Page 120
AP® Physics C
1984, 1988, 1993 Multiple Choice Questions
Mechanics
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Copyright © 1988-2002 by College Entrance Examination Board. All rights reserved.
College Board, Advanced Placement Program, AP, SAT, and the acorn logo are registered trademarks of the College Entrance Examination Board.
Multiple Choice 1984 C
1.
2.
Torque is the rotational analogue of
(A) kinetic energy
(B) linear momentum
(C) acceleration
(D) force
(E) mass
An object slides off a roof 10 meters above the
ground with an initial horizontal speed of 5
meters per second as shown above. The time
between the object's leaving the roof and hitting
the ground is most nearly
1
(A) 2 s
2s
3.
Page 121
(E)
1
(B)
2s
(C)
2 s
(D)
5 2 s
A simple pendulum of length l. whose bob has
mass m, oscillates with a period T. If the bob is
replaced by one of mass 4m, the period of
oscillation is
1
(A) 4 T
1
(B) 2 T
(C) T
5.
From time t = 0 to time t = 40 seconds, the areas
under both curves are equal. Therefore, which
of the following is true at time t = 40 seconds?
(A) Car Y is behind car X.
(B) Car Y is
passing car X.
(C) Car Y is in front of car X.
(D) Both cars have the same acceleration.
(E) Car X is accelerating faster than car Y.
6.
An ice skater is spinning about a vertical axis
with arms fully extended. If the arms are pulled
in closer to the body, in which of the following
ways are the angular momentum and kinetic
energy of the skater affected?
Angular Momentum
Kinetic Energy
(A) Increases
Increases
(B) Increases
Remains
Constant
(C) Remains Constant
Increases
(D) Remains Constant
Remains
Constant
(E) Decreases
Remains
Constant
(D) 2T
(E)4T
At time t = 0, car X traveling with speed v0 passes car
Y. which is just starting to move. Both cars then
travel on two parallel lanes of the same straight road.
The graphs of speed v versus time t for both cars are
shown above.
4.
Which of the following is true at time t = 20
seconds?
(A) Car Y is behind car X.
(B) Car Y is
passing car X.
(C) Car Y is in front of car X.
( D) Both cars have the same acceleration.
(E) Car X is accelerating fester then car Y.
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Multiple Choice 1984 C
7.
Page 122
The parabola above is a graph of speed v as a
function of time t for an object. Which of the
following graphs best represents the magnitude F
of the net force exerted on the object as a
function of time t ?
(A) F
(B) F
Questions 10-12
A cylinder rotates with constant angular acceleration
about a fixed axis. The cylinder’s moment of inertial
about the axis is 4 kg m2. At time t = 0 the cylinder
is at rest. At time t = 2 seconds its angular velocity is
1 radian per second.
10.
What is the angular acceleration of the cylinder
between t = 0 and t = 2 seconds?
(A) 0.5 radian/s² (B) 1 radian/s² (C) 2
radian/s²
(D) 4 radian/s² (E) 5 radian/s²
11.
What is the angular momentum of the cylinder
at time t = 2 seconds?
(A) 1 kgm m²/s (B) 2 kgm m²/s (C) 3 kgm
m²/s (D) 4 kgm m²/s
(E) It cannot be determined without knowing
the radius of the cylinder.
12.
What is the kinetic energy of the cylinder at
time t = 2 seconds?
(A) 1 J
(B) 2 J
(C) 3 J
(D) 4 J
(E)
cannot be determined without knowing the
radius of the cylinder
Questions 13-14
8.
9.
An object of mass m is lifted at constant velocity
a vertical distance H in time T. The power
supplied by the lifting force is
(A) mgHT
(B) mgH/T
(C) mg/HT
(D) mgT/H
(E) zero
When the frictionless system shown above is
accelerated by an applied force of magnitude F,
the tension in the string between the blocks is
(A) 2 F
(B) F
(C) (2/3)F
(D) 0.5F
(E) (1/3)F
A system consists of two objects having masses ml
and m2 (ml < m2). The objects are connected by a
massless string, hung over a pulley as shown above,
and then released.
13. When the speed of each object is v, the
magnitude of the total linear momentum of the
system is
(A) (m1 + m2) v
(B) (m2 - m1) v
(C)
½(ml+m2)v
(D) ½(m2 - m1)v
(E) m2v
14. When the object of mass m2 has descended a
distance h, the potential energy of the system has
decreased by
(A) (m2 - ml)gh
(B) m2gh
(C) (m1 +
m2)gh
(D) ½(ml + m2)gh
(E) 0
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Multiple Choice 1984 C
Page 123
15.
The following graphs, all drawn to the same
scale, represent the net force F as a function of
displacement x for an object that moves along a
straight line. Which graph represents the force that
will cause the greatest change in the kinetic energy of
the object from x = 0 to x = x1?
17. Two particles of equal mass mo, moving with
equal speeds vO along paths inclined at 60° to the
x-axis as shown above, collide and stick
together. Their velocity after the collision has
magnitude
v0
(A) 4
3v 0
2
16. A square piece of plywood on a horizontal
tabletop is subjected to the two horizontal forces
shown above right. Where should a third force of
magnitude 5 newtons be applied to put the piece
of plywood into equilibrium?
v0
(B) 2
(C)
2v 0
2
(D)
(E) vo
18. Which of the following is true for a system consisting of a mass oscillating on the end of an
ideal spring?
(A) The kinetic and potential energies are equal
at all times.
(B) The kinetic and potential energies are both
constant.
(C) The maximum potential energy is achieved
when the mass passes through its equilibrium
position.
(D) The maximum kinetic energy and maximum potential energy are equal, but occur at
different times.
(E) The maximum kinetic energy occurs at
maximum displacement of the mass from its
equilibrium position.
19. A particle is moving in a circle of radius 2
meters according to the relation  = 3t2 + 2t,
where  is measured in radians and t in seconds.
The speed of the particle at t = 4 seconds is
(A) 13 m/s
(B) 16m/s
(C) 26m/s
(D)
52 m/ s
(E) 338 m/ s
20. The mass of Planet X is one-tenth that of the
Earth, and its diameter is one-half that of the
Earth. The acceleration due to gravity at the
surface of Planet X is most nearly
(A) 2m/s2
(B) 4m/s2
(C) 5m/s2
(D) 7
m/s2
(E) 10 m/s2
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Multiple Choice 1984 C
Page 124
21. A person pushes a box across a horizontal
surface at a constant speed of 0.5 meter per
second. The box has a mass of 40 kilograms, and
the coefficient of sliding friction is 0.25. The
power supplied to the box by the person is
(A) 0.2 W
(B) 5 W
(C) 50 W
(D)
100 W
(E) 200 W
Questions 23-24
A 0. l -kilogram block is attached to an initially
unstretched spring of force constant k = 40 newtons
per meter as shown above. The block is released from
rest at time t = 0.
23. What is the amplitude of the resulting simple
harmonic motion of the block?
1
(A) 40 m
1
m
(D) 2
22. A uniform rigid bar of weight W is supported in
a horizontal orientation as shown above by a
rope that makes a 30° angle with the horizontal.
The force exerted on the bar at point O, where it
is pivoted, is best represented by a vector whose
direction is which of the following?
(B)
(C)
(D)
1
m
(C) 4
(E) 1m
24. At what time after release will the block first
return to its initial position?

(A) 40
(D)
(A)
1
m
(B) 20

s

s
5
(B) 20

s
(E) 4
s
(C)

s
10
(E)
25. A particle moves in simple harmonic motion
represented by the graph above. Which of the
following represents the velocity of the particle
as a function of time?
