/s
C. 2.0 × 10−22 kg · m/s
D. 2.2 × 10−22 kg · m/s
E. 8.7 × 10−23 kg · m/s
ans: B
Chapter 38:
PHOTONS AND MATTER WAVES
579
29. Consider the following:
1. a photoelectric process in which some emitted electrons have kinetic energy greater
than hf , where f is the frequency of the incident light.
2. a photoelectric process in which all emitted electrons have energy less than hf .
3. Compton scattering from stationary electrons for which the emitted light has a wavelength that is greater than that of the incident light.
4. Compton scattering from stationary electrons for which the emitted light has a wavelength that is less than that of the incident light.
The only possible processes are:
A. 1
B. 3
C. 1 and 3
D. 2 and 3
E. 2 and 4
ans: D
30. J. J. Thompson’s measurement of e/m for electrons provides evidence of the:
A. wave nature of matter
B. particle nature of matter
C. wave nature of radiation
D. particle nature of radiation
E. transverse wave nature of light
ans: B
31. Evidence for the wave nature of matter is:
A. electron diffraction experiments of Davisson and Germer
B. Thompson’s measurement of e/m
C. Young’s double slit experiment
D. the Compton effect
E. Lenz’s law
ans: A
32. Which of the following is NOT evidence for the wave nature of matter?
A. The photoelectric effect
B. The diffraction pattern obtained when electrons pass through a slit
C. Electron tunneling
D. The validity of the Heisenberg uncertainty principle
E. The interference pattern obtained when electrons pass through a two-slit system
ans: A
33. Of
A.
B.
C.
D.
E.
580
the following which is the best evidence for the wave nature of matter?
The photoelectric effect
The Compton effect
The spectral radiancy of cavity radiation
The relationship between momentum and energy for an electron
The reflection of electrons by crystals
ans: E
Chapter 38:
PHOTONS AND MATTER WAVES
34. Monoenergetic electrons are incident on a single slit barrier. If the energy of each incident
electron is increased the central maximum of the diffraction pattern:
A. widens
B. narrows
C. stays the same width
D. widens for slow electrons and narrows for fast electrons
E. narrows for slow electrons and widens for fast electrons
ans: B
35. A free electron and a free proton have the same kinetic energy. This means that, compared to
the matter wave associated with the proton, the matter wave associated with the electron has:
A. a shorter wavelength and a greater frequency
B. a longer wavelength and a greater frequency
C. a shorter wavelength and the same frequency
D. a longer wavelength and the same frequency
E. a shorter wavelength and a smaller frequency
ans: D
36. A free electron and a free proton have the same momentum. This means that, compared to
the matter wave associated with the proton, the matter wave associated with the electron:
A. has a shorter wavelength and a greater frequency
B. has a longer wavelength and a greater frequency
C. has the same wavelength and the same frequency
D. has the same wavelength and a greater frequency
E. has the same wavelength and a smaller frequency
ans: D
37. A free electron and a free proton have the same speed. This means that, compared to the
matter wave associated with the proton, the matter wave associated with the electron:
A. has a shorter wavelength and a greater frequency
B. has a longer wavelength and a greater frequency
C. has the same wavelength and the same frequency
D. has the same wavelength and a greater frequency
E. has a longer wavelength and a smaller frequency
ans: E
38. Consider the following three particles:
1. a free electron with speed v0
2. a free proton with speed v0
3. a free proton with speed 2v0
Rank them according to the wavelengths of their matter waves, least to greatest.
A. 1, 2, 3
B. 3, 2, 1
C. 2, 3, 1
D. 1, 3, 2
E. 1, then 2 and 3 tied
ans: B
Chapter 38:
PHOTONS AND MATTER WAVES
581
39. Consider the following three particles:
1. a free electron with kinetic energy K0
2. a free proton with kinetic energy K0
3. a free proton with kinetic energy 2K0
Rank them according to the wavelengths of their matter waves, least to greatest.
A. 1, 2, 3
B. 3, 2, 1
C. 2, 3, 1
D. 1, 3, 2
E. 1, then 2 and 3 tied
ans: B
40. A free electron has a momentum of 5.0 × 10−24 kg · m/s. The wavelength of its wave function
is:
A. 1.3 × 10−8 m
B. 1.3 × 10−10 m
C. 2.1 × 10−11 m
D. 2.1 × 10−13 m
E. none of these
ans: B
41. The frequency and wavelength of the matter wave associated with a 10-eV free electron are:
A. 1.5 × 1034 Hz, 3.9 × 10−10 m
B. 1.5 × 1034 Hz, 1.3 × 10−34 m
C. 2.4 × 1015 Hz, 1.2 × 10−9 m
D. 2.4 × 1015 Hz, 3.9 × 10−10 m
E. 4.8 × 1015 Hz, 1.9 × 10−10 m
ans: D
42. If the kinetic energy of a non-relativistic free electron doubles, the frequency of its wave function
changes by the factor:
√
A. 1/ 2
B. 1/2
C. 1/4
√
2
D.
E. 2
ans: E
43. A non-relativistic free electron has kinetic energy K. If its wavelength doubles, its kinetic
energy is:
A. 4K
B. 2K
C. still K
D. K/2
E. K/4
ans: E
582
Chapter 38:
PHOTONS AND MATTER WAVES
44. The probability that a particle is in a given small region of space is proportional to:
A. its energy
B. its momentum
C. the frequency of its wave function
D. the wavelength of its wave function
E. the square of the magnitude of its wave function
ans: E
45. ψ(x) is the wave function for a particle moving along the x axis. The probability that the
particle is in the interval from x = a to x = b is given by:
A. ψ(b) − ψ(a)
B. |ψ(b)|/|ψ(a)|
C. |ψ(b)|2 /|ψ(a)|2
$b
D. a ψ(x) dx
$b
E. a |ψ(x)|2 dx
ans: E
46. The significance of |ψ|2 is:
A. probability
B. energy
C. probability density
D. energy density
E. wavelength
ans: C
47. Maxwell’s equations are to electric and magnetic fields as
for a particle.
A. Einstein’s
B. Fermi’s
C. Newton’s
D. Schrödinger’s
E. Bohr’s
ans: D
equation is to the wave function
48. A free electron in motion along the x axis has a localized wave function. The uncertainty in
its momentum is decreased if:
A. the wave function is made more narrow
B. the wave function is made less narrow
C. the wave function remains the same but the energy of the electron is increased
D. the wave function remains the same but the energy of the electron is decreased
E. none of the above
ans: B
Chapter 38:
PHOTONS AND MATTER WAVES
583
49. The uncertainty in position of an electron in a certain state is 5 × 10−10 m. The uncertainty in
its momentum might be:
A. 5.0 × 10−24 kg · m/s
B. 4.0 × 10−24 kg · m/s
C. 3.0 × 10−24 kg · m/s
D. all of the above
E. none of the above
ans: D
50. The reflection coefficient R for a certain barrier tunneling problem is 0.80. The corresponding
transmission coefficient T is:
A. 0.80
B. 0.60
C. 0.50
D. 0.20
E. 0
ans: D
51. An electron with energy E is incident upon a potential energy barrier of height Epot > E and
thickness L. The transmission coefficient T :
A. is zero
B. decreases exponentially with L
C. is proportional to 1/L
D. is proportional to 1/L2
E. is non-zero and independent of L
ans: B
52. In order to tunnel through a potential barrier a particle must:
A. have energy greater than the barrier height
B. have spin
C. be massive
D. have a wavelength longer than the barrier width
E. none of the above
ans: E
53. An electron with energy E is incident on a potential energy barrier of height Epot and thickness
L. The probability of tunneling increases if:
A. E decreases without any other changes
B. Epot increases without any other changes
C. L decreases without any other changes
D. E and Epot increase by the same amount
E. E and Epot decrease by the same amount
ans: C
584
Chapter 38:
PHOTONS AND MATTER WAVES
54. Identical particles, each with energy E, are incident on the following four potential energy
barriers:
1. barrier height = 5E, barrier width = 2L
2. barrier height = 10E, barrier width = L
3. barrier height = 17E, barrier width = L/2
4. barrier height = 26E, barrier width = L/3
Rank the barriers in terms of the probability that the particles tunnel through them, from least
probability to greatest probability.
A. 1, 2, 3, 4
B. 4, 3, 2, 1
C. 1 and 2 tied, then 3, then 4
D. 2, then 1 and 3 tied, then 4
E. 3, 2, 1, 4
ans: A
Chapter 38:
PHOTONS AND MATTER WAVES
585
Chapter 39:
1. If a
A.
B.
C.
D.
E.
MORE ABOUT MATTER WAVES
wave function ψ for a particle moving along the x axis is normalized, then:
$
2
$ |ψ|2 dt = 1
|ψ| dx = 1
∂ψ/∂x = 1
∂ψ/∂t = 1
|ψ|2 = 1
ans: B
2. The energy of a particle in a one-dimensional trap with zero potential energy in the interior
and infinite potential energy at the walls is proportional to (n = quantum number):
A. n
B. 1/n
2
C. 1/n
√
D.
n
2
E. n
ans: E
3. The ground state energy of an electron in a one-dimensional trap with zero potential energy
in the interior and infinite potential energy at the walls is 2.0 eV. If the width of the well is
doubled, the ground state energy will be:
A. 0.5 eV
B. 1.0 eV
C. 2.0 eV
D. 4.0 eV
E. 8.0 eV
ans: A
4. An electron is in a one-dimensional trap with zero potential energy in the interior and infinite
potential energy at the walls. The ratio E3 /E1 of the energy for n = 3 to that for n = 1 is:
A. 1/3
B. 1/9
C. 3/1
D. 9/1
E. 1/1
ans: D
586
Chapter 39:
MORE ABOUT MATTER WAVES
5. A particle is trapped in a one-dimensional well with infinite potential energy at the walls. Three
possible pairs of energy levels are
1. n = 3 and n = 1
2. n = 3 and n = 2
3. n = 4 and n = 3
Order these pairs according to the difference in energy, least to greatest.
A. 1, 2, 3
B. 3, 2, 1
C. 2, 3, 1
D. 1, 3, 2
E. 3, 1, 2
ans: C
6. Identical particles are trapped in one-dimensional wells with infinite potential energy at the
walls. The widths L of the traps and the quantum numbers n of the particles are
1. L = 2L0 , n = 2
2. L = 2L0 , n = 4
3. L = 3L0 , n = 3
4. L = 4L0 , n = 2
Rank them according to the kinetic energies of the particles, least to greatest.
A. 1, 2, 3, 4
B. 4, 3, 2, 1
C. 1 and 3 tied, then 2, 4
D. 4, 2, then 1 and 3 tied
E. 1, 3, then 2 and 4 tied
ans: D
7. Four different particles are trapped in one-dimensional wells with infinite potential energy at
their walls. The masses of the particles and the width of the wells are
1. mass = 4m0 , width = 2L0
2. mass = 2m0 , width = 2L0
3. mass = 4m0 , width = L0
4. mass = m0 , width = 2L0
Rank them according to the kinetic energies of the particles when they are in their ground
states.
A. 1, 2, 3, 4
B. 1, 2, 3 and 4 tied
C. 1 and 2 tied, then 3, 4
D. 4, 3, 2, 1
E. 3, 1, 2, 4
ans: B
Chapter 39:
MORE ABOUT MATTER WAVES
587
8. The ground state energy of an electron in a one-dimensional trap with zero potential energy in
the interior and infinite potential energy at the walls:
A. is zero
B. decreases with temperature
C. increases with temperature
D. is independent of temperature
E. oscillates with time
ans: D
9. An electron is in a one-dimensional trap with zero potential energy in the interior and infinite
potential energy at the walls. A graph of its wave function ψ(x) versus x is shown. The value
of quantum number n is:
ψ
..........
..........
... ....
... .....
...
...
..
..
...
...
.
..
.
...
...
..
...
...
...
..
...
.
.
.
... .
... ..
... ..
... ..
........
.....
A.
B.
C.
D.
E.
x
0
2
4
6
8
ans: C
10. An electron is in a one-dimensional trap with zero potential energy in the interior and infinite
potential energy at the walls. A graph of its probability density P (x) versus x is shown. The
value of the quantum number n is:
P
....
....
... ....
... ....
... ....
... ....
... .
...
..
.... ...
....
..
.
....
A.
B.
C.
D.
E.