(A) v(t) = 4 cos t
(B) v(t)= Cost
(C) v(t) = -2cost
(D) v(t) =-4 sint
(E)
v(t) = - 4sint
26. A particle of mass m moves with a constant
speed v along the dashed line y = a. When the
x-coordinate of the particle is xo, the magnitude
of the angular momentum of the particle with
respect to the origin of the system is
(A) zero
(B) mva
(C) mvxo (D)
mva
mv x  a
2
2
(E)
x2  a2
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Multiple Choice 1984 C
Page 125
27. A uniform stick has length L. The moment of
inertia about the center of the stick is Io. A
particle of mass M is attached to one end of the
stick. The moment of inertia of the combined
system about the center of the stick is
1
1
I 0  ML2
I 0  ML2
4
2
(A)
(B)
1
I 0  ML2
2
2
(D) I 0  ML
5
I 0  ML2
4
(E)
(C)
28. A body moving in the positive x direction passes
the origin at time t = 0. Between t = 0 and t = 1
second, the body has a constant speed of 24
meters per second. At t = 1 second, the body is
given a constant acceleration of 6 meters per
second squared in the negative x direction. The
position x of the body at t = 11 seconds is
(A) +99 m (B) +36 m
(C) -36 m
(D)
-75 m
(E) -99 m
L
29. The center of mass of a uniform wire, bent in the
shape shown above, is located closest to point
(A) A
(B) B
(C) C
(D) D
(E) E
30. A racing car is moving around the circular track
of radius 300 meters shown above. At the instant
when the car's velocity is directed due east, its
acceleration is directed due south and has a
magnitude of 3 meters per second squared. When
viewed from above, the car is moving
(A) clockwise at 30 m/s
(B) clockwise at 10
m/ s
(C) counterclockwise at 30 m/s
(D) counterclockwise at 10 m/s
(E) with
constant velocity
31. Mass M1 is moving with speed v toward
stationary mass M2. The speed of the center of
mass of the system is

M1 
M1
1 
v
v
M


M
2
2
(A)
( B)


M2 
M1 
1 
v
1 
v
M1 
M



2
(D)

M1 

v
 M1  M 2 
(C)
(E)
32. A 100-newton weight is suspended by two cords
as shown in the figure above. The tension in t
slanted cord is
(A) 50 N
(B) 100 N
(C) 150 N
( D)
200 N
(E) 250 N
33. If a particle moves in such a way that its position
x is described as a function of time t by x = t3/2,
then its kinetic energy is proportional to
(A) t2 (B) t3/2
(C) t
(D) t1/2
(E) t°
(i.e., kinetic energy is constant)
34. From the top of a 70-meter-high building, a
l-kilogram ball is thrown directly downward with
an initial speed of 10 meters per second. If the
ball reaches the ground with a speed of 30 meters
per second, the energy lost to friction is most
nearly
(A) 0J
(B) 100 J
(C) 300 J
( D) 400 J
(E) 700 J
35. A light rigid rod with masses attached to its ends
is pivoted about a horizontal axis as shown
above. When released from rest in a horizontal
orientation, the rod begins to rotate with an
angular acceleration of magnitude
g
(A) 7 l
g
(E) l
g
(B) 5l
g
(C) 4 l
5g
(D) 7 l
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Multiple Choice 1984 C
Page 126
36.
A parallel-plate capacitor has a capacitance
Co. A second parallel-plate capacitor has plates with
twice the area and twice the separation. The
capacitance of the second capacitor is most nearly
(A) ¼Co
(B) ½Co
(C) Co
(D) 2Co
(E) 4Co
37. When lighted, a 100-watt light bulb operating on
a 110-volt household circuit has a resistance
closest to
(A) 10-2 
(B) 10-1 
(C) 1 
(D) 10 
(E) 100 
41. In the circuit shown above, what is the resistance
R?
(A) 3 
(B) 4 
(c) 6 
(D) 12 
(E) 18 
38. If i is current, t is time, E is electric field
intensity, and x is distance, the ratio of
 idt to
 Edx may be expressed in
(A) coulombs
(B) joules
(D) farads
(E) henrys
(C) newtons
39. The electric field E just outside the surface of a
charged conductor is
(A) directed perpendicular to the surface
(B) directed parallel to the surface
(C) independent of the surface charge density
(D) zero
(E) infinite
40. A closed surface, in the shape of a cube of side a,
is oriented as shown above in a region where
there is a constant electric field of magnitude E
parallel to the x-axis. The total electric flux
through the cubical surface is
(A) -Ea2
(B) zero (C) Ea2
(D) 2Ea2
2
(E) 6Ea
42. The figure above shows a spherical distribution of
charge of radius R and constant charge density .
Which of the following graphs best represents
the electric field strength E as a function of the
distance r from the center of the sphere?
43. Points R and S are each the same distance d from
two unequal charges, +Q and +2Q, as shown
above. The work required to move a charge -Q
from point R to point S is
(A) dependent on the path taken from R to S
(B) directly proportional to the distance between
R and S
(C) positive
(D) zero
(E) negative
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Multiple Choice 1984 C
44. The five resistors shown below have the lengths
and cross-sectional areas indicated and are made
of material with the same resistivity. Which has
the greatest resistance?
45. A 12-volt storage battery, with an internal
resistance of 2, is being charged by a current of
2 amperes as shown in the diagram above. Under
these circumstances, a voltmeter connected
across the terminals of the battery will read
(A) 4 V
(B) 8 V
(C) 10 V
(D) 12 V
(E) 16 V
46. A galvanometer has a resistance of 99 ohms and
deflects full scale when a current of 10-3 ampere
passes through it. In order to convert this
galvanometer into an ammeter with a full-scale
deflection of 0.1 ampere, one should connect a
resistance of
(A) 1  in series with it
(B) 901  in series with it
(C) 9,900  in series with it
(D) 1  in parallel with it
(E) 9,900  in parallel with it
47. Two long, parallel wires, fixed in space, carry
currents I1 and I2. The force of attraction has
magnitude F. What currents will give an
attractive force of magnitude 4F?
(A) 2I1 and ½I2
(B) I1 and ¼I2
(C) ½I1 and ½I2
(D) 2I1 and 2I2
(E) 4I1 and 4I2
Page 127
48. In each of the following situations, a bar magnet
is aligned along the axis of a conducting loop.
The magnet and the loop move with the
indicated velocities. In which situation will the
bar magnet NOT induce a current in the
conducting loop?
Questions 49-50
The ends of a metal bar rest on two horizontal
north-south rails as shown above. The bar may slide
without friction freely with its length horizontal and
lying east and west as shown above. There is a
magnetic field parallel to the rails and directed north.
49. If the bar is pushed northward on the rails, the
electromotive force induced in the bar as a result
of the magnetic field will
(A) be directed upward
(B) be zero
(C) produce a westward current
(D) produce an eastward current
(E) stop the motion of the bar
50. A battery is connected between the rails and
causes the electrons in the bar to drift to the east.
The resulting magnetic force on the bar is
directed
(A) north
(B) south
(C) east
(D) west
(E) vertically
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Multiple Choice 1984 C
51. A charged particle is projected with its initial
velocity parallel to a uniform magnetic field. The
resulting path is a
(A) spiral
(B) parabolic arc
(C) circular arc
(D) straight line parallel to the field
(E) straight line perpendicular to the field
Page 128
Questions 54-56
Questions 52-53
Two positive charges of magnitude q are each a
distance d from the origin A of a coordinate systen.
as shown above.
52. At which of the following points is the electric
field least in magnitude?
(A) A
(B) B
(C) C
(D) D
(E) E
53. At which of the following points is the electric
potential greatest in magnitude?
(A) A
(B) B
(C) C
(D) D
(E) E
The batteries in each of the circuits shown above are
identical and the wires have negligible resistance.
54. In which circuit is the current furnished by the
battery the greatest?
(A)
(B)
(C)
(D)
(E)
55. In which circuit is the equivalent resistance
connected to the battery the greatest?
(A)
(B)
(C)
(D)
(E)
56. Which circuit dissipates the least power?
(A)
(B)
(C)
(D)
(E)
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Multiple Choice 1984 C
Page 129
Questions 57-59 refer to the circuit shown below.
Assume the capacitor C is initially uncharged. The
following graphs may represent different quantities
related to the circuit as functions of time t after the
switch S is closed
57. Which graph best represents the voltage versus
time across the resistor R ?
(A)
(B)
(C)
(D)
(E)
58. Which graph best represents the current versus
time in the circuit?
(A)
(B)
(C)
(D)
(E)
59. Which graph best represents the voltage across
the capacitor versus time?
(A)
(B)
(C)
(D)
(E)
Questions 60-61
Three 6-microfarad capacitors are connected in series
with a 6-volt battery.
60. The equivalent capacitance of the set of
capacitors is
(A) 0.5 F
(B) 2 F
(C) 3 F
F
(E) 18 F
61. The energy stored in each capacitor is
(A) 4 J
(B) 6 J
(C) 12 J
J
(E) 36 J
62. A rigid insulated rod, with two unequal charges
attached to its ends, is placed in a uniform
electric field E as shown above. The rod
experiences a
(A) net force to the left and a clockwise rotation
(B) net force to the left and a counterclockwise
rotation
(C) net force to the right and a clockwise rotation
(D) net force to the right and a counterclockwise
rotation
(E) rotation, but no net force
63. A loop of wire is pulled with constant velocity v
to the right through a region of space where there
is a uniform magnetic field B directed into the
page, as shown above. The magnetic force on the
loop is
(A) directed to the left both as it enters and as it
leaves the region
(B) directed to the right both as it enters and as it
leaves the region
(C) directed to the left as it enters the region and
to the right as it leaves
(D) directed to the right as it enters the region
and to the left as it leaves
(E) zero at all times
(D) 9
(D) 18
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Multiple Choice 1984 C
Page 130
67. A solid cylindrical conductor of radius R carries
a current I uniformly distributed throughout its
interior. Which of the following graphs best
represents the magnetic field intensity as a
function of r, the radial distance from the axis of
the cylinder
64. The electric field of two long coaxial cylinders is
represented by lines of force as shown above.
The charge on the inner cylinder is +Q. The
charge on the outer cylinder is
(A) +3Q
(B) +Q
(C) 0
(D) - Q
(E) -3 Q
65. Two identical conducting spheres are charged to
+2Q and -Q. respectively, and are separated by a
distance d (much greater than the radii of the
spheres) as shown above. The magnitude of the
force of attraction on the left sphere is F1 After
the two spheres are made to touch and then are
reseparated by distance d the magnitude of the
force on the left sphere is F2. Which of the
following relationships is correct?
( A) 2 F1 = F2
(B) F1 = F2
(C) F1 = 2F2
(D) F1 = 4F2
(E) F1 = 8F2
66. An isolated capacitor with air between its plates
has a potential difference Vo and a charge Qo.
After the space between the plates is filled with
oil, the difference in potential is V and the
charge is Q. Which of the following pairs of
relationships is correct?
(A) Q=Qo and V>Vo
(B) Q=Qo and V<Vo
(C) Q>Qo and V=Vo
(D) Q< Qo and V<Vo
(E) Q>Qo and V>Vo
68. The cross section above shows a long solenoid of
length l and radius r consisting of N closely
wound turns of wire. When the current in the
wire is I, the magnetic field within this solenoid
has magnitude Bo. A solenoid with the same
number of turns N, length l, and current I, but
with radius 2r, would have a magnetic field of
magnitude most nearly equal to
(A) Bo/4
(B) Bo/2
(C) Bo
(D) 2Bo
(E) 4Bo
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Multiple Choice 1984 C
69. In the circuit shown above, the capacitor C is
first charged by throwing switch S to the left,
then discharged by throwing S to the right. The
time constant for discharge could be increased by
which of the following?
(A) Placing another capacitor in parallel with C
(B) Placing another capacitor in series with C
(C) Placing another resistor in parallel with the
resistor R
(D) Increasing battery emf 
(E) Decreasing battery emf 
70. Concentric conducting spheres of radii a and 2a
bear equal but opposite charges +Q and -Q.
respectively. Which of the following graphs best
represents the electric potential V as a function
of r ?
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Page 131
Multiple Choice 1988 C
1.
Page 132
Which of the following pairs of graphs shows the
distance traveled versus time and the speed
versus time for an object uniformly accelerated
from rest?
2.
The final speed of the first 4-kilogram mass is
(A) 0 m/s
(B) 2 m/s
(C) 3 m/s
(D) 4 m/s
(E) 6 m/s
3.
The final speed of the two 4-kilogram masses
that stick together is
(A) 0 m/s
(B) 2 m/s
(C) 3 m/s
(D) 4 m/s
(E) 6 m/s
4.
A particle of mass m moves along a straight path
with a speed v defined by the function v = bt2 +
c, where b and c are constants and t is time.
What is the magnitude F of the net force on the
particle at time t = t1 ?
(A) bt1 2 + c
(B) 3mbt1 + 2c
(C) mbt1
(D) mbt1 + c
(E) 2mbt1
5.
An object released from rest at time t = 0 slides
down a frictionless incline a distance of 1 meter
during the first second. The distance traveled by
the object during the time interval from t = 1
second to t = 2 seconds is
(A) 1 m (B) 2 m (C) 3 m
(D) 4m (E)
Sm
6.
Two people are in a boat that is capable of a
maximum speed of 5 kilometers per hour in still
water, and wish to cross a river 1 kilometer wide
to a point directly across from their starting
point. If the speed of the water in the river is 5
kilometers per hour, how much time is required
for the crossing?
(A) 0.05 hr
(B) 0.1 hr
(C) 1 hr
(D) 10
hr
(E) The point directly across from the starting
point cannot be reached under these conditions.
7.
Vectors V1, and V2 shown above have equal
magnitudes. The vectors represent the velocities
of an object at times t1, and t2, respectively. The
average acceleration of the object between time
t1 and t2 was
(A) zero
(B) directed north
(C) directed
west
(D) directed north of east
(E) directed
north of west
Speed
Distance
(A)
t
o
t
o
Speed
Distance
(B)
t
o
t
o
Speed
Distance
(C)
t
o
t
o
Speed
Distance
(D)
t
o
t
o
Speed
Distance
(E)
o
t
o
t
Questions 2 and 3
A 4-kilogram mass has a speed of 6 meters per
second on a horizontal frictionless surface, as
shown above. The mass collides head-on and
elastically with an identical 4-kilogram mass
initially at rest. The second 4-kilogram mass then
collides head-on and sticks to a third 4-kilogram
mass initially at rest.
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Multiple Choice 1988 C
8.
Page 133
A projectile of mass M1 is fired horizontally
from a spring gun that is initially at rest on a
frictionless surface. The combined mass of the
gun and projectile is M2. If the kinetic energy of
the projectile after firing is K, the gun will recoil
with a kinetic energy equal to
(A) K
M2
K
M
1
(B)
M1
K
M 2  M1
(E)
M 12
2 K
M
2
(C)
M1
K
M 2  M1
D)
12. A figure skater is spinning on frictionless ice
with her arms fully extended horizontally. She
then drops her arms to her sides. Which of the
following correctly describes her rotational
kinetic energy and angular momentum as her
arms fall?
Rotational Kinetic
Angular
Energy
Momentum
(A) Remains constant
Remains constant
(B) Decreases
Increases
(C) Decreases
Decreases
(D) Increases
Decreases
(E) Increases
Remains
constant
13. A ball is dropped from a height of 10 meters
onto a hard surface so that the collision at the
surface may be assumed elastic. Under such
conditions the motion of the ball is
(A) simple harmonic with a period of about 1.4 s
(B) simple harmonic with a period of about 2.8 s
(C) simple harmonic with an amplitude of 5 m
9.