588
0
1
2
3
4
ans: C
Chapter 39:
MORE ABOUT MATTER WAVES
x
11. A particle is trapped in an infinite potential energy well. It is in the state with quantum
number n = 14. How many nodes does the probability density have (counting the nodes at the
ends of the well)?
A. none
B. 7
C. 13
D. 14
E. 15
ans: E
12. A particle is trapped in an infinite potential energy well. It is in the state with quantum
number n = 14. How many maxima does the probability density have?
A. none
B. 7
C. 13
D. 14
E. 15
ans: D
13. A particle is confined to a one-dimensional trap by infinite potential energy walls. Of the
following states, designed by the quantum number n, for which one is the probability density
greatest near the center of the well?
A. n = 2
B. n = 3
C. n = 4
D. n = 5
E. n = 6
ans: B
14. Two one-dimensional traps have infinite potential energy at their walls Trap A has width L
and trap B has width 2L. For which value of the quantum number n does a particle in trap B
have the same energy as a particle in the ground state of trap A?
A. n = 1
B. n = 2
C. n = 3
D. n = 4
E. n = 5
ans: B
15. An electron is trapped in a deep well with a width of 0.3 nm. If it is in the state with quantum
number n = 3 its kinetic energy is:
A. 6.0 × 10−28 J
B. 1.8 × 10−27 J
C. 6.7 × 10−19 J
D. 2.0 × 10−18 J
E. 6.0 × 10−18 J
ans: E
Chapter 39:
MORE ABOUT MATTER WAVES
589
16. An electron is in a one-dimensional well with finite potential energy barriers at the walls. The
matter wave:
A. is zero at the barriers
B. is zero everywhere within each barrier
C. is zero in the well
D. extends into the barriers
E. is discontinuous at the barriers
ans: D
17. A particle is confined by finite potential energy walls to a one-dimensional trap from x = 0 to
x = L. Its wave function in the region x > L has the form:
A. ψ(x) = A sin(kx)
B. ψ(x) = Aekx
C. ψ(x) = Ae−kx
D. ψ(x) = Aeikx
E. ψ(x) = 0
ans: C
18. A particle is trapped in a finite potential energy well that is deep enough so that the electron
can be in the state with n = 4. For this state how many nodes does the probability density
have?
A. none
B. 1
C. 3
D. 5
E. 7
ans: C
19. A particle in a certain finite potential energy well can have any of five quantized energy values
and no more. Which of the following would allow it to have any of six quantized energy levels?
A. Increase the momentum of the particle
B. Decrease the momentum of the particle
C. Decrease the well width
D. Increase the well depth
E. Decrease the well depth
ans: D
20. A particle in a certain finite potential energy well can have any of five quantized energy values
and no more. Which of the following would allow it to have any of six quantized energy levels?
A. Increase the energy of the particle
B. Decrease the energy of the particle
C. Make the well shallower
D. Make the well deeper
E. Make the well narrower
ans: D
590
Chapter 39:
MORE ABOUT MATTER WAVES
21. An electron in an atom initially has an energy 5.5 eV above the ground state energy. It drops
to a state with energy 3.2 eV above the ground state energy and emits a photon in the process.
The wave associated with the photon has a wavelength of:
A. 5.4 × 10−7 m
B. 3.0 × 10−7 m
C. 1.7 × 10−7 m
D. 1.15 × 10−7 m
E. 1.0 × 10−7 m
ans: A
22. An electron in an atom drops from an energy level at −1.1 × 10−18 J to an energy level at
−2.4 × 10−18 J. The wave associated with the emitted photon has a frequency of:
A. 2.0 × 1017 Hz
B. 2.0 × 1015 Hz
C. 2.0 × 1013 Hz
D. 2.0 × 1011 Hz
E. 2.0 × 109 Hz
ans: B
23. An electron in an atom initially has an energy 7.5 eV above the ground state energy. It drops
to a state with an energy of 3.2 eV above the ground state energy and emits a photon in the
process. The momentum of the photon is:
A. 1.7 × 10−27 kg · m/s
B. 2.3 × 10−27 kg · m/s
C. 4.0 × 10−27 kg · m/s
D. 5.7 × 10−27 kg · m/s
E. 8.0 × 10−27 kg · m/s
ans: B
24. The quantum number n is most closely associated with what property of the electron in a
hydrogen atom?
A. Energy
B. Orbital angular momentum
C. Spin angular momentum
D. Magnetic moment
E. z component of angular momentum
ans: A
25. Take the potential energy of a hydrogen atom to be zero for infinite separation of the electron
and proton. Then, according to quantum theory the energy En of a state with principal
quantum number n is proportional to:
A. n
B. n2
C. 1/n
D. 1/n2
E. none of the above
ans: D
Chapter 39:
MORE ABOUT MATTER WAVES
591
26. The binding energy of an electron in the ground state in a hydrogen atom is about:
A. 13.6 eV
B. 3.4 eV
C. 10.2 eV
D. 1.0 eV
E. 27.2 eV
ans: A
27. Take the potential energy of a hydrogen atom to be zero for infinite separation of the electron
and proton. Then the ground state energy is −13.6 eV. The energy of the first excited state is:
A. 0
B. −3.4 eV
C. −6.8 eV
D. −9.6 eV
E. −27 eV
ans: B
28. Take the potential energy of a hydrogen atom to be zero for infinite separation of the electron
and proton. Then the ground state energy is −13.6 eV. The negative sign indicates:
A. the kinetic energy is negative
B. the potential energy is positive
C. the electron might escape from the atom
D. the electron and proton are bound together
E. none of the above
ans: D
29. Take the potential energy of a hydrogen atom to be zero for infinite separation of the electron
and proton. Then the ground state energy of a hydrogen atom is −13.6 eV. When the electron
is in the first excited state its excitation energy is:
A. 0
B. 3.4 eV
C. 6.8 eV
D. 10.2 eV
E. 13.6 eV
ans: D
30. Take the potential energy of a hydrogen atom to be zero for infinite separation of the electron
and proton. Then the ground state energy is −13.6 eV. When the electron is in the first excited
state the ionization energy is:
A. 0
B. 3.4 eV
C. 6.8 eV
D. 10.2 eV
E. 13.6 eV
ans: B
592
Chapter 39:
MORE ABOUT MATTER WAVES
31. The diagram shows the energy levels for an electron in a certain atom. Of the transitions
shown, which represents the emission of a photon with the most energy?
n=4
n=3
n=2
n=1
.......
........
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
A
...
.
.........
......
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
.
.........
.....
.
B
C
...
..
...
...
...
..
.........
......
D
.
.......
.......
....
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
E
ans: C
32. When a hydrogen atom makes the transition from the second excited state to the ground state
(at −13.6 eV) the energy of the photon emitted is:
A. 0
B. 1.5 eV
C. 9.1 eV
D. 12.1 eV
E. 13.6 eV
ans: D
33. The series limit for the Balmer series represents a transition m → n, where (m, n) is
A. (2, 1)
B. (3, 2)
C. (∞, 0)
D. (∞, 1)
E. (∞, 2)
ans: E
34. The Balmer series of hydrogen is important because it:
A. is the only one for which the quantum theory can be used
B. is the only series that occurs for hydrogen
C. is in the visible region
D. involves the lowest possible quantum number n
E. involves the highest possible quantum number n
ans: C
35. The principle of complementarity is due to:
A. Einstein
B. Maxwell
C. Newton
D. Bohr
E. Schrodinger
ans: D
Chapter 39:
MORE ABOUT MATTER WAVES
593
36. Which of the following sets of quantum numbers is possible for an electron in a hydrogen atom?
A. n = 4, = 3, mf = −3
B. n = 4, = 4, mf = −2
C. n = 5, = −1, mf = 2
D. n = 3, = 1, mf = −2
E. n = 2, = 3, mf = −2
ans: A
37. The wave function for an electron in a state with zero angular momentum:
A. is zero everywhere
B. is spherically symmetric
C. depends on the angle from the z axis
D. depends on the angle from the x axis
E. is spherically symmetric for some shells and depends on the angle from the z axis for others
ans: B
38. Consider the following:
1. the probability density for an = 0 state
2. the probability density for a state with = 0
3. the average of the probability densities for all states in an
Of these which are spherically symmetric?
A. only 1
B. only 2
C. only 1 and 2
D. only 1 and 3
E. 1, 2, and 3
ans: D
= 0 subshell
39. If the wave function ψ is spherically symmetric then the radial probability density is given by:
A. 4πr2 ψ
B. |ψ|2
C. 4πr 2 |ψ|2
D. 4π|ψ|2
E. 4πr|ψ|2
ans: C
40. If P (r) is the radial probability density then the probability that the separation of the electron
and proton is between r and r + dr is:
A. P dr
B. |P |2 dr
C. 4πr 2 P dr
D. 4πr2 |P | dr
E. 4π|P |2 dr
ans: A
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Chapter 39:
MORE ABOUT MATTER WAVES
41. The radial probability density for the electron in the ground state of a hydrogen atom has a
peak at about:
A. 0.5 pm
B. 5 pm
C. 50 pm
D. 500 pm
E. 5000 pm
ans: C
Chapter 39:
MORE ABOUT MATTER WAVES
595
Chapter 40:
ALL ABOUT ATOMS
1. The magnitude of the orbital angular momentum of an electron in an atom is what multiple
of h̄? ( is a positive integer.)
A. 1
B. 0
1/2
( + 1)
C.
D. 2 + 1
E. 2
ans: C
2. The magnetic quantum number m is most closely associated with what property of an electron
in an atom?
A. Magnitude of the orbital angular momentum
B. Energy
C. z component of the spin angular momentum
D. z component of the orbital angular momentum
E. Radius of the orbit
ans: D
3. The quantum number m s is most closely associated with what property of the electron in an
atom?
A. Magnitude of the orbital angular momentum
B. Energy
C. z component of the spin angular momentum
D. z component of the orbital angular momentum
E. Radius of the orbit
ans: C
4. Possible values of the principal quantum number n for an electron in an atom are:
A. only 0 and 1
B. only 0, 1, 2, . . ., ∞
C. only 0, 1, . . ., − 1
D. only 1/2 and −1/2
E. only 1, 2, 3, . . ., ∞
ans: E
5. The number of values of the orbital quantum number
number n = 3 is:
A. 1
B. 2
C. 3
D. 4
E. 7
ans: C
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Chapter 40:
ALL ABOUT ATOMS
associated with the principal quantum
6. The number of possible values of the magnetic quantum number m associated with a given
value of the orbital quantum number is:
A. 1
B. 2
C.
D. 2
E. 2 + 1
ans: E
7. An atom is in a state with orbital quantum number
quantum number m are:
A. 1, 2
B. 0, 1, 2
C. 0, 1
D. −1, 0, 1
E. −2, −1, 0, 1, 2
ans: E
= 2. Possible values of the magnetic
8. An √
electron is in a quantum state for which the magnitude of the orbital angular momentum
is 6 2h̄. How many allowed values of the z component of the angular momentum are there?
A. 4
B. 5
C. 7
D. 8
E. 9
ans: D
9. An electron is in a quantum state for which there are seven allowed values of the z component
of the angular momentum. The magnitude of the angular momentum is:
√
A. √3h̄
B. √7h̄
C. √9h̄
D. √12h̄
14h̄
E.
ans: D
10. The number of states in a subshell with orbital quantum number
A. 2
B. 3
C. 7
D. 9
E. 14
ans: E
Chapter 40:
= 3 is:
ALL ABOUT ATOMS
597
11. The number of states in a shell with principal quantum number n = 3 is:
A. 3
B. 9
C. 15
D. 18
E. 25
ans: D
12. An electron in an atom is in a state with principal quantum number n = 4. The possible values
of the orbital quantum number are:
A. 1, 2, 3
B. 1, 2, 3, 4
C. −3, −2, −1, 0, 1, 2, 3
D. 0, 1, 2, 3
E. 0, 1, 2
ans: D
13. Space quantization means that:
A. space is quantized
B. Lz can have only certain discrete values
→
C. L and −
µ are in the same direction
−
→
D. L and µ are in opposite directions
E. an electron has a magnetic dipole moment
ans: B
14. An electron in an atom is in a state with
axis is:
A. 48.2◦
B. 60◦
C. 30◦
D. 35.3◦
E. 54.7◦
ans: E
= 3 and m = 2. The angle between L and the z
15. An
is:
A.
B.
C.
D.