A piece of wire of uniform cross section is bent
in the shape shown above. What are the
coordinates
(x, y) of the center of mass?
(A) (15/14, 6/7)
8/7)
(D) (1,1)
(B) (6/7, 6/7)
(E) (1,6/7)
(C) (15/14,
10. A projectile is fired from the surface of the Earth
with a speed of 200 meters per second at an
angle of 30° above the horizontal. If the ground
is level, what is the maximum height reached by
the projectile?
(A) 5 m (B) 10 m (C) 500 m (D) 1,000
m
(E) 2,000 m
11. A particle moves along the x-axis with a nonconstant acceleration described by a = 12t, where
a is in meters per second squared and t is in
seconds. If the particle starts from rest so that
its speed v and position x are zero when t = 0,
where is it located when t = 2 seconds?
(A) x = 12 m (B) x = 16m
(C) x = 24 m
(D) x = 32 m
(E) x = 48 m
(D) periodic with a period of about 2.8 s but not
simple harmonic
(E) motion with constant momentum
Questions 14-15
An object moving in a straight line has a velocity v in
meters per second that varies with time t in seconds
according to the following function.
v = 4 + 0.5 t2
14. The instantaneous acceleration of the object at t
= 2 seconds is
(A) 2 m/s2 (B) 4 m/s2
(C) 5 m/s2
(D)
2
2
6 m/s
(E) 8 m/s
15. The displacement of the object between t = 0 and
t = 6 seconds is
(A) 22 m
(B) 28 m
(C) 40 m
(D) 42
m
(E) 60 m
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Multiple Choice 1988 C
Page 134
Questions 18-19 refer to the graph below of the
displacement x versus time t for a particle in simple
harmonic motion.
16. A pendulum consists of a ball of mass m
suspended at the end of a massless cord of length
L as shown above. The pendulum is drawn aside
through an angle of 60. with the vertical and
released. At the low point of its swing, the speed
of the pendulum ball is
(A)
gL
gL
(B)
(E) 2gL
2gL
(C) ½gL
18. Which of the following graphs shows the kinetic
energy K of the particle as a function of time t
for one cycle of motion?
(D)
17. A rock is lifted for a certain time by a force F
that is greater in magnitude than the rock's
weight W. The change in kinetic energy of the
rock during this time is equal to the
(A) work done by the net force (F - W)
(B) work done by F alone
(C) work done by W alone
(D)
difference in the momentum of the rock before
and after this time (E) difference in the potential
energy of the rock before and after this time.
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Multiple Choice 1988 C
Page 135
19. Which of the following graphs shows the kinetic
energy K of the particle as a function of its
displacement x ?
22. Two artificial satellites, 1 and 2, orbit the Earth
in circular orbits having radii R1 and R2, respectively, as shown above. If R2 = 2R1, the accelerations a2 and a1 of the two satellites are related by
which of the following?
(A) a2 = 4a1
(B) a2 = 2a1
(C) a2 = a1
(D) a2 = a1/2
(E) a2 = a1/4
23 A bowling ball of mass M and radius R. whose
moment of inertia about its center is (2/5)MR2,
rolls without slipping along a level surface at
speed v. The maximum vertical height to which
it can roll if it ascends an incline is
v2
(A) 5g
7v 2
(D) 10g
20. A satellite travels around the Sun in an elliptical
orbit as shown above. As the satellite travels
from point X to point Y. which of the following
is true about its speed and angular momentum?
Speed
Angular Momentum
(A) Remains constant Remains constant
(B) Increases
Increases
(C) Decreases
Decreases
(D) Increases
Remains constant
(E) Decreases
Remains constant
21. A newly discovered planet, "Cosmo," has a mass
that is 4 times the mass of the Earth. The radius
of the Earth is Re. The gravitational field strength
at the surface of Cosmo is equal to that at the
surface of the Earth if the radius of Cosmo is
equal to
(A) ½Re
(B) Re
(C) 2Re
(D) R e
2v 2
(B) 5g
v2
(E) g
v2
(C) 2g
24. A ball of mass m is attached to the end of a
string of length Q as shown above. The ball is
released from rest from position P. where the
string is horizontal. It swings through position Q.
where the string is vertical, and then to position
R. where the string is again horizontal. What are
the directions of the acceleration vectors of the
ball at positions Q and R?
Position Q
Position R
(A) Downward
Downward
(B) Downward
To the right
(C) Upward
Downward
(D) Upward
To the left
(E) To the right
To the left
(E) Re2
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Multiple Choice 1988 C
Page 136
25. A mass m moves on a curved path from point X
to point Y. Which of the following diagrams
indicates a possible combination of the net force
F on the mass, and the velocity v and
acceleration a of the mass at the location shown?
29. Two blocks are pushed along a horizontal
frictionless surface by a force of 20 newtons to
the right, as shown above. The force that the
2-kilogram block exerts on the 3-kilogram block
is
(A) 8 newtons to the left
(B) 8 newtons to the right
(C) 10 newtons to the left
(D) 12 newtons to the right
(E) 20 newtons to the left
30. When a mass m is hung on a certain ideal spring,
the spring stretches a distance d. If the mass is
then set oscillating on the spring, the period of
oscillation is proportional to
(A)
d
g
(B)
2
(D)
Questions 26-27
A particle moves in a circle in such a way that the x and y-coordinates of its motion are given in meters as
functions of time t in seconds by:
x = 5cos(3t)
y = 5 sin (3t)
26. What is the period of revolution of the particle?
(A) 1/3 s
(B) 3 s
(C) 2/3 s
(D) 3/2 s
(E) 6 s
m g
d
(E)
g
d
(C)
d
mg
m
g
31. In which of the following diagrams is the torque
about point O equal in magnitude to the torque
about point X in the diagram above? (All forces
lie in the plane of the paper.)
27. Which of the following is true of the speed of the
particle?
(A) It is always equal to 5 m/s.
(B) It is always equal to 15 m/s.
(C) It oscillates between 0 and 5 m/s.
(D) It oscillates between 0 and 15 m/s.
(E) It oscillates between 5 and 15 m/s.
28. The radius of the Earth is approximately 6,000
kilometers. The acceleration of an astronaut in a
perfectly circular orbit 300 kilometers above the
Earth would be most nearly
(A) 0 m/s2
(B) 0.05 m/s2
(C) 5 m/s2
2
2
(D) 9 m/s
(E) 11 m/s
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Multiple Choice 1988 C
Page 137
32. A 10-kilogram body is constrained to move
along the x-axis. The potential energy U of the
body in joules is given as a function of its
position x in meters by
U(x) = 6x2 - 4x + 3
The force on the particle at x = 3 meters is
(A) 32 N in +x direction
(B) 32N in -x direction
(C) 45 N in +x direction
(D) 45 N in -x direction
(E) 98 N in +x direction
33. A rock is dropped from the top of a 45-meter
tower, and at the same time a ball is thrown from
the top of the tower in a horizontal direction. Air
resistance is negligible. The ball and the rock hit
the level ground a distance of 30 meters apart.
The horizontal velocity of the ball thrown was
most nearly
(A) 5 m/s
(B) 10 m/s
(C) 14.1 m/s
(D) 20 m/s
(E) 28.3 m/s
34. Two objects of equal mass hang from
independent springs of unequal spring constant
and oscillate up and down. The spring of greater
spring constant must have the
(A) smaller amplitude of oscillation
(B) larger amplitude of oscillation
(C) shorter period of oscillation
(D) longer period of oscillation
(E) lower frequency of oscillation
35. A satellite moves in a stable circular orbit with
speed vo at a distance R from the center of a
planet. For this satellite to move in a stable
circular orbit a distance 2R from the center of the
planet, the speed of the satellite must be
v0
v0
(A) 2
(B) 2
(D) 2v 0
(E) 2vo
(C) vo
36. Two small spheres have equal charges q and are
separated by a distance d. The force exerted on
each sphere by the other has magnitude F. If the
charge on each sphere is doubled and d is halved,
the force on each sphere has magnitude
(A) F
(B) 2F
(C) 4F
(D) 8F
(E) 16F
37. Which of the following statements about
conductors under electrostatic conditions is true?
(A) Positive work is required to move a positive
charge over the surface of a conductor.
(B) Charge that is placed on the surface of a
conductor always spreads evenly over the
surface.
(C) The electric potential inside a conductor is
always zero.
(D) The electric field at the surface of a
conductor is tangent to the surface.
(E) The surface of a conductor is always an
equipotential surface.
38. A charged particle traveling with a velocity v in
an electric field E experiences a force F that
must be
(A) parallel to v (B) perpendicular to v (C)
parallel to v x E (D) parallel to E (E)
perpendicular to E
39. Two resistors of the same length, both made of
the same material, are connected in a series to a
battery as shown above. Resistor II has a greater
cross. sectional area than resistor I. Which of the
following quantities has the same value for each
resistor?
(A) Potential difference between the two ends
(B) Electric field strength within the resistor
(C) Resistance
(D) Current per unit area
(E) Current
40. A positive charge of 3.0 x 10-8 coulomb is placed
in an upward directed uniform electric field of
4.0 x 104N/c. When the charge is moved 0.5
meter upward, the work done by the electric
force on the charge is
(A) 6 x 10-4 J
(B) 12 x 10-4 J
(C) 2 x 104 J
4
4
(D) 8 x 10 J
(E) 12 x 10 J
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Multiple Choice 1988 C
41. Which of the following can be used along with
fundamental constants, but no other quantities, to
calculate the magnitude of the electric field
between the plates of a parallel-plate capacitor
whose plate dimensions and spacing are not
known?
(A) The flux between the plates
(B) The total charge on either plate
(C) The potential difference between the plates
(D) The surface charge density on either plate
(E) The total energy stored in the capacitor
Page 138
Questions 44-45
A proton traveling with speed v enters a uniform
electric field of magnitude E, directed parallel to the
plane of the page, as shown in the figure above.
There is also a magnetic force on the proton that is in
the direction opposite to that of the electric force.
44. Which of the following is a possible direction for
the magnetic field?
(A)
42. Two very long parallel wires carry equal currents
in the same direction into the page, as shown
above. At point P, which is 10 centimeters from
each wire, the magnetic field is
(A) zero
(B) directed into the page
(C) directed out of the page
(D) directed to the left
(E) directed to the right
(B)
(C)
(D)  (directed out of the page)
(E) (directed into the page)
45. If e represents the magnitude of the proton
charge, what minimum magnitude of the
magnetic field could balance the electric force on
the proton?
(A) E/v
(B) eE/v
(C) vE
(D) eE
(E) evE
43. When two identical parallel-plate capacitors are
connected in series, which of the following is
true of the equivalent capacitance?
(A) It depends on the charge on each capacitor.
(B) It depends on the potential difference across
both capacitors.
(C) It is larger than the capacitance of each
capacitor.
(D) It is smaller than the capacitance of each
capacitor.
(E) It is the same as the capacitance of each
capacitor.
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Multiple Choice 1988 C
Page 139
Questions 47-48 relate to the following
configurations of electric charges located at the
vertices of an equilateral triangle. Point P is
equidistant from the charges.
46. At time t = 0 the switch is closed in the circuit
shown above. Which of the following graphs
best describes the potential difference V, across
the resistance as a function of time t ?
47. In which configuration is the electric field at P
equal to zero?
(A)
(B)
(C)
(D)
(E)
48. In which configuration is the electric field at P
pointed at the midpoint between two of the
charges?
(A)
(B)
(C)
(D)
(E)
49. Two square parallel-plate capacitors of
capacitances C1 and C2 have the dimensions
shown in the diagrams above. The ratio of C1 to
C2 is
(A) 1 to 4
(B) 1 to 2
(C) 1 to 1
(D) 2 to 1
(E) 4 to 1
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Multiple Choice 1988 C
50. A current I, uniformly distributed over the cross
section of a long cylindrical conductor of radius
a, is directed as shown above. Which of the
following graphs best represents the intensity B
of the magnetic field as a function of the distance
r from the axis of the cylinder?
Page 140
52. In a region of space there is a uniform B field in
the plane of the page but no E field. A positively
charged particle with velocity v directed into the
page is subject to a force F in the plane of the
page as shown above. Which of the following
vectors best represents the direction of B?
(A)
(B)
(D)
(C)
(E)
53. Two conducting spheres, X and Y. have the
same positive charge +Q, but different radii
(rx > ry) as shown above. The spheres are
separated so that the distance between them is
large compared with either radius. If a wire is
connected between them, in which direction will
current be directed in the wire?
(A) From X to Y
(B) From Y to X
(C) There will be no current in the wire.
(D) It cannot be determined without knowing the
magnitude of Q.
(E) It cannot be determined without knowing
whether the spheres are solid or hollow.
51. At point X a charged particle has a kinetic
energy of 9 microjoules ( J ). It follows the path
shown above from X to Y through a region in
which there is an electric field and a magnetic
field. At Y the particle has a kinetic energy of
11 J. What is the work done by the magnetic
field on the particle?
(A) 11 J
(B) 2 J
(C) - 2 J
(D) -11 J
(E) None of the above
54. The emf of a battery is 12 volts. When the
battery delivers a current of 0.5 ampere to a load,
the potential difference between the terminals of
the battery is 10 volts. The internal resistance of
the battery is
(A) 1 
(B) 2 
(C) 4 
(D) 20  (E) 24 
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Multiple Choice 1988 C
55. A square loop of wire of side 0.5 meter and
resistance 10-2 ohm is located in a uniform
magnetic field of intensity 0.4 tesla directed out
of the page as shown above. The magnitude of
the field is decreased to zero at a constant rate in
2 seconds. As the field is decreased, what are
the magnitude and direction of the current in the
loop?
(A) Zero
(B) 5 A, counterclockwise (C) 5
A, clockwise (D) 20 A, counterclockwise
(E) 20 A, clockwise
Page 141
59. A negatively charged particle in a uniform
magnetic field B moves with constant speed v in
a circular path of radius r, as shown above.
Which of of following graphs best represents the
radius r as a function of the magnitude of B, if
the speed v is constant?
Questions 56-57 refer to a sphere of radius R that has
positive charge Q uniformly distributed on its
surface
56. Which of the following represents the magnitude
of the electric field E and the potential V as
functions of r, the distance from the center of the
sphere, when r < R ?
E
V
(A) 0
kQ/R
(B) 0
kQ/r
(C) 0
0
(D) kQ/r2 0
(E) kQ/R2 0
57. Which of the following represents the
magnitude, of the electric field E and the
potential V as functions of r, the distance from
the center of sphere, when r > R ?
E
V
(A) kQ/R2 kQ/R
(B) kQ/R kQ/R
(C) kQ/R kQ/r
(D) kQ/r2 kQ/r
(E) kQ/r2 kQ/r2
58. If R is 1 ohm and L is 1 henry, then L/R is
(A) 1 volt
(B) 1 farad
(C) 1 ampere
(D) 1 coulomb
(E) 1 second
60. In the circuit shown above, the capacitor is
initially uncharged. At time t = 0, switch S is
closed. The natural logarithmic base is e. Which
of the following is true at time t = RC?
(A) The current is /eR .
(B) The current is /R
(C) The voltage across the capacitor is .
(D) The voltage across the capacitor is /e .