E.
electron in an atom is in a state with = 5. The minimum angle between L and the z axis
598
Chapter 40:
0◦
18.0◦
24.1◦
36.7◦
33.6◦
ans: C
ALL ABOUT ATOMS
16. In the relation µz = −m µB , the quantity µB is:
A. the Bohr magneton
B. the component of the dipole moment along the magnetic field
C. the permeability of the material
D. a friction coefficient
E. none of the above
ans: A
17. The electron states that constitute a single shell for an atom all have:
A. the same value of n
B. the same value of
C. the same value of n and the same value of
D. the same value of and the same value of m
E. the same set of all four quantum numbers
ans: A
18. The electron states that constitute a single subshell for an atom all have:
A. only the same value of n
B. only the same value of
C. only the same value of n and the same value of
D. only the same value of and the same value of m
E. the same set of all four quantum numbers
ans: C
19. The total number of electron states with n = 2 and
A. two
B. four
C. six
D. eight
E. ten
ans: C
= 1 for an atom is:
20. The possible values for the magnetic quantum number ms of an electron in an atom:
A. depend on n
B. depend on
C. depend on both n and
D. depend on whether there is an external magnetic field present
E. are ±1/2
ans: E
21. The Stern-Gerlach experiment makes use of:
A. a strong uniform magnetic field
B. a strong non-uniform magnetic field
C. a strong uniform electric field
D. a strong non-uniform electric field
E. strong perpendicular electric and magnetic fields
ans: B
Chapter 40:
ALL ABOUT ATOMS
599
22. The magnetic field B is along the z axis in a Stern-Gerlach experiment. The force it exerts on
a magnetic dipole with dipole moment µ is proportional to:
A. µ2z
B. B 2
C. dB/dz
D. $d2 B/dz 2
E.
B dz
ans: C
23. A magnetic dipole µ is placed in a strong uniform magnetic field B. The associated force
exerted on the dipole is:
A. along µ
B. along −µ
C. along B
D. along µ × B
E. zero
ans: E
24. The force exerted on a magnetic dipole as it moves with velocity v through a Stern-Gerlach
apparatus is:
A. proportional to v
B. proportional to 1/v
C. zero
D. proportional to v2
E. independent of v
ans: E
25. A magnetic dipole is placed between the poles of a magnet as shown. The direction of the
associated force exerted on the dipole is:
y
N
x
A.
B.
C.
D.
E.
600
...................................... ..
..................................
..
...
.....
...
...
.....
....
...
.....
..
...
...
.....
... ............................................ .........
...
...
.....
...
...
....
.....
...
...
.....
..
.....
...
...
...
....
...
...
...
.
...
...
.....
....
...
...
...
...
...
..................................................................... ..
...
.....
...
...
....
...
...
...
...
...
...
...
...
.
.
.
................................................................................................................................................................................
positive x
positive y
negative x
negative y
into or out of the page
ans: C
Chapter 40:
ALL ABOUT ATOMS
µ
S
26. To
A.
B.
C.
D.
E.
observe the Zeeman effect one uses:
a strong uniform magnetic field
a strong non-uniform magnetic field
a strong uniform electric field
a strong non-uniform electric field
mutually perpendicular electric and magnetic fields
ans: B
27. An
A.
B.
C.
D.
E.
electron in a K shell of an atom has the principal quantum number:
n=0
n=1
n=2
n=3
n=∞
ans: B
28. An
A.
B.
C.
D.
E.
electron in an L shell of an atom has the principal quantum number:
n=0
n=1
n=2
n=3
n=∞
ans: C
29. The most energetic photon in a continuous x-ray spectrum has an energy approximately equal
to:
A. the energy of all the electrons in a target atom
B. the kinetic energy of an incident-beam electron
C. the rest energy, mc2 , of an electron
D. the total energy of a K-electron in the target atom
E. the kinetic energy of a K-electron in the target atom
ans: B
30. Two different electron beams are incident on two different targets and both produce x rays.
The cutoff wavelength for target 1 is shorter than the cutoff wavelength for target 2. We can
conclude that:
A. target 2 has a higher atomic number than target 1
B. target 2 has a lower atomic number than target 1
C. the electrons in beam 1 have greater kinetic energy than those in beam 2
D. the electrons in beam 1 have less kinetic energy than those in beam 2
E. target 1 is thicker than target 2
ans: C
Chapter 40:
ALL ABOUT ATOMS
601
31. A photon with the smallest wavelength in the continuous z-ray spectrum is emitted when:
A. an electron is knocked from a K shell
B. a valence electron is knocked from the atom
C. the incident electron becomes bound to the atom
D. the atom has the greatest recoil energy
E. the incident electron loses all its energy in a single decelerating event
ans: E
32. Radiation with the minimum wavelength as well as the K x-ray lines are detected for a certain
target. The energy of the incident electrons is then doubled, with the result that
A. the minimum wavelength increases and the wavelengths of the K lines remain the same
B. the minimum wavelength decreases and the wavelengths of the K lines remain the same
C. the minimum wavelength and the wavelengths of the K lines all increase
D. the minimum wavelength and the wavelengths of the K lines all decrease
E. the minimum wavelength increases and the wavelengths of the K lines all decrease
ans: B
33. Characteristic K x-radiation of an element occurs when:
A. the incident electron is absorbed by a target nucleus
B. the incident electron is scattered by a target atom without an energy loss
C. an electron is ejected from an outer shell of a target atom
D. an electron in a target atom makes a transition to the lowest energy state
E. the incident electron goes into the lowest energy state
ans: D
34. The Kα x rays arising from a cobalt (Z = 27) target have a wavelength of about 179 pm. The
atomic number of a target that gives rise to Kα x rays with a wavelength one-third as great
(≈ 60 pm) is:
A. Z = 9
B. Z = 10
C. Z = 12
D. Z = 16
E. Z = 46
ans: E
35. In connection with x-ray emission the symbol Kα refers to:
A. an alpha particle radiation
B. an effect of the dielectric constant on energy levels
C. x-ray radiation from potassium
D. x-ray radiation associated with an electron going from n = ∞ to n = 1
E. x-ray radiation associated with an electron going from n = 2 to n = 1
ans: E
602
Chapter 40:
ALL ABOUT ATOMS
36. In connection with x-ray emission the symbol Lβ refers to:
A. a beta particle radiation
B. an atomic state of angular momentum h/2π
C. the inductance associated with an orbiting electron
D. x-radiation associated with an electron going from n = 4 to n = 2
E. none of the above
ans: D
37. The transition shown gives rise to an x-ray. The correct label for this is:
...
...
...
...
...
...
...
...
........
......
K
L
M
A.
B.
C.
D.
E.
Kα
Kβ
Lα
Lβ
KL
ans: A
38. In a Moseley graph:
A. the x-ray frequency is plotted as a function of atomic number
B. the square of the x-ray frequency is plotted as a function of atomic number
C. the square root of the x-ray frequency is plotted as a function of atomic number
D. the x-ray frequency is plotted as a function of the square root of atomic number
E. the square root of the x-ray frequency is plotted as a function of atomic mass
ans: C
39. In calculating the x-ray energy levels the effective charge of the nucleus is taken to be Z − b,
where Z is the atomic number. The parameter b enters because:
A. an electron is removed from the inner shell
B. a proton is removed from the nucleus
C. the quantum mechanical force between two charges is less than the classical force
D. the nucleus is screened by electrons
E. the Pauli exclusion principle must be obeyed
ans: D
40. The ratio of the wavelength of the Kα x-ray line for Nb (Z = 41) to that of Ga (Z = 31) is:
A. 9/16
B. 16/9
C. 3/4
D. 4/3
E. 1.15
ans: A
Chapter 40:
ALL ABOUT ATOMS
603
41. The Pauli exclusion principle is obeyed by:
A. all particles
B. all charged particles
C. all particles with spin quantum numbers of 1/2
D. all particles with spin quantum numbers of 1
E. all particles with mass
ans: C
42. No
to:
A.
B.
C.
D.
E.
state in an atom can be occupied by more than one electron. This is most closely related
the wave nature of matter
the finite value for the speed of light
the Bohr magneton
the Pauli exclusion principle
the Einstein-de Haas effect
ans: D
43. Electrons are in a two-dimensional square potential energy well with sides of length L. The
potential energy is infinite at the sides and zero inside. The single-particle energies are given
by (h2 /8mL2 )(n2x + n2y ), where nx and ny are integers. At most the number of electrons that
can have energy 8(h2 /8mL2 ) is:
A. 1
B. 2
C. 3
D. 4
E. any number
ans: B
44. Five electrons are in a two-dimensional square potential energy well with sides of length L.
The potential energy is infinite at the sides and zero inside. The single-particle energies are
given by (h2 /8mL2 )(n2x + n2y ), where nx and ny are integers. In units of (h2 /8mL2 ) the energy
of the ground state of the system is:
A. 0
B. 10
C. 19
D. 24
E. 48
ans: C
604
Chapter 40:
ALL ABOUT ATOMS
45. Five electrons are in a two-dimensional square potential energy well with sides of length L.
The potential energy is infinite at the sides and zero inside. The single-particle energies are
given by (h2 /8mL2 )(n2x + n2y ), where nx and ny are integers. In units of (h2 /8mL2 ) the energy
of the first excited state of the system is:
A. 13
B. 22
C. 24
D. 25
E. 27
ans: B
46. Electrons are in a two-dimensional square potential energy well with sides of length L. The
potential energy is infinite at the sides and zero inside. The single-particle energies are given
by (h2 /8mL2 )(n2x + n2y ), where nx and ny are integers. The number of single-particle states
with energy 5(h2 /8mL2 ) is:
A. 1
B. 2
C. 3
D. 4
E. 5
ans: B
47. Six electrons are in a two-dimensional square potential energy well with sides of length L. The
potential energy is infinite at the sides and zero inside. The single-particle energies are given
by (h2 /8mL2 )(n2x + n2y ), where nx and ny are integers. If a seventh electron is added to the
system when it is in its ground state the least energy the additional electron can have is:
A. 2(h2 /8mL2 )
B. 5(h2 /8mL2 )
C. 10(h2 /8mL2 )
D. 13(h2 /8mL2 )
E. 18(h2 /8mL2 )
ans: C
48. When a lithium atom is made from a helium atom by adding a proton (and neutron) to the
nucleus and an electron outside, the electron goes into an n = 2, = 0 state rather than an
n = 1, = 0 state. This is an indication that electrons:
A. obey the Pauli exclusion principle
B. obey the minimum energy principle
C. undergo the Zeeman effect
D. are diffracted
E. and protons are interchangeable
ans: A
Chapter 40:
ALL ABOUT ATOMS
605
49. When a lithium atom in its ground state is made from a helium atom by adding a proton (and
neutron) to the nucleus and an electron outside, the electron goes into an n = 2, = 0 state
rather than an n = 3, = 0 state. This is an indication that electrons:
A. obey the Pauli exclusion principle
B. obey the minimum energy principle
C. undergo the Zeeman effect
D. are diffracted
E. and protons are interchangeable
ans: B
50. If electrons did not have intrinsic angular momentum (spin) but still obeyed the Pauli exclusion
principle, the states occupied by electrons in the ground state of helium would be:
A. (n = 1, = 0); (n = 1, = 0)
B. (n = 1, = 0); (n = 1, = 1)
C. (n = 1, = 0); (n = 2, = 0)
D. (n = 2, = 0); (n = 2, = 1)
E. (n = 2, = 1); (n = 2, = 1)
ans: C
51. The minimum energy principle tells us that:
A. the energy of an atom with a high atomic number is less than the energy of an atom with
a low atomic number
B. the energy of an atom with a low atomic number is less than the energy of an atom with
a high atomic number
C. when an atom makes an upward transition the energy of the absorbed photon is the least
possible
D. the ground state configuration of any atom is the one with the least energy
E. the ground state configuration of any atom is the one with the least ionization energy
ans: D
52. Which of the following (n, , m , ms ) combinations is impossible for an electron in an atom?
A. 3, 1, 1, −1/2
B. 6, 2, 0, 1/2
C. 3, 2, −2, −1/2
D. 3, 1, −2, 1/2
E. 1, 0, 0, −1/2
ans: D
53. Which of the following subshells cannot exist?
A. 3p
B. 2p
C. 4d
D. 3d
E. 2d
ans: E
606
Chapter 40:
ALL ABOUT ATOMS
54. For
A.
B.
C.
D.