(E) The voltages across the capacitor and resistor
are equal.
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Multiple Choice 1988 C
Page 142
61. Which of the following equations implies that it
is impossible to isolate a magnetic pole?
 E  dA  q / 
E  dl   d / dt
(B) 
B  dA  0
(C) 
B  dl   i   
(D) 
0
(A)
Questions 64-65 relate to the two long parallel wires
shown below. Initially the wires arc a distance d
apart and each has a current i directed into the page.
The force per unit length on each wire has magnitude
Fo
E
0
0 0
d E / dt
(E) None of the above
Questions 62-63 refer to the diagram below of two
conducting loops having a common axis.
64. The direction of the force on the right-hand wire
due to the current in the left-hand wire is
(A) to the right
(B) to the left
(C) upward
in the plane of the page
(D) downward in the plane of the page
(E)
into the page
65. The wires are moved apart to a separation 2d and
the current in each wire is increased to 2i. The
new force per unit length on each wire is
(A) F0/4
(B) Fo/2
(C) Fo
(D) 2Fo
(E) 4Fo
62. After the switch S is closed, the current through
resistor R2 is
(A) from point X to point Y
(B) from point Y to point X
(C) zero at all times
(D) oscillating with decreasing amplitude
(E) oscillating with constant amplitude
63. After the switch S has been closed for a very
long time, the currents in the two circuits are
(A) zero in both circuits
(B) zero in circuit 1 and V/R2 in circuit 2
(C) V/R1 in circuit 1 and zero in circuit 2
(D) V/R1 in circuit I and V/R2 in circuit 2
(E) oscillating with constant amplitude in both
circuits
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Multiple Choice 1988 C
Page 143
Questions 66-67
Positive charge Q is uniformly distributed over a thin
ring of radius a that lies in a plane perpendicular to
the x-axis. with its center at the origin 0, as shown
above.
66. The potential V at points on the x-axis is
represented by which of the following functions?
kQ
kQ
(A) V ( x ) 
(B) V ( x ) 
2
2
x a
a2  x2
kQ
kQ
(C) V ( x ) 
(D) V ( x ) 
2
x
x
kQ
(E) V ( x ) 
ax
67. Which of the following graphs best represents the
electric field along the positive x-axis?
68. In the circuit shown above, the emf's of the
batteries are given, as well as the currents in the
outside branches and the resistance in the middle
branch. What is the magnitude of the potential
difference between X and Y ?
(A) 4 V
(B) 8 V
(C) 10 V
(D) 12 V
(E) 16 V
69. Two identical parallel conducting rings have a
common axis and are separated by a distance a,
as shown above. The two rings each carry a
current I, but in opposite directions. At point P,
the center of the ring on the left the magnetic
field due to these currents is
(A) zero
(B) in the plane perpendicular to the x-axis
(C) directed in the positive x-direction
(D) directed in the negative x-direction
(E) none of the above
70. A sheet of mica is inserted between the plates of
an isolated charged parallel-plate capacitor.
Which of the following statements is true?
(A) The capacitance decreases.
(B) The potential difference across the capacitor
decreases.
(C) The energy of the capacitor does not change.
(D) The charge on the capacitor plates decreases
(E) The electric field between the capacitor
plates increases.
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Multiple Choice 1993 C
1.
Page 144
In the absence of air friction, an object dropped
near the surface of the Earth experiences a
constant acceleration of about 9.8 m/s2. This
means that the
(A) speed of the object increases 9.8 m/s during
each second
(B) speed of the object as it falls is 9.8 m/s
(C) object falls 9.8 meters during each second
(D) object falls 9.8 meters during the first second
only
(E) derivative of the distance with respect to time
for the object equals 9.8 m/s2
2.
A 500-kilogram sports car accelerates uniformly
from rest, reaching a speed of 30 meters per
second in 6 seconds. During the 6 seconds, the
car has traveled a distance of
(A) 15 m
(B) 30 m
(C) 60 m
(D) 90 m
(E) 180 m
3.
At a particular instant, a stationary observer on
the ground sees a package falling with speed v1
at an angle to the vertical. To a pilot flying
horizontally at constant speed relative to the
ground, the package appears to be falling
vertically with a speed v2 at that instant. What is
the speed of the pilot relative to the ground?
(A) v1 + v2
(B) v1 - v2
(C) v2-v1
(D)
v1 v 2
2
2
(E)
v1 v 2
2
5.
If F1 is the magnitude of the force exerted by the
Earth on a satellite in orbit about the Earth and
F2 is the magnitude of the force exerted by the
satellite on the Earth, then which of the
following is true?
(A) F1 is much greater than F2. (B) F1 is slightly
greater than F2.
(C) F1 is equal to F2.
(D) F2 is slightly
greater than F1
(E) F2 is much greater than
F1
6.
A ball is thrown upward. At a height of 10
meters above the ground, the ball has a potential
energy of 50 joules (with the potential energy
equal to zero at ground level) and is moving
upward with a kinetic energy of 50 joules. Air
friction is negligible. The maximum height
reached by the ball is most nearly
(A) 10 m
(B) 20 m
(C) 30 m
(D) 40 m
(E) 50 m
2
A block on a horizontal frictionless plane is attached
to a spring, as shown above. The block oscillates
along the x-axis with simple harmonic motion of
amplitude A.
4.
A ball initially moves horizontally with velocity
vi, as shown above. It is then struck by a stick.
After leaving the stick, the ball moves vertically
with a velocity vf, which is smaller in magnitude
than vi. Which of the following vectors best
represents the direction of the average force that
the stick exerts on the ball?
7.
Which of the following statements about the
block is correct?
(A) At x = 0, its velocity is zero.
(B) At x = 0, its acceleration is at a maximum.
(C) At x = A, its displacement is at a maximum.
(D) At x = A, its velocity is at a maximum.
(E) At x = A, its acceleration is zero.
8.
Which of the following statements about energy
is correct?
(A) The potential energy of the spring is at a
minimum at x = 0.
(B) The potential energy of the Spring is at a
minimum at x = A.
(C) The kinetic energy of the block is at a
minimum at x =0.
(D) The kinetic energy of the block is at a
maximum at x = A.
(E) The kinetic energy of the block is always
equal to the potential energy of the spring.
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Multiple Choice 1993 C
9
Two 0.60-kilogram objects are connected by a
thread that passes over a light, frictionless
pulley, as shown above. The objects are initially
held at rest. If a third object with a mass of 0.30
kilogram is added on top of one of the
0.60-kilogram objects as shown and the objects
are released, the magnitude of the acceleration of
the 0.30-kilogram object is most nearly
(A) 10.0 m/s2
(B) 6.0 m/s2
(C) 3.0 m/s2
(D) 2.0 m/s2
(E) 1.0 m/s2
Page 145
11. Two balls are on a frictionless horizontal
tabletop. Ball X initially moves at 10 meters per
second, as shown in Figure I above. It then
collides elastically with identical ball Y. which is
initially at rest. After the collision, ball X moves
at 6 meters per second along a path at 530 to its
original direction, as shown in Figure II above.
Which of the following diagrams best represents
the motion of ball Y after the collision?
10. During a certain time interval, a constant force
delivers an average power of 4 watts to an
object. If the object has an average speed of 2
meters per second and the force acts in the
direction of motion of the object, the magnitude
of the force is
(A) 16 N
(B) 8 N
(C) 6 N
(D) 4N
(E) 2N
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Multiple Choice 1993 C
Page 146
Questions 12-13
An ant of mass m clings to the rim of a flywheel of
radius r, as shown above. The flywheel rotates
clockwise on a horizontal shaft S with constant
angular velocity . As the wheel rotates, the ant
revolves past the stationary points I, II, III, and IV.
The ant can adhere to the wheel with a force much
greater than its own weight.