E.
any atom other than hydrogen and helium all electrons in the same shell have:
the same energy
the same magnitude of angular momentum
the same magnetic quantum number
the same spin quantum number
none of the above
ans: E
55. The states being filled from the beginning to end of the lanthanide series of atoms are:
A. n = 3, = 2 states
B. n = 4, = 1 states
C. n = 4, = 2 states
D. n = 4, = 3 states
E. n = 5, =2 states
ans: D
56. The most energetic electron in any atom at the beginning of a period of the periodic table is
in:
A. an = 0 state
B. an = 1 state
C. an = 2 state
D. an n = 0 state with unspecified angular momentum
E. an n = 1 state with unspecified angular momentum
ans: A
57. The most energetic electron in any atom at the end of a period of the periodic table is in:
A. an = 0 state
B. an = 1 state
C. an = 2 state
D. an n = 0 state with unspecified angular momentum
E. an n = 1 state with unspecified angular momentum
ans: B
58. The group of atoms at the ends of periods of the periodic table are called:
A. alkali metals
B. rare earths
C. transition metal atoms
D. alkaline atoms
E. inert gas atoms
ans: E
Chapter 40:
ALL ABOUT ATOMS
607
59. The group of atoms at the beginning of periods of the periodic table are called:
A. alkali metal atoms
B. rare earth atoms
C. transition metal atoms
D. alkaline atoms
E. inert gas atoms
ans: A
60. Suppose the energy required to ionize an argon atom is i, the energy to excite it is e, and its
thermal energy at room temperature is t. In increasing order, these three energies are:
A. i, e, t
B. t, i, e
C. e, t, i
D. i, t, e
E. t, e, i
ans: C
61. The ionization energy of an atom in its ground state is:
A. the energy required to remove the least energetic electron
B. the energy required to remove the most energetic electron
C. the energy difference between the most energetic electron and the least energetic electron
D. the same as the energy of a Kα photon
E. the same as the excitation energy of the most energetic electron
ans: B
62. The effective charge acting on a single valence electron outside a closed shell is about N e, where
N is:
A. the atomic number of the nucleus
B. the atomic mass of the atom
C. usually between 1 and 3
D. half the atomic number
E. less than 1
ans: C
63. In a laser:
A. excited atoms are stimulated to emit photons by radiation external to the laser
B. the transitions for laser emission are directly to the ground state
C. the states which give rise to laser emission are usually very unstable states that decay
rapidly
D. the state in which an atom is initially excited is never between two states that are involved
in the stimulated emission
E. a minimum of two energy levels are required.
ans: D
608
Chapter 40:
ALL ABOUT ATOMS
64. Photons in a laser beam have the same energy, wavelength, polarization direction, and phase
because:
A. each is produced in an emission that is stimulated by another
B. all come from the same atom
C. the lasing material has only two quantum states
D. all photons are alike, no matter what their source
E. none of the above
ans: A
65. A laser must be pumped to achieve:
A. a metastable state
B. fast response
C. stimulated emission
D. population inversion
E. the same wavelength for all photons
ans: D
66. Photons in a laser beam are produced by:
A. transitions from a metastable state
B. transitions to a metastable state
C. transitions from a state that decays rapidly
D. splitting of other photons
E. pumping
ans: A
67. Which of the following is essential for laser action to occur between two energy levels of an
atom?
A. the lower level is metastable
B. the upper level is metastable
C. the lower level is the ground state
D. there are more atoms in the lower level than in the upper level
E. the lasing material is a gas
ans: B
68. Which of the following is essential for laser action to occur between two energy levels of an
atom?
A. the lower level is metastable
B. there are more atoms the upper level than in the lower level
C. there are more atoms in the lower level than in the upper level
D. the lower level is the ground state
E. the lasing material is a gas
ans: B
Chapter 40:
ALL ABOUT ATOMS
609
69. Population inversion is important for the generation of a laser beam because it assures that:
A. spontaneous emission does not occur more often than stimulated emission
B. photons do not split too rapidly
C. more photons are emitted than are absorbed
D. photons do not collide with each other
E. photons do not make upward transitions
ans: C
70. A metastable state is important for the generation of a laser beam because it assures that:
A. spontaneous emission does not occur more often than stimulated emission
B. photons do not split too rapidly
C. more photons are emitted than are absorbed
D. photons do not collide with each other
E. photons do not make upward transitions
ans: A
71. Electrons in a certain laser make transitions from a metastable state to the ground state.
Initially there are 6 × 1020 atoms in the metastable state and 2 × 1020 atoms in the ground
state. The number of photons that can be produced in a single burst is about:
A. 2 × 1020
B. 3 × 1020
C. 4 × 1020
D. 6 × 1020
E. 8 × 1020
ans: C
72. In a helium-neon laser, the laser light arises from a transition from a
state.
A. He, He
B. Ne, Ne
C. He, Ne
D. Ne, He
E. N, He
ans: B
73. The purpose of the mirrors at the ends of a helium-neon laser is:
A. to assure that no laser light leaks out
B. to increase the number of stimulated emissions
C. to absorb some of the photons
D. to keep the light used for pumping inside the laser
E. to double the effective length of the laser
ans: B
610
Chapter 40:
ALL ABOUT ATOMS
state to a
74. A group of electromagnetic waves might
I. be monochromatic
II. be coherent
III. have the same polarization direction
Which of these describe the waves from a laser?
A. I only
B. II only
C. III only
D. I and II only
E. I, II, and III
ans: E
75. A laser beam can be sharply focused because it is:
A. highly coherent
B. plane polarized
C. intense
D. circularly polarized
E. highly directional
ans: E
76. The “e” in laser stands for:
A. electric
B. emf
C. energy
D. emission
E. entropy
ans: D
Chapter 40:
ALL ABOUT ATOMS
611
Chapter 41:
CONDUCTION OF ELECTRICITY IN SOLIDS
1. In a pure metal the collisions that are characterized by the mean free time τ in the expression
for the resistivity are chiefly between:
A. electrons and other electrons
B. electrons with energy about equal to the Fermi energy and atoms
C. all electrons and atoms
D. electrons with energy much less than the Fermi energy and atoms
E. atoms and other atoms
ans: B
2. A certain metal has 5.3 × 1029 conduction electrons/m3 and an electrical resistivity of 1.9 ×
10−9 Ω · m. The average time between collisions of electrons with atoms in the metal is:
A. 5.6 × 10−33 s
B. 1.3 × 10−31 s
C. 9.9 × 10−22 s
D. 4.6 × 10−15 s
E. 3.5 × 10−14 s
ans: C
3. Which one of the following statements concerning electron energy bands in solids is true?
A. The bands occur as a direct consequence of the Fermi-Dirac occupancy probability function
B. Electrical conduction arises from the motion of electrons in completely filled bands
C. Within a given band, all electron energy levels are equal to each other
D. An insulator has a large energy separation between the highest filled band and the lowest
empty band
E. Only insulators have energy bands
ans: D
4. If E0 and ET are the average energies of the “free” electrons in a metal at 0 K and room
temperature, respectively, then the ratio ET /E0 is approximately:
A. 0
B. 1
C. 100
D. 106
E. infinity
ans: B
5. The energy gap (in eV) between the valence and conduction bands of an insulator is of the
order of:
A. 10−19
B. 0.001
C. 0.1
D. 10
E. 1000
ans: D
612
Chapter 41:
CONDUCTION OF ELECTRICITY IN SOLIDS
6. The energy level diagram shown applies to:
.......................................
.......................................
.......................................
.......................................
.......................................
.......................................
.......................................
.......................................
....................
..........................................................
.......................................
.......................................
....................
unfilled:
.......
.......
.......
.......
filled:
A.
B.
C.
D.
E.
a conductor
an insulator
a semiconductor
an isolated molecule
an isolated atom
ans: A
7. The energy level diagram shown applies to:
↑|
10 eV
↓|
.......................................
.......................................
.......................................
.......................................
.......................................
.......................................
.......................................
.......................................
....................
unfilled:
.......
.......
.......
.......
filled:
A.
B.
C.
D.
E.
a conductor
an insulator
a semiconductor
an isolated atom
a free-electron gas
ans: B
Chapter 41:
CONDUCTION OF ELECTRICITY IN SOLIDS
613
8. The energy level diagram shown applies to:
...
...
...
...
.
........
.
1 eV
...
.......
...
..
....
...
.......................................
.......................................
.......................................
.......................................
.......................................
.......................................
.......................................
.......................................
unfilled:
.......
.......
.......
.......
filled:
A.
B.
C.
D.
E.
a conductor
an insulator
a semiconductor
an isolated molecule
an isolated atom
ans: C
9. Possible units for the density of states function N (E) are:
A. J/m3
B. 1/J
C. m−3
D. J−1 ·m−3
E. kg/m3
ans: D
10. The density of states for a metal depends primarily on:
A. the temperature
B. the energy
C. the density of the metal
D. the volume of the sample
E. none of these
ans: B
11. The Fermi-Dirac occupancy probability P (E) varies between:
A. 0 and 1
B. 0 and infinity
C. 1 and infinity
D. −1 and 1
E. 0 and EF
ans: A
614
Chapter 41:
CONDUCTION OF ELECTRICITY IN SOLIDS
12. For a metal at absolute temperature T , with Fermi energy EF , the occupancy probability is
given by:
A. e(E−EF )/kT
B. e−(E−EF )/kT
1
C. (E−E )/kT
F
e
+1
1
D. −(E−E )/kT
F
e
+1
1
E. (E−E )/kT
F
e
−1
ans: C
13. In a metal at 0 K, the Fermi energy is:
A. the highest energy of any electron
B. the lowest energy of any electron
C. the mean thermal energy of the electrons
D. the energy of the top of the valence band
E. the energy at the bottom of the conduction band
ans: A
14. The occupancy probability for a state with energy equal to the Fermi energy is:
A. 0
B. 0.5
C. 1
D. 1.5
E. 2
ans: B
15. The Fermi energy of a metal depends primarily on:
A. the temperature
B. the volume of the sample
C. the mass density of the metal
D. the size of the sample
E. the number density of conduction electrons
ans: E
16. The speed of an electron with energy equal to the Fermi energy for copper is on the order of:
A. 106 m/s
B. 10−6 m/s
C. 10 m/s
D. 10−1 m/s
E. 109 m/s
ans: A
Chapter 41:
CONDUCTION OF ELECTRICITY IN SOLIDS
615
17. At
A.
B.
C.
D.
E.
T = 0 K the probability that a state 0.50 eV below the Fermi level is occupied is about:
0
5.0 × 10−9
5.0 × 10−6
5.0 × 10−3
1
ans: E
18. At
A.
B.
C.
D.
E.
T = 0 K the probability that a state 0.50 eV above the Fermi level is occupied is about:
0
5.0 × 10−9
5.0 × 10−6
5.0 × 10−3
1
ans: A
19. At room temperature kT is about 0.0259 eV. The probability that a state 0.50 eV above the
Fermi level is occupied at room temperature is:
A. 1
B. 0.05
C. 0.025
D. 5.0 × 10−6
E. 4.1 × 10−9
ans: E
20. At room temperature kT is about 0.0259 eV. The probability that a state 0.50 eV below the
Fermi level is unoccupied at room temperature is:
A. 1
B. 0.05
C. 0.025
D. 5.0 × 10−6
E. 4.1 × 10−9
ans: E
21. If the density of states is N (E) and the occupancy probability is P (E), then the density of
occupied states is:
A. N (E) + P (E)
B. N (E)/P (E)
C. N (E) − P (E)
D. N (E)P (E)
E. P (E)/N (E)
ans: D
616
Chapter 41:
CONDUCTION OF ELECTRICITY IN SOLIDS
22. A hole refers to:
A. a proton
B. a positively charged electron
C. an electron that has somehow lost its charge
D. a microscopic defect in a solid
E. the absence of an electron in an otherwise filled band
ans: E
23. Electrons in a full band do not contribute to the current when an electric field exists in a solid
because:
A. the field cannot exert a force on them
B. the individual contributions cancel each other
C. they are not moving
D. they make transitions to other bands
E. they leave the solid
ans: B
24. For
A.
B.
C.
D.
E.
a pure semiconductor the Fermi level is:
in the conduction band
well above the conduction band
in the valence band
well below the valence band
near the center of the gap between the valence and conduction bands
ans: E
25. The number density n of conduction electrons, the resistivity ρ, and the temperature coefficient
of resistivity α are given below for five materials. Which is a semiconductor?
A. n = 1029 m−3 , ρ = 10−8 Ω · m, α = +10−3 K−1
B. n = 1028 m−3 , ρ = 10−9 Ω · m, α = −10−3 K−1
C. n = 1028 m−3 , ρ = 10−9 Ω · m, α = +10−3 K−1
D. n = 1015 m−3 , ρ = 103 Ω · m, α = −10−2 K−1
E. n = 1015 m−3 , ρ = 10−7 Ω · m, α = +10−3 K−1
ans: D
26. A pure semiconductor at room temperature has:
A. more electrons/m3 in its conduction band than holes/m3 in its valence band
B. more electrons/m3 in its conduction band than a typical metal
C. more electrons/m3 in its valence band than at T = 0 K
D. more holes/m3 in its valence band than electrons/m3 in its valence band
E. none of the above
ans: E
Chapter 41:
CONDUCTION OF ELECTRICITY IN SOLIDS
617
27. For a metal at room temperature the temperature coefficient of resistivity is determined primarily by:
A. the number of electrons in the conduction band
B. the number of impurity atoms
C. the binding energy of outer shell electrons
D. collisions between conduction electrons and atoms
E. none of the above
ans: D
28. For a pure semiconductor at room temperature the temperature coefficient of resistivity is
determined primarily by:
A. the number of electrons in the conduction band
B. the number of replacement atoms
C. the binding energy of outer shell electrons
D. collisions between conduction electrons and atoms
E. none of the above
ans: A
29. A certain material has a resistivity of 7.8 × 103 Ω · m at room temperature and it increases as
the temperature is raised by 100◦ C. The material is most likely:
A. a metal
B. a pure semiconductor
C. a heavily doped semiconductor
D. an insulator
E. none of the above
ans: C
30. A certain material has a resistivity of 7.8 × 103 Ω · m at room temperature and it decreases as
the temperature is raised by 100◦ C. The material is most likely:
A. a metal
B. a pure semiconductor
C. a heavily doped semiconductor
D. an insulator
E. none of the above
ans: B
31. A certain material has a resistivity of 7.8 × 10−8 Ω · m at room temperature and it increases as
the temperature is raised by 100◦ C. The material is most likely:
A. a metal
B. a pure semiconductor
C. a heavily doped semiconductor
D. an insulator
E. none of the above
ans: A
618
Chapter 41:
CONDUCTION OF ELECTRICITY IN SOLIDS
32. Donor atoms introduced into a pure semiconductor at room temperature:
A. increase the number of electrons in the conduction band
B. increase the number of holes in the valence band
C. lower the Fermi level
D. increase the electrical resistivity
E. none of the above
ans: A
33. Acceptor atoms introduced into a pure semiconductor at room temperature:
A. increase the number of electrons in the conduction band
B. increase the number of holes in the valence band
C. raise the Fermi level
D. increase the electrical resistivity
E. none of the above
ans: B
34. An
A.
B.
C.
D.
E.
acceptor replacement atom in silicon might have
3
4
5
6
7
ans: A
35. A donor replacement atom in silicon might have
A. 1
B. 2
C. 3
D. 4
E. 5
ans: E
electrons in its outer shell.
electrons in its outer shell.
36. A given doped semiconductor can be identified as p or n type by:
A. measuring its electrical conductivity
B. measuring its magnetic susceptibility
C. measuring its coefficient of resistivity
D. measuring its heat capacity
E. performing a Hall effect experiment
ans: E
37. The contact electric field in the depletion region of a p-n junction is produced by:
A. electrons in the conduction band alone
B. holes in the valence band alone
C. electrons and holes together
D. charged replacement atoms
E. an applied bias potential difference
ans: D
Chapter 41:
CONDUCTION OF ELECTRICITY IN SOLIDS
619
38. For
is:
A.
B.
C.
D.
E.
an unbiased p-n junction, the energy at the bottom of the conduction band on the n side
higher than the energy at the bottom of the conduction band on the p side
lower than the energy at the bottom of the conduction band on the p side
lower than the energy at the top of the valence band on the n side
lower than the energy at the top of the valence band on the p side
the same as the energy at the bottom of the conduction band on the p side
ans: B
39. In an unbiased p-n junction:
A. the electric potential vanishes everywhere
B. the electric field vanishes everywhere
C. the drift current vanishes everywhere
D. the diffusion current vanishes everywhere
E. the diffusion and drift currents cancel each other
ans: E
40. Application of a forward bias to a p-n junction:
A. narrows the depletion zone
B. increases the electric field in the depletion zone
C. increases the potential difference across the depletion zone
D. increases the number of donors on the n side
E. decreases the number of donors on the n side
ans: A
41. Application of a forward bias to a p-n junction:
A. increases the drift current in the depletion zone
B. increases the diffusion current in the depletion zone
C. decreases the drift current on the p side outside the depletion zone
D. decreases the drift current on the n side outside the depletion zone
E. does not change the current anywhere
ans: B
42. When a forward bias is applied to a p-n junction the concentration of electrons on the p side:
A. increases slightly
B. increases dramatically
C. decreases slightly
D. decreases dramatically
E. does not change
ans: B
620
Chapter 41:
CONDUCTION OF ELECTRICITY IN SOLIDS
43. Which of the following is NOT true when a back bias is applied to a p-n junction?
A. Electrons flow from the p to the n side
B. Holes flow from the p to the n side
C. The electric field in the depletion zone increases
D. The potential difference across the depletion zone increases
E. The depletion zone narrows
ans: B
44. Switch S is closed to apply a potential difference V across a p-n junction as shown. Relative to
the energy levels of the n-type material, with the switch open, the electron levels of the p-type
material are:
....
....
....
....
.................................................... ..
...
...
...
...
+ ......
.
S
..........................................................................
....
...
...
..
p
n..
V
...
...
...
...
....
...
...
...
..
.
.
.
...........................................................................................................................................................................................
A.
B.
C.
D.
E.
unchanged
lowered by the amount e−V e/kT
lowered by the amount V e
raised by the amount e−V e/kT
raised by the amount V e
ans: C
45. A sinusoidal potential difference Vin = Vm sin(ωt) is applied to the p-n junction as shown.
Which graph correctly shows Vout as a function of time?
......
...... ........
.
...
....................................................................................................................................................................................
.
...
....
....................
...
............
.....
............
......
in
............
..........
...
...
.
...............................................................................................................................................................................
....
V
Vout
..........
...........
.... ...... ... .......
.
.
......
..
..
R
Vout
t
..........
...... .......... .......
.
.
.
............
....
Vout
Vout
t
.....
.....
...... .... ........... .... ...
.
.
.
.
.
.
........
.........
......
B
A
Vout
........
........
... ....
... ....
.
.
.. .... ... ....
... .
...
...
....
.......
...
D
C
Vout
t
t
..........
... ....
.
.
..........
... ....
.
.
t
E
ans: E
Chapter 41:
CONDUCTION OF ELECTRICITY IN SOLIDS
621
46. In normal operation the current in a MOSFIT device is controlled by changing:
A. the number of donors and acceptors
B. the width of the depletion zone
C. the size of the sample
D. the density of electron states
E. the temperature
ans: B
47. “LED” stands for:
A. Less Energy Donated
B. Light Energy Degrader
C. Luminescent Energy Developer
D. Laser Energy Detonator
E. none of the above
ans: E
48. A light emitting diode emits light when:
A. electrons are excited from the valence to the conduction band
B. electrons from the conduction band recombine with holes from the valence band
C. electrons collide with atoms
D. electrons are accelerated by the electric field in the depletion region
E. the junction gets hot
ans: B
49. The gap between the valence and conduction bands of a certain semiconductor is 0.85 eV.
When this semiconductor is used to form a light emitting diode, the wavelength of the light
emitted:
A. is in a range above 1.5 × 10−6 m
B. is in a range below 1.5 × 10−6 m
C. is always 1.5 × 10−6 m
D. is in a range centered on 1.5 × 10−6 m
E. has nothing to do with the gap
ans: B
622
Chapter 41:
CONDUCTION OF ELECTRICITY IN SOLIDS
Chapter 42:
NUCLEAR PHYSICS
1. The smallest particle of any chemical element that can exist by itself and yet retain the qualities
that distinguish it as that element is:
A. an electron
B. a proton
C. a neutron
D. an atom
E. a molecule
ans: D
2. Of
A.
B.
C.
D.
E.
the following, which has the smallest rest energy?
A neutron
An electron
An ion
A proton
An atom
ans: B
3. The mass of an electron:
A. is almost the same as that of a neutron
B. is negative
C. equals that of a proton
D. is zero if the electron is at rest
E. is much less than that of a proton
ans: E
4. The mass of a neutron:
A. equals that of an electron
B. equals that of a proton
C. is a little more than that of a proton
D. is exactly that of a proton plus an electron
E. is as yet unmeasured
ans: C
5. The mass of a hydrogen atom, in kilograms, is approximately:
A. 10−27
B. 10−31
C. 10−24
D. 10−13
E. 10−8
ans: A
Chapter 42:
NUCLEAR PHYSICS
623
6. 1 atomic mass unit is about:
A. 1.66 × 10−31 kg
B. 9.11 × 10−31 kg
C. 1.66 × 10−27 kg
D. 9.11 × 10−27 kg
E. 1.66 × 10−25 kg
ans: C
7. The atomic number of an element is:
A. the whole number nearest to its mass
B. the number of protons in its nucleus
C. the nearest whole number of hydrogen atoms having the same mass as a single atom of the
given element
D. the number of neutrons in its nucleus
E. its order of discovery
ans: B
8. Iron has atomic number 26. Naturally mined iron contains isotopes of mass numbers 54, 56,
57, and 58. Which of the following statements is FALSE?
A. Every atom of iron has 26 protons
B. Some iron atoms have 30 neutrons
C. Some iron atoms have 54 neutrons
D. The isotopes may be separated in a mass spectrometer
E. There are four kinds of naturally occurring iron atoms with the same chemical properties
ans: C
9. Let Z denote the atomic number and A denote the mass number of a nucleus. The number of
neutrons in this nucleus is:
A. Z
B. A − Z
C. A − 2Z
D. A
E. 2A − Z
ans: B
10. The isotopes of an element:
A. cannot be separated at all
B. occur well separated in nature
C. have similar chemical behavior
D. cannot be separated by physical methods
E. have equal masses
ans: C
624
Chapter 42:
NUCLEAR PHYSICS
11. Bromine, with atomic mass 79.942 u, is composed of nearly equal amounts of two isotopes, one
of which contains 79 nucleons per atom. The mass number of the other isotope is:
A. 78
B. 79
C. 80
D. 81
E. 82
ans: D
12. The mass density of an atomic nucleus is:
3
A. about 1015 kg/m
B. about 1012 kg/m3
C. increases with increasing nuclear mass
D. increases with decreasing nuclear radius
E. about the same as that of all other nuclei
ans: E
13. Volumes of atomic nuclei are proportional to:
A. the mass number
B. the atomic number
C. the total nuclear spin
D. the number of neutrons
E. none of these
ans: A
14. A femtometer is:
A. larger than 10−9 m
B. 10−9 m
C. 10−12 m
D. 10−15 m
E. 10−18 m
ans: D
15. A nucleus with a mass number of 64 has a mean radius of about:
A. 4.8 fm
B. 19 fm
C. 77 fm
D. 260 fm
E. 2.6 × 105 fm
ans: A
Chapter 42:
NUCLEAR PHYSICS
625
16. A proton in a large nucleus:
A. attracts all other protons
B. repels all other protons
C. repels all neutrons
D. attracts some protons and repels others
E. attracts some neutrons and repels others
ans: D
17. Two protons are separated by 10−16 m. The nuclear (N), electrostatic (E), and gravitational
(G) forces between these protons, in order of increasing strength, are:
A. E, N, G
B. N, G, E
C. G, E, N
D. G, N, E
E. E, G, N
ans: C
18. Two protons are about 10−10 m apart. Their relative motion is chiefly determined by:
A. gravitational forces
B. electrical forces
C. nuclear forces
D. magnetic forces
E. torque due to electric dipole moments
ans: B
19. The binding energy of a nucleus is the energy that must be supplied to:
A. remove a nucleon
B. remove an alpha particle
C. remove a beta particle
D. separate the nucleus into its constituent nucleons
E. separate the nucleus into a collection of alpha particles
ans: D
20. If a nucleus has mass M , Z protons (mass mp ), and N neutrons (mass mn ), its binding energy
is equal to:
A. M c2
B. (M − Zmp − N mn )c2
C. (Zmp + N mn − M )c2
D. (Zmp + N mn )c2
E. (Zmp − M )c2
ans: C
626
Chapter 42:
NUCLEAR PHYSICS
21. Stable nuclei generally:
A. have a greater number of protons than neutrons
B. have low mass numbers
C. have high mass numbers
D. are beta emitters
E. none of the above
ans: E
22. Let A be the mass number and Z be the atomic number of a nucleus. Which of the following
is approximately correct for light nuclei?