12. It will be most difficult for the ant to adhere to
the wheel as it revolves past which of the four
points?
(A) I
(B) II
(C) III
(D) IV
(E) It will be equally difficult for the ant to
adhere to the wheel at all points.
13. What is the magnitude of the minimum adhesion
force necessary for the ant to stay on the flywheel
at point III?
(A) mg
(B) m2r
(C) m2r2 + mg
(D) m2r - mg
(E) m2r + mg
14. A weight lifter lifts a mass m at constant speed to
a height h in time t How much work is done by
the weight lifter?
(A) mg
(B) mh
(C) mgh
(D) mght
(E) mgh/t
15. A conservative force has the potential energy
function U(x), shown by the graph above. A
particle moving in one dimension under the
influence of this force has kinetic energy 1.0
joule when it is at position x1 Which of the
following is a correct statement about the motion
of the particle?
(A) It oscillates with maximum position x2 and
minimum position x0.
(B) It moves to the right of x3 and does not
return.
(C) It moves to the left of x0 and does not return.
(D) It comes to rest at either x0 or x2.
(E) It cannot reach either x0 or x2.
16. A balloon of mass M is floating motionless in
the air. A person of mass less than M is on a
rope ladder hanging from the balloon. The
person begins to climb the ladder at a uniform
speed v relative to the ground. How does the
balloon move relative to the ground?
(A) Up with speed v
(B) Up with a speed less than v
(C) Down with speed v
(D) Down with a speed less than v
(E) The balloon does not move.
17. If one knows only the constant resultant force
acting on an object and the time during which
this force acts, one can determine the
(A) change in momentum of the object
(B) change in velocity of the object
(C) change in kinetic energy of the object
(D) mass of the object
(E) acceleration of the object
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Multiple Choice 1993 C
Page 147
18. When an object is moved from rest at point A to
rest at point B in a gravitational field, the net
work done by the field depends on the mass of
the object and
(A) the positions of A and B only
(B) the path taken between A and B only
(C) both the positions of A and B and the path
taken between them
(D) the velocity of the object as it moves
between A and B
(E) the nature of the external force moving the
object from A to B
19. An object is shot vertically upward into the air
with a positive initial velocity. Which of the
following correctly describes the velocity and
acceleration of the object at its maximum
elevation?
Velocity
Acceleration
(A) Positive
Positive
(B) Zero
Zero
(C) Negative
Negative
(D) Zero
Negative
(E) Positive
Negative
20. A turntable that is initially at rest is set in motion
with a constant angular acceleration . What is
the angular velocity of the turntable after it has
made one complete revolution?
(A) 2
(D) 2
(B) 2
(E) 4
(C)
4
21. An object of mass m is moving with speed v0 to
the right on a horizontal frictionless surface, as
shown above, when it explodes into two pieces.
Subsequently, one piece of mass 2/5 m moves
with a speed v0/2 to the left. The speed of the
other piece of the object is
(A) vo/2
(B) vo/3
(C) 7vo/5
(D) 3vo/2
(E) 2vo
Questions 23-24
Two identical massless springs are hung from a
horizontal support. A block of mass 1.2 kilograms is
suspended from the pair of springs, as shown above.
When the block is in equilibrium, each spring is
stretched an additional 0.15 meter.
23. The force constant of each spring is most nearly
(A) 40 N/m
(B) 48 N/m
(C) 60 N/m
(D) 80 N/m
(E) 96 N/m
24. When the block is set into oscillation with
amplitude A, it passes through its equilibrium
point with a speed v. In which of the following
cases will the block, when oscillating with
amplitude A, also have speed v when it passes
through its equilibrium point?
I. The block is hung from only one of the two
springs.
II. The block is hung from the same two springs,
but the springs are connected in series rather than
in parallel.
III. A 0.5 kilogram mass is attached to the block.
(A) None
(B) III only
(C) I and II only
(D) II and III only
(E) I, II, and III
25. A spring-loaded gun can fire a projectile to a
height h if it is fired straight up. If the same gun
is pointed at an angle of 45° from the vertical,
what maximum height can now be reached by
the projectile?
(A) h/4
(D)
22. A newly discovered planet has twice the mass of
the Earth, but the acceleration due to gravity on
the new planet's surface is exactly the same as
the acceleration due to gravity on the Earth's
surface. The radius of the new planet in terms of
the radius R of Earth is
(A) ½R
(B)
(D) 2R
(E) 4R
2
2
R
(C)
h
2
(B)
h
2 2
(C) h/2
(E) h
2R
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Multiple Choice 1993 C
Page 148
28. Which of the following best indicates the
direction of the net force on the ball at point P ?
(A)
(B)
(C)
(D)
(E)
26. The rigid body shown in the diagram above
consists of a vertical support post and two
horizontal crossbars with spheres attached. The
masses of the spheres and the lengths of the
crossbars are indicated in the diagram. The body
rotates about a vertical axis along the support
post with constant angular speed . If the masses
of the support post and the crossbars are
negligible, what is the ratio of the angular
momentum of the two upper spheres to that of
the two lower spheres?
(A) 2/1
(B) 1/1
(C) 1/2
(D) 1/4
(E) 1/8
Questions 27-28
Questions 29 - 30
A 5-kilogram sphere is connected to a 10-kilogram
sphere by a rigid rod of negligible mass, as
shown above.
29. Which of the five lettered points represents the
center of mass of the sphere-rod combination?
(A) A
(B) B
(C) C
(D) D
(E) E
30. The sphere-rod combination can be pivoted
about an axis that is perpendicular to the plane of
the page and that passes through one of the five
lettered points. Through which point should the
axis pass for the moment of inertia of the
sphere-rod combination about this axis to be
greatest?
(A) A
(B) B
(C) C
(D) D
(E) E
A ball is thrown and follows a parabolic path, as
shown above. Air friction is negligible. Point Q is the
highest point on the path.
27. Which of the following best indicates the
direction of the acceleration, if any, of the ball at
point Q ?
(A)
(B)
(C)
(D)
(E) There is no acceleration of the ball at point
Q.
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Multiple Choice 1993 C
Page 149
31. A small mass is released from rest at a very great
distance from a larger stationary mass. Which of
the following graphs best represents the
gravitational potential energy U of the system of
the two masses as a function of time t?
(A)
U
O
(B)
32. A satellite S is in an elliptical orbit around a
planet P, as shown above, with r1 and r2 being its
closest and farthest distances, respectively, from
the center of the planet. If the satellite has a
speed v1 at its closest distance, what is its speed
at its farthest distance?
t
U
O
t
(A)
(C)
U
O
t
(D)
U
O
(E)
U
O
t
t
r1
v
r2 1
(C)
r
(E)
r 2 r 1
v
r 1r 2 1
2
 r 2 v 1
(B)
r2
v
r1 1
r 1r 2
(D)
v1
2
33. A simple pendulum consists of a l.0-kilogram
brass bob on a string about 1.0 meter long. It has
a period of 2.0 seconds. The pendulum would
have a period of 1.0 second if the
(A) string were replaced by one about 0.25 meter
long
(B) string were replaced by one about 2.0 meters
long
(C) bob were replaced by a 0.25-kg brass sphere
(D) bob were replaced by a 4.0-kg brass sphere
(E) amplitude of the motion were increased
34. A block of mass 5 kilograms lies on an inclined
plane, as shown above. The horizontal and
vertical supports for the plane have lengths of 4
meters and 3 meters, respectively. The
coefficient of friction between the plane and the
block is 0.3. The magnitude of the force F
necessary to pull the block up the plane with
constant speed is most nearly
(A) 30 N
(B) 42 N
(C) 49 N
(D) 50 N
(E) 58 N
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Multiple Choice 1993 C
Page 150
B) infinite only if the net charge enclosed by the
surface is zero
C) zero if only negative charges are enclosed by
the surface
D) zero if only positive charges are enclosed by
the surface
E) zero if the net charge enclosed by the surface
is zero
35. A rod of negligible mass is pivoted at a point that
is off-center, so that length l 1 is different from
length l2. The figures above show two cases in
which masses are suspended from the ends of the
rod. In each case the unknown mass m is
balanced by a known mass, M1 or M2, so that the
rod remains horizontal. What is the value of m in
terms of the known masses?