A. Z = 2A
B. Z = A
C. Z = A/2
√
D. Z = A
E. Z = A2
ans: C
23. The greatest binding energy per nucleon occurs for nuclides with masses near that of:
A. helium
B. sodium
C. iron
D. mercury
E. uranium
ans: C
24. Which of the following nuclides is least likely to be detected?
A. 52 Fe (Z = 26)
B. 115 Nd (Z = 60)
C. 175 Lu (Z = 71)
D. 208 Pb (Z = 82)
E. 238 U (Z = 92)
ans: B
25. The half-life of a radioactive substance is:
A. half the time it takes for the entire substance to decay
B. usually about 50 years
C. the time for radium to change into lead
D. calculated from E = mc2
E. the time for half the substance to decay
ans: E
Chapter 42:
NUCLEAR PHYSICS
627
26. Which expression correctly describes the radioactive decay of a substance whose half-life is T ?
A. N (t) = N0 e−(t ln 2)/T
B. N (t) = N0 e−t/T
C. N (t) = N0 e−tT
D. N (t) = N0 e−tT ln 2
E. N (t) = N0 e−t/T ln 2
ans: A
27. Radioactive element A decays to the stable element B with a half-life T . Starting with a
sample of pure A and no B, which graph below correctly shows the number of A atoms, NA ,
as a function of time t?
NA .
....
....
....
....
....
....
....
....
....
.
T
A
NA .......................................
...
...
...
............
t
NA ................................
....
...
...
...
...
...
...
.......
T
C
t
T
B
NA .
......
......
.......
........
.........
......
NA
t
..........
........
.
.
.
.
....
....
.
.
..
...
.. .
T
D
t
t
T
E
ans: D
28. A large collection of nuclei are undergoing alpha decay. The rate of decay at any instant is
proportional to:
A. the number of undecayed nuclei present at that instant
B. the time since the decays started
C. the time remaining before all have decayed
D. the half-life of the decay
E. the average time between decays
ans: A
29. The relation between the disintegration constant λ and the half-life T of a radioactive substance
is:
A. λ = 2T
B. λ = 1/T
C. λ = 2/T
D. λT = ln 2
E. λT = ln(1/2)
ans: D
628
Chapter 42:
NUCLEAR PHYSICS
30. Possible units for the disintegration constant λ are:
A. kg/s
B. s/kg
C. hour
D. day−1
E. cm−1
ans: D
31. The half-life of a given nuclear disintegration A → B:
A. depends on the initial number of A atoms
B. depends on the initial number of B atoms
C. is an exponentially increasing function of time
D. is an exponentially decreasing function of time
E. none of the above
ans: E
32. The graph shows the activity R as a function of time t for three radioactive samples. Rank the
samples according to their half-lives, shortest to longest.
R
........
...........
.... .........
..... ........
...... ...........1
..
......
....... ........................
.................
........2
........
................................................................
.......... .......................................................................
...............................
3
...
t
A.
B.
C.
D.
E.
1, 2, 3
1, 3, 2
2, 1, 3
2, 3, 1
3, 1, 2
ans: C
33. The half-life of radium is about 1600 years. If a rock initially contains 1 g of radium, the
amount left after 6400 years will be about:
A. 938 mg
B. 62 mg
C. 31 mg
D. 16 mg
E. less than 16 mg
ans: C
Chapter 42:
NUCLEAR PHYSICS
629
34. Starting with a sample of pure 66 Cu, 7/8 of it decays into Zn in 15 minutes. The corresponding
half-life is:
A. 15 minutes
B. 5 minutes
C. 7 minutes
D. 3.75 minutes
E. 10 minutes
ans: B
35.
210
Bi (an isotope of bismuth) has a half-life of 5.0 days. The time for three-quarters of a sample
Bi to decay is:
of
A. 2.5 days
B. 10 days
C. 15 days
D. 20 days
E. 3.75 days
ans: B
210
36. Radioactive
60 years?
A. 0%
B. 25%
C. 50%
D. 75%
E. 14%
ans: B
90
Sr has a half-life of 30 years. What percent of a sample of 90 Sr will remain after
37. The half-life of a radioactive isotope is 6.5 h. If there are initially 48 × 1032 atoms of this
isotope, the number of atoms of this isotope remaining after 26 h is:
A. 12 × 1032
B. 6 × 1032
C. 3 × 1032
D. 6 × 104
E. 3 × 102
ans: C
38. At the end of 14 min, 1/16 of a sample of radioactive polonium remains. The corresponding
half-life is:
A. (7/8) min
B. (8/7) min
C. (7/4) min
D. (7/2) min
E. (14/3) min
ans: D
630
Chapter 42:
NUCLEAR PHYSICS
39. The half-life of a radioactive isotope is 140 days. In how many days does the decay rate of a
sample of this isotope decrease to one-fourth of its initial decay rate?
A. 35
B. 105
C. 187
D. 210
E. 280
ans: E
40. Of the three common types of radiation (alpha, beta, gamma) from radioactive sources, electric
charge is carried by:
A. only beta and gamma
B. only beta
C. only alpha and gamma
D. only alpha
E. only alpha and beta
ans: E
41. An
A.
B.
C.
D.
E.
alpha particle is:
a helium atom with two electrons removed
an aggregate of two or more electrons
a hydrogen atom
the ultimate unit of positive charge
sometimes negatively charged
ans: A
42. A nucleus with mass number A and atomic number Z emits an alpha particle. The mass
number and atomic number, respectively, of the daughter nucleus are:
A. A, Z − 2
B. A − 2, Z − 2
C. A − 2, Z
D. A − 4, Z
E. A − 4, Z − 2
ans: E
43. Radioactive polonium,
A. 214 Po (Z = 84)
B. 210 Pb (Z = 82)
C. 214 At (Z = 85)
D. 218 Po (Z = 84)
E. 210 Bi (Z = 83)
ans: B
214
Po (Z = 84), decays by alpha emission to:
Chapter 42:
NUCLEAR PHYSICS
631
44. A radium atom, 226 Ra (Z = 86) emits an alpha particle. The number of protons in the resulting
atom is:
A. 84
B. 85
C. 86
D. 88
E. some other number
ans: A
45. Some alpha emitters have longer half-lives than others because:
A. their alpha particles have greater mass
B. their alpha particles have less mass
C. their barriers to decay are higher and wider
D. their barriers to decay are lower and narrower
E. their decays include the emission of a photon
ans: C
46. In an alpha decay the disintegration energy appears chiefly as:
A. photon energies
B. the kinetic energies of the alpha and the daughter nucleus
C. the excitation energy of the daughter nucleus
D. the excitation energy of the alpha particle
E. heat
ans: B
47. Rank the following collections of particles according to the total binding energy of all the
particles in each collection, least to greatest.
collection 1: 244 Pu (Z = 94) nucleus alone
collection 2: 240 U (Z = 92) nucleus, α particle
collection 3: 240 U (Z = 92) nucleus, two separated protons, two separated neutrons
A. 1, 2, 3
B. 3, 2, 1
C. 2, 1, 3
D. 1, 3, 2
E. 2, 3, 1
ans: D
48. A beta particle is:
A. a helium nucleus
B. an electron or a positron
C. a radioactive element
D. any negative particle
E. a hydrogen atom
ans: B
632
Chapter 42:
NUCLEAR PHYSICS
49. Beta particles from various radioactive sources all have:
A. the same mass
D. the same speed
B. the same charge
E. the same deflection
C. the same energy in a magnetic field
ans: A
50. A radioactive atom X emits a β− particle. The resulting atom:
A. must be very reactive chemically
B. has an atomic number that is one more than that of X
C. has a mass number that is one less than that of X
D. must be radioactive
E. is the same chemical element as X
ans: B
51. A nucleus with mass number A and atomic number Z undergoes β − decay. The mass number
and atomic number, respectively, of the daughter nucleus are:
A. A, Z − 1
B. A − 1, Z
C. A + 1, Z − 1
D. A, Z + 1
E. A, Z − 1
ans: D
52. A nucleus with mass number A and atomic number Z undergoes β + decay. The mass number
and atomic number, respectively, of the daughter nucleus are:
A. A − 1, Z − 1
B. A − 1, Z + 1
C. A + 1, Z − 1
D. A, Z + 1
E. A, Z − 1
ans: E
53. In addition to the daughter nucleus and an electron or positron, the products of a beta decay
include:
A. a neutron
B. a neutrino
C. a proton
D. an alpha particle
E. no other particle
ans: B
Chapter 42:
NUCLEAR PHYSICS
633
54. The energies of electrons emitted in β− decays have a continuous spectrum because:
A. the original neutron has a continuous spectrum
B. a neutrino can carry off energy
C. the emitted electron is free
D. energy is not conserved
E. the daughter nucleus may have any energy
ans: B
55. If 204 Tl (Z = 81) emits a β − particle from its nucleus:
A. stable Tl is formed
B. 202 Hg (Z = 80) is formed
C. 204 Pb (Z = 82) is formed
D. radioactive Tl is formed
E. 197 Au (Z = 79) is formed
ans: C
56. An atom of 235 U (Z = 92) disintegrates to
years by emitting seven alpha particles and
A. 3
B. 4
C. 5
D. 6
E. 7
ans: B
207
Pb (Z = 82) with a half-life of about a billion
β − particles:
57. When ordinary sodium (23 Na, Z = 11) is bombarded with deuterons, the products are a
neutron and:
A. 27 Al, Z = 13
B. 24 Na, Z = 11
C. 24 Mg, Z = 12
D. 25 Mg, Z = 12
E. 20 Ne, Z = 10
ans: D
58.
634
65
Cu can be turned into
with:
A. protons
B. neutrons
C. deuterons
D. electrons
E. alpha particles
ans: B
Chapter 42:
66
Cu, with no accompanying product except a gamma, if bombarded
NUCLEAR PHYSICS
59. Magnesium has atomic number 12, hydrogen has atomic number 1, and helium has atomic
number 2. In the nuclear reaction 24 Mg + 2 H → ( ) + 4 He the missing quantity is:
A. 23 Na (Z = 11)
B. 22 Ne (Z = 10)
C. 21 Na (Z = 11)
D. 21 Ne (Z = 10)
E. 22 Na (Z = 11)
ans: E
60. Aluminum has atomic number 13, helium has atomic number 2, and silicon has atomic number
14. In the nuclear reaction 27 Al + 4 He → 30 Si + ( ) the missing particle is:
A. an α particle
B. a positron
C. an electron
D. a proton
E. a neutron
ans: D
61. The 66 Cu (Z = 29) produced in a nuclear bombardment is unstable, changing to
by the emission of:
A. a proton
B. a gamma ray photon
C. a positron
D. an electron
E. an alpha particle
ans: D
66
Zn (Z = 30)
62. When ordinary sulfur, 32 S (Z = 16), is bombarded with neutrons, the products are 32 P (Z = 15)
and:
A. alpha particles
B. protons
C. deuterons
D. gamma ray particles
E. electrons
ans: B
63. A certain nucleus, after absorbing a neutron, emits a β − and then splits into two alpha particles.
The (A, Z) of the original nucleus must have been:
A. 6, 2
B. 6, 3
C. 7, 2
D. 7, 3
E. 8, 4
ans: D
Chapter 42:
NUCLEAR PHYSICS
635
64. When 23 Na (Z = 11) is bombarded with protons, the products are
A. a neutron
B. an alpha particle
C. a deuteron
D. a gamma ray particle
E. two beta particles
ans: B
20
Ne (Z = 10) and:
65. Bombardment of 28 Si (Z = 14) with alpha particles may produce:
A. a proton and 31 P (Z = 15)
B. hydrogen and 32 S (Z = 16)
C. a deuteron and 27 Al (Z = 13)
D. helium and 31 P (Z = 15)
E. 35 Cl (Z = 17)
ans: A
66. The becquerel is the correct unit to use in reporting the measurement of:
A. the rate of decay of a radioactive source
B. the ability of a beam of gamma ray photons to produce ions in a target
C. the energy delivered by radiation to a target
D. the biological effect of radiation
E. none of the above
ans: A
67. The gray is the correct unit to use in reporting the measurement of:
A. the rate of decay of a radioactive source
B. the ability of a beam of gamma ray photons to produce ions in a target
C. the energy per unit mass of target delivered by radiation to a target
D. the biological effect of radiation
E. none of the above
ans: C
68. The sievert is the correct unit to use in reporting the measurement of:
A. the rate of decay of a radioactive source
B. the ability of a beam of gamma ray photons to produce ions in a target
C. the energy delivered by radiation to a target
D. the biological effect of radiation
E. none of the above
ans: D
636
Chapter 42:
NUCLEAR PHYSICS
Chapter 43:
ENERGY FROM THE NUCLEUS
1. If the nucleus of a lead atom were broken into two identical nuclei, the total mass of the
resultant nuclei would be:
A. the same as before
B. greater than before
C. less than before
D. converted into radiation
E. converted into kinetic energy
ans: C
2. Consider the following energies:
1. minimum energy needed to excite a hydrogen atom
2. energy needed to ionize a hydrogen atom
3. energy released in 235 U fission
4. energy needed to remove a neutron from a 12 C nucleus
Rank them in order of increasing value.
A. 1, 2, 3, 4
B. 1, 3, 2, 4
C. 1, 2, 4, 3
D. 2, 1, 4, 3
E. 2, 4, 1, 3
ans: C
3. The binding energy per nucleon:
A. increases for all fission events
B. increases for some, but not all, fission events
C. decreases for all fission events
D. decreases for some, but not all, fission events
E. remains the same for all fission events
ans: A
4. When uranium undergoes fission as a result of neutron bombardment, the energy released is
due to:
A. oxidation of the uranium
B. kinetic energy of the bombarding neutrons
C. radioactivity of the uranium nucleus
D. radioactivity of the fission products
E. a reduction in binding energy
ans: E
Chapter 43:
ENERGY FROM THE NUCLEUS
637
5. The energy supplied by a thermal neutron in a fission event is essentially its:
A. excitation energy
B. binding energy
C. kinetic energy
D. rest energy
E. electric potential energy
ans: B
6. The barrier to fission comes about because the fragments:
A. attract each other via the strong nuclear force
B. repel each other electrically
C. produce magnetic fields
D. have large masses
E. attract electrons electrically
ans: A
7.
235
U is readily made fissionable by a thermal neutron but 238 U is not because:
A. the neutron has a smaller binding energy in 236 U
B. the neutron has a smaller excitation energy in 236 U
C. the potential barrier for the fragments is less in 239 U
D. the neutron binding energy is greater than the barrier height for 236 U and less than the
barrier height for 239 U
E. the neutron binding energy is less than the barrier height for 236 U and greater than the
barrier height for 239 U
ans: D
8. An
A.
B.
C.
D.
E.
explosion does not result from a small piece of 235 U because:
it does not fission
the neutrons released move too fast
238
U is required
too many neutrons escape, preventing a chain reaction from starting
a few neutrons must be injected to start the chain reaction
ans: D
9. When 236 U fissions the fragments are:
A. always 140 Xe and 94 Sr
B. always identical
C. never 140 Xe and 94 Sr
D. never identical
E. none of the above
ans: E
638
Chapter 43:
ENERGY FROM THE NUCLEUS
10. Fission fragments usually decay by emitting:
A. alpha particles
B. electrons and neutrinos
C. positrons and neutrinos
D. only neutrons
E. only electrons
ans: B
11. When 236 U fissions, the products might be:
A. 146 Ba, 89 Kr, and a proton
B. 146 Ba, 89 Kr, and a neutron
C. 148 Cs and 85 Br
D. 133 I, 92 Sr, and an alpha particle
E. two uranium nuclei
ans: B
12. Consider all possible fission events. Which of the following statements is true?
A. Light initial fragments have more protons than neutrons and heavy initial fragments have
fewer protons than neutrons
B. Heavy initial fragments have more protons than neutrons and light initial fragments have
fewer protons than neutrons
C. All initial fragments have more protons than neutrons
D. All initial fragments have about the same number of protons and neutrons
E. All initial fragments have more neutrons than protons
ans: E
13. Which one of the following represents a fission reaction that can be activated by slow neutrons?
A. 238 U92 + 1 n0 → 90 Kr36 + 146 Cs55 + 2 H1 + 1 n0
B. 239 Pu94 + 1 n0 → 96 Sr38 + 141 Ba56 + 3 1 n0
C. 238 U92 → 234 Th90 + 4 He2
D. 3 H1 + 2 H1 → 4 He2 + 1 n0
E. 107 Ag47 + 1 n0 → 108 Ag47 → 108 Cd48 + 0 e−1
ans: B
14. In the uranium disintegration series:
A. the emission of a β − particle increases the mass number A by one and decreases the atomic
number Z by one
B. the disintegrating element merely ejects atomic electrons
C. the emission of an α particle decreases the mass number A by four and decreases the atomic
number Z by two
D. the nucleus always remains unaffected
E. the series of disintegrations continues until an element having eight outermost orbital electrons is obtained
ans: C
Chapter 43:
ENERGY FROM THE NUCLEUS
639
15. Separation of the isotopes of uranium requires a physical, rather than chemical, method because:
A. mixing other chemicals with uranium is too dangerous
B. the isotopes are chemically the same
C. the isotopes have exactly the same number of neutrons per nucleus
D. natural uranium contains only 0.7% 235 U
E. uranium is the heaviest element in nature
ans: B
16. Which one of the following is NOT needed in a nuclear fission reactor?
A. Moderator
B. Fuel
C. Coolant
D. Control device
E. Accelerator
ans: E
17. The function of the control rods in a nuclear reactor is to:
A. increase fission by slowing down the neutrons
B. decrease the energy of the neutrons without absorbing them
C. increase the ability of the neutrons to cause fission
D. decrease fission by absorbing neutrons
E. provide the critical mass for the fission reaction
ans: D
18. A nuclear reactor is operating at a certain power level, with its multiplication factor adjusted
to unity. The control rods are now used to reduce the power output to one-half its former
value. After the reduction in power the multiplication factor is maintained at:
A. 1/2
B. 1/4
C. 2
D. 4
E. 1
ans: E
19. The purpose of a moderator in a nuclear reactor is to:
A. provide neutrons for the fission process
B. slow down fast neutrons to increase the probability of capture by uranium
C. absorb dangerous gamma radiation
D. shield the reactor operator from dangerous radiation
E. none of the above
ans: B
640
Chapter 43:
ENERGY FROM THE NUCLEUS
20. In a neutron-induced fission process, delayed neutrons come from:
A. the fission products
B. the original nucleus just before it absorbs the neutron
C. the original nucleus just after it absorbs the neutron
D. the moderator material
E. the control rods
ans: A
21. In a nuclear reactor the fissionable fuel is formed into pellets rather than finely ground and the
pellets are mixed with the moderator. This reduces the probability of:
A. non-fissioning absorption of neutrons
B. loss of neutrons through the reactor container
C. absorption of two neutrons by single fissionable nucleus
D. loss of neutrons in the control rods
E. none of the above
ans: A
22. In a subcritical nuclear reactor:
A. the number of fission events per unit time decreases with time
B. the number of fission events per unit time increases with time
C. each fission event produces fewer neutrons than when the reactor is critical
D. each fission event produces more neutrons than when the reactor is critical
E. none of the above
ans: A
23. In the normal operation of a nuclear reactor:
A. control rods are adjusted so the reactor is subcritical
B. control rods are adjusted so the reactor is critical
C. the moderating fluid is drained
D. the moderating fluid is continually recycled
E. none of the above
ans: B
24. In a nuclear power plant, the power discharged to the environment:
A. can be made zero by proper design
B. must be less than the electrical power generated
C. must be greater than the electrical power generated
D. can be entirely recycled to produce an equal amount of electrical power
E. is not any of the above
ans: E
Chapter 43:
ENERGY FROM THE NUCLEUS
641
25. The binding energy per nucleon:
A. increases for all fusion events
B. increases for some, but not all, fusion events
C. remains the same for some fusion events
D. decreases for all fusion events
E. decreases for some, but not all, fusion events
ans: A
26. To
A.
B.
C.
D.
E.
produce energy by fusion of two nuclei, the nuclei must:
have at least several thousand electron volts of kinetic energy
both be above iron in mass number
have more neutrons than protons
be unstable
be magic number nuclei
ans: A
27. Which one of the following represents a fusion reaction that yields large amounts of energy?
A. 238 U92 + 1 n0 → 90 Kr36 + 146 Cs55 + 2 H1 + 1 n0
B. 239 Pu92 + 1 n0 → 96 Sr38 + 141 Ba56 + 31 n0
C. 238 U92 → 234 Th90 + 4 He2
D. 3 H1 + 2 H1 → 4 He2 + 1 n0
E. 107 Ag47 + 1 n0 → 108 Ag47 → 108 Cd48 + 0 e−1
ans: D
28. The barrier to fusion comes about because protons:
A. attract each other via the strong nuclear force
B. repel each other electrically
C. produce magnetic fields
D. attract neutrons via the strong nuclear force
E. attract electrons electrically
ans: B
29. High temperatures are required in thermonuclear fusion so that:
A. some nuclei are moving fast enough to overcome the barrier to fusion
B. there is a high probability some nuclei will strike each other head on
C. the atoms are ionized
D. thermal expansion gives the nuclei more room
E. the uncertainty principle can be circumvented
ans: A
30. For
A.
B.
C.
D.
E.
a controlled nuclear fusion reaction, one needs:
high number density n and high temperature T
high number density n and low temperature T
low number density n and high temperature T
low number density n and low temperature T
high number density n and temperature T = 0 K
ans: A
642
Chapter 43:
ENERGY FROM THE NUCLEUS
31. Most of the energy produced by the Sun is due to:
A. nuclear fission
B. nuclear fusion
C. chemical reaction
D. gravitational collapse
E. induced emfs associated with the Sun’s magnetic field
ans: B
32. Nuclear fusion in stars produces all the chemical elements with mass numbers less than:
A. 56
B. 66
C. 70
D. 82
E. 92
ans: A
33. Nuclear fusion in the Sun is increasing its supply of:
A. hydrogen
B. helium
C. nucleons
D. positrons
E. neutrons
ans: B
34. Which of the following chemical elements is not produced by thermonuclear fusion in stars?
A. Carbon (Z = 6, A ≈ 12)
B. Silicon (Z = 14, A ≈ 28)
C. Oxygen (Z = 8, A ≈ 16)
D. Mercury (Z = 80, A ≈ 200)
E. Chromium (Z = 24, A ≈ 52)
ans: D
35. The first step of the proton-proton cycle is:
A. 1 H + 1 H → 2 H
B. 1 H + 1 H → 2 H + e+ + ν
C. 1 H + 1 H → 2 H + e− + ν
D. 1 H + 1 H → 2 H + γ
E. 1 H + 1 H → 3 H + e− + ν
ans: B
36. The overall proton-proton cycle is equivalent to:
A. 2 1 H → 2 H
B. 4 1 H → 4 H
C. 4 1 H → 4 H + 4n
D. 4 1 H + 2e− → 4 He + 2ν + 6γ
E. 4 1 H + 2e+ → 4 He + 2ν + 3γ
ans: D
Chapter 43:
ENERGY FROM THE NUCLEUS
643
37. The energy released in a complete proton-proton cycle is about:
A. 3 keV
B. 30 keV
C. 3 MeV
D. 30 MeV
E. 300 MeV
ans: D
38. For purposes of a practical (energy producing) reaction one wants a disintegration energy Q
that is:
A. positive for fusion reactions and negative for fission reactions
B. negative for fusion reactions and positive for fission reactions
C. negative for both fusion and fission reactions
D. positive for both fusion and fission reactions
E. as close to zero as possible for both fusion and fission reactions
ans: D
39. Lawson’s number is 1020 s · m−3 . If the density of deuteron nuclei is 2 × 1021 m−3 what should
the confinement time be to achieve sustained fusion?
A. 16 ms
B. 50 ms
C. 160 ms
D. 250 ms
E. 500 ms
ans: B
40. Tokamaks confine deuteron plasmas using:
A. thick steel walls
B. magnetic fields
C. laser beams
D. vacuum tubes
E. electric fields
ans: B
41. Most magnetic confinement projects attempt:
A. proton-proton fusion
B. proton-deuteron fusion
C. deuteron-deuteron fusion
D. deuteron-triton fusion
E. triton-triton fusion
ans: C
644
Chapter 43:
ENERGY FROM THE NUCLEUS
42. Compared to fusion in a tokamak, laser fusion makes use of:
A. smaller particle number densities
B. greater particle number densities
C. longer confinement times
D. higher temperatures
E. lower temperatures
ans: B
43. Most laser fusion projects attempt:
A. proton-proton fusion
B. proton-deuteron fusion
C. deuteron-deuteron fusion
D. deuteron-triton fusion
E. triton-triton fusion
ans: D
44. In laser fusion, the laser light is:
A. emitted by the reacting nuclei
B. used to cause transitions between nuclear energy levels
C. used to cause transitions between atomic energy levels
D. used to replace the emitted gamma rays
E. used to heat the fuel pellet
ans: E
Chapter 43:
ENERGY FROM THE NUCLEUS
645
Chapter 44:
QUARKS, LEPTONS, AND THE BIG BANG
1. Which of the following particles is stable?
A. Neutron
B. Proton
C. Pion
D. Muon
E. Kaon
ans: B
2. The stability of the proton is predicted by the laws of conservation of energy and conservation
of:
A. momentum
B. angular momentum
C. baryon number
D. lepton number
E. strangeness
ans: C
3. When a kaon decays via the strong interaction the products must include a:
A. baryon
B. lepton
C. strange particle
D. electron
E. neutrino
ans: C
4. A particle with spin angular momentum h̄/2 is called a:
A. lepton
B. hadron
C. fermion
D. boson
E. electron
ans: C
5. A particle with spin angular momentum h̄ is called a:
A. lepton
B. hadron
C. fermion
D. boson
E. electron
ans: D
646
Chapter 44:
QUARKS, LEPTONS, AND THE BIG BANG
6. An
A.
B.
C.
D.
E.
example of a fermion is a:
photon
pion
neutrino
kaon
none of these
ans: C
7. An
A.
B.
C.
D.
E.
example of a boson is a:
photon
electron
neutrino
proton
neutron
ans: A
8. All
A.
B.
C.
D.
E.
particles with spin angular momentum h̄/2:
interact via the strong force
travel at the speed of light
obey the Pauli exclusion principle
have non-zero rest mass
are charged
ans: C
9. All
A.
B.
C.
D.
E.
leptons interact with each other via the:
strong force
weak force
electromagnetic force
strange force
none of these
ans: B
10. An
A.
B.
C.
D.
E.
electron participates in:
the strong force only
the strong and weak forces only
the electromagnetic and gravitational forces only
the electromagnetic, gravitational, and weak forces only
the electromagnetic, gravitational, and strong forces only
ans: D
11. Which of the following particles has a lepton number of zero?
A. e+
B. µ+
C. νe
D. ν µ
E. p
ans: E
Chapter 44:
QUARKS, LEPTONS, AND THE BIG BANG
647
12. Which of the following particles has a lepton number of +1?
A. e+
B. µ+
C. µ−
D. ν e
E. p
ans: C
13. π+ represents a pion (a meson), µ− represents a muon (a lepton), νe represents an electron
neutrino (a lepton), νµ and p represents a proton represents a muon neutrino (a lepton). Which
of the following decays might occur?
A. π + −→ µ− + νµ
B. π + −→ p + νe
C. π + −→ µ+ + ν e
D. π+ −→ p + ν µ
E. π + −→ µ+ + νµ
ans: E
14. A particle can decay to particles with greater total rest mass:
A. only if antiparticles are produced
B. only if photons are also produced
C. only if neutrinos are also produced
D. only if the original particle has kinetic energy
E. never
ans: E
15. The interaction π− + p → π − + Σ+ violates the principle of conservation of:
A. baryon number
B. lepton number
C. strangeness
D. angular momentum
E. none of these
ans: C
16. The interaction π− + p → K − + Σ+ violates the principle of conservation of:
A. baryon number
B. lepton number
C. strangeness
D. angular momentum
E. none of these
ans: E
648
Chapter 44:
QUARKS, LEPTONS, AND THE BIG BANG
17. A neutral muon cannot decay into two neutrinos. Of the following conservation laws, which
would be violated if it did?
A. Energy
B. Baryon number
C. Charge
D. Angular momentum
E. None of the above
ans: D
18. A positron cannot decay into three neutrinos. Of the following conservation laws, which would
be violated if it did?
A. Energy
B. Baryon number
C. Lepton number
D. Linear momentum
E. Angular momentum
ans: C
19. Two particles interact to produce only photons, with the original particles disappearing. The
particles must have been:
A. mesons
B. strange particles
C. strongly interacting
D. leptons
E. a particle, antiparticle pair
ans: E
20. Two baryons interact to produce pions only, the original baryons disappearing. One of the
baryons must have been:
A. a proton
B. an omega minus
C. a sigma
D. an antiparticle
E. none of these
ans: D
21. A baryon with strangeness −1 decays via the strong interaction into two particles, one of which
is a baryon with strangeness 0. The other might be:
A. a baryon with strangeness 0
B. a baryon with strangeness +1
C. a meson with strangeness −1
D. a meson with strangeness +1
E. a meson with strangeness 0
ans: C
Chapter 44:
QUARKS, LEPTONS, AND THE BIG BANG
649
22. A baryon with strangeness 0 decays via the strong interaction into two particles, one of which
is a baryon with strangeness +1. The other might be:
A. a baryon with strangeness 0
B. a baryon with strangeness +1
C. a baryon with strangeness −1
D. a meson with strangeness +1
E. a meson with strangeness −1
ans: E
23. In order of increasing strength the four basic interactions are:
A. gravitational, weak, electromagnetic, and strong
B. gravitational, electromagnetic, weak, and strong
C. weak, gravitational, electromagnetic, and strong
D. weak, electromagnetic, gravitational, and strong
E. weak, electromagnetic, strong, and gravitational
ans: A
24. The two basic interactions that have finite ranges are:
A. electromagnetic and gravitational
B. electromagnetic and strong
C. electromagnetic and weak
D. gravitational and weak
E. weak and strong
ans: E
25. A certain process produces baryons that decay with a lifetime of 4 × 10−24 s. The decay is a
result of:
A. the gravitational interaction
B. the weak interaction
C. the electromagnetic interaction
D. the strong interaction
E. some combination of the above
ans: D
26. A certain process produces mesons that decay with a lifetime of 6 × 10−10 s. The decay is a
result of:
A. the gravitational interaction
B. the weak interaction
C. the electromagnetic interaction
D. the strong interaction
E. some combination of the above
ans: B
650
Chapter 44:
QUARKS, LEPTONS, AND THE BIG BANG
27. Compared to the lifetimes of particles that decay via the weak interaction, the lifetimes of
particles that decay via the strong interaction are:
A. 10−12 times as long
B. 10−23 times as long
C. 1024 times as long
D. 1012 times as long
E. about the same
ans: A
28. Strangeness is conserved in:
A. all particle decays
B. no particle decays
C. all weak particle decays
D. all strong particle decays
E. some strong particle decays
ans: D
29. Different types of neutrinos can be distinguished from each other by:
A. the directions of their spins
B. the leptons with which they interact
C. the baryons with which they interact
D. the number of photons that accompany them
E. their baryon numbers
ans: B
30. All
A.
B.
C.
D.
E.
known quarks have:
charges that are multiples
charges that are multiples
charges that are multiples
charges that are multiples
charges that are multiples
ans: D
of
of
of
of
of
e and integer baryon numbers
e and baryon numbers that are either +1/3 or −1/3
e/3 and integer baryon numbers
e/3 and baryon numbers that are either +1/3 or −1/3
2e/3 and baryon numbers that are either +1/3 or −1/3
31. The baryon number of a quark is:
A. 0
B. 1/2
C. 1/3
D. 2/3
E. 1
ans: C
Chapter 44:
QUARKS, LEPTONS, AND THE BIG BANG
651
32. Quarks are the constituents of:
A. all particles
B. all leptons
C. all strongly interacting particles
D. only strange particles
E. only mesons
ans: C
33. Any meson is a combination of:
A. three quarks
B. two quarks and an antiquark
C. one quark and two antiquarks
D. one quark and one antiquark
E. two quarks
ans: D
34. Any baryon is a combination of:
A. three quarks
B. two quarks and an antiquark
C. one quark and two antiquarks
D. one quark and one antiquark
E. two quarks
ans: A
35. The quark content of a proton is:
A. uuu
B. uud
C. udd
D. ddd
E. uds
ans: B
36. The quark content of a π+ meson is:
A. uu
B. uu
C. ud
D. ud
E. dd
ans: D
37. In terms of quark content a beta decay can be written:
A. udd → uud + e − + ν
B. udd → udd + dd + ν
C. udd → udd + dd + e −
D. udd → uud + ud + ν
E. udd → uud + ud + e − + ν
ans: A
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Chapter 44:
QUARKS, LEPTONS, AND THE BIG BANG
38. The up quark u has charge +2e/3 and strangeness 0; the down quark d has charge −e/3 and
strangeness 0; the strange quark s has charge −e/3 and strangeness −1. This means there can
be no baryon with:
A. charge 0 and strangeness 0
B. charge −e and strangeness −1
C. charge +e and strangeness −1
D. charge +e and strangeness −2
E. charge 0 and strangeness +2
ans: C
39. The up quark u has charge +2e/3 and strangeness 0; the down quark d has charge −e/3 and
strangeness 0; the strange quark s has charge −e/3 and strangeness −1. This means there can
be no meson with:
A. charge 0 and strangeness −1
B. charge −e and strangeness −1
C. charge +e and strangeness −1
D. charge +e and strangeness +1
E. charge 0 and strangeness +1
ans: C
40. Messenger particles of the electromagnetic interaction are called:
A. gluons
B. photons
C. W and Z
D. gravitons
E. pions
ans: B
41. Messenger particles of the strong interaction are called:
A. gluons
B. photons
C. W and Z
D. gravitons
E. pions
ans: A
42. Messenger particles of the weak interaction are called:
A. gluons
B. photons
C. W and Z
D. gravitons
E. pions
ans: C
Chapter 44:
QUARKS, LEPTONS, AND THE BIG BANG
653
43. A down quark can be changed into an up quark (plus other particles perhaps) by
A. the gravitational interaction
B. the electromagnetic interaction
C. the weak interaction
D. the strong interaction
E. none of these
ans: C
44. The color theory explains why quarks:
A. form particles in pairs and triplets
B. have charge that is a multiple of e/3
C. have spin
D. have mass
E. none of the above
ans: A
45. Color is carried by:
A. only quarks
B. only leptons
C. only quarks and leptons
D. only quarks and gluons
E. only photons and gluons
ans: D
46. Hubble’s law is evidence that:
A. the speed of light is increasing
B. the universe is expanding
C. the Earth is slowing down in its orbit
D. galaxies have rotational motion
E. none of the above
ans: B
47. Objects in the universe are receding from us with a speed that is proportional to:
A. the reciprocal of their distance from us
B. the reciprocal of the square of their distance from us
C. their distance from us
D. the square of their distance from us
E. their distance from the center of the universe
ans: C
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Chapter 44:
QUARKS, LEPTONS, AND THE BIG BANG
48. The velocities of distant objects in the universe indicate that the time elapsed since the big
bang is about:
A. 105 y
B. 1010 y
C. 1015 y
D. 1020 y
E. 1025 y
ans: B
49. The intensity of the microwave background radiation, a remnant of the big bang:
A. is greatest in directions toward the center of the galaxy
B. is least in directions toward the center of the galaxy
C. is proportional to the reciprocal of the distance from us
D. is proportional to the square of the distance from us
E. is nearly the same in all directions
ans: E
50. As a result of the big bang there is, in addition to the microwave background radiation, a
uniform distribution of background:
A. electrons
B. quarks
C. gluons
D. neutrinos
E. atoms
ans: D
51. Dark matter is suspected to exist in the universe because:
A. the night sky is dark between stars
B. the orbital period of stars in the outer parts of a galaxy is greater than the orbital period
of stars near the galactic center
C. the orbital period of stars in the outer parts of a galaxy is less than the orbital period of
stars near the galactic center
D. the orbital period of stars in the outer parts of a galaxy is about the same as the orbital
period of stars near the galactic center
E. all galaxies have about the same mass
ans: D
52. If dark matter did not exist it is likely that:
A. the universe would expand forever
B. the universe would begin contracting soon
C. the night sky would be brighter
D. the night sky would be darker
E. we would be able to see the center of the universe
ans: A
Chapter 44:
QUARKS, LEPTONS, AND THE BIG BANG
655
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