(A) Ml + M2
(B) ½(Ml + M2)
(C) Ml
M2
(D) ½M1M2
(E)
M1 M 2
36. From the electric field vector at a point, one can
determine which of the following?
I. The direction of the electrostatic force on
a test charge of known sign at that point
II. The magnitude of the electrostatic force
exerted per unit charge on a test charge at that
point
III. The electrostatic charge at that point
A) I only B) III only C) I and II only
D) II and III only E) I, II, and III
37. A circular ring made of an insulating material is
cut in half. One half is given a charge -q
uniformly distributed along its arc. The other
half is given a charge + q also uniformly
distributed along its arc. The two halves are then
rejoined with insulation at the junctions J, as
shown above. If there is no change in the charge
distributions, what is the direction of the net
electrostatic force on an electron located at the
center of the circle?
A) Toward the top of the page B) Toward the
bottom of the page C) To the right
D) To the left E) Into the page.
Questions 39-40 refer to the system of six
2-microfarad capacitors shown below.
39. The equivalent capacitance of the system of
capacitors is
A) 2/3F
B) 4/3 F
C) 3 F
D) 6
F
E) 12 F
40. What potential difference must be applied
between points X and Y so that the charge on
each plate of each capacitor will have magnitude
6 microcoulombs?
A) 1.5 V
B) 3V
C) 6 V
D) 9 V
E) 18 V
41. Four positive charges of magnitude q are
arranged at the corners of a square, as shown
above. At the center C of the square, the
potential due to one charge alone is Vo and the
electric field due to one charge alone has
magnitude Eo. Which of the following correctly
gives the electric potential and the magnitude of
the electric field at the center of the square due to
all four charges?
Electric Potential Electric Field
A)
Zero
Zero
B)
Zero
2Eo
C)
2 Vo
4Eo
D)
4 Vo
Zero
E)
4 Vo
2Eo
38. The net electric flux through a closed surface is
A) infinite only if there are no charges enclosed
by the surface
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Multiple Choice 1993 C
42. A large parallel-plate capacitor is being charged
and the magnitude of the electric field between
the plates of the capacitor is increasing at the rate
dE/dt. Which of the following statements is
correct about the magnetic field in the region
between the plates of the charging capacitor?
A) It is parallel to the electric field.
B) Its magnitude is directly proportional to
dE/dt.
C) Its magnitude is inversely proportional to
dE/dt.
D) Nothing about the field can be determined
unless the charging current is known.
E) Nothing about the field can be determined
unless the instantaneous electric field is known.
Page 151
Questions 45-47
In the circuit above, the emf's and the resistances
have the values shown. The current I in the circuit is
2 amperes.
45. The resistance R is
A) 1 
B) 2
E) 6 
C) 3 
D) 4 
46. The potential difference between points X and Y
is
A) 1.2 V
B) 6.0 V
C) 8.4 V
D)
10.8 V
E) 12.2 V
43. A cross section of a long solenoid that carries
current I is shown above. All of the following
statements about the magnetic field B inside the
solenoid are correct EXCEPT:
A) B is directed to the left.
B) An approximate value for the magnitude of B
may be determined by using Ampere's law.
C) The magnitude of B is proportional to the
current I.
D) The magnitude of B is proportional to the
number of turns of wire per unit length.
E) The magnitude of B is proportional to the
distance from the axis of the solenoid.
44. The power dissipated in a wire carrying a
constant electric current I may be written as a
function of I, the length l of the wire, the
diameter d of the wire, and the resistivity  of the
material in the wire. In this expression, the
power dissipated is directly proportional to
which of the following?
A) l only
B) d only
C) l and  only
D) d and  only
E) l, d, and 
47. How much energy is dissipated by the 1.5-ohm
resistor in 60 seconds?
A) 6 J
B) 180 J
C) 360 J
D) 720 J
E) 1,440 J
48. A conducting sphere of radius R carries a charge
Q. Another conducting sphere has a radius R/2,
but carries the same charge. The spheres are far
apart. The ratio of the electric field near the
surface of the smaller sphere to the field near the
surface of the larger sphere is most nearly
A) 1/4
B) 1/2
C) 1
D) 2
E) 4
49. Two charges, -2Q and +Q, are located on the
x-axis, as shown abovE) Point P, at a distance
of 3D from the origin O, is one of two points on
the positive x-axis at which the electric potential
is zero. How far from the origin O is the other
point?
A) (2/3) D
B) D
C) 3/2 D
D) 5/3 D
E) 2D
50. What is the radial component of the electric field
associated with the potential V = ar-2 where a is a
constant?
A) -2ar-3
B) -2ar-1
C) ar-1
D) 2ar-1
-3
E) 2ar
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Multiple Choice 1993 C
Questions 51-52
Two concentric, spherical conducting shells have
radii r1 and r2 and charges Q1 and Q2, as shown
above. Let r be the distance from the center of the
spheres and consider the region r1 < r < r2.
51. In this region the electric field is proportional to
A) Q1/r2
B) (Q1 + Q2)/r2
C) (Q1 + Q2)/r
D) Q1/r1 + Q2/r
E) Q1/r + Q2/r2
52. In this region the electric potential relative to
infinity is proportional to
A) Q1/r2
B) (Q1 + Q2)/r2
C) (Q1 + Q2)/r
D) Q1/r1 + Q2/r
E) Q1/r + Q2/r2
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Page 152
Multiple Choice 1993 C
Page 153
Questions 52-53
A battery or batteries connected to two parallel plates
produce the equipotential lines between the plates
shown above.
53. Which of the following configurations is most
likely to produce these equipotential lines?
55. Two metal spheres that are initially uncharged
are mounted on insulating stands, as shown
above. A negatively charged rubber rod is
brought close to, but does not make contact with,
sphere X. Sphere Y is then brought close to X
on the side opposite to the rubber rod. Y is
allowed to touch X and then is removed some
distance away. The rubber rod is then moved far
away from X and Y. What are the final charges
on the spheres?
Sphere X
Sphere Y
A) Zero
Zero
B) Negative
Negative
C) Negative
Positive
D) Positive
Negative
E) Positive
Positive
56. The potential of an isolated conducting sphere of
radius R is given as a function of the charge q on
the sphere by the equation V = kq/R. If the
sphere is initially uncharged, the work W
required to gradually increase the total charge on
the sphere from zero to Q is given by which of
the following expressions?
A) W = kQ/R
B) W = kQ2/R
C) W
=

Q
0
( kq / R)dq
E) W =

Q
0
D) W =

Q
0
( kq 2 / R)dq
2
( kq / R )dq
Questions 57-58
54. The force on an electron located on the 0-volt
potential line is
A) 0 N B) I N, directed to the right
C) I
N, directed to the left
D) directed to the right, but its magnitude cannot
be determined without knowing the distance
between the lines
E) directed to the left, but its magnitude cannot
be determined without knowing the distance
between the lines
In the circuit shown above, the battery supplies a
constant voltage V when the switch S is closed. The
value of the capacitance is C, and the value of the
resistances are R1 and R2.
57. Immediately after the switch is closed, the
current supplied by the battery is
A) V/(R1 + R2)
B) V/R1
C) V/R2
D) V(R1 + R2)/R1R2
E) zero
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Multiple Choice 1993 C
58. A long time after the switch has been closed, the
current supplied by the battery is
A) V/(R1 + R2)
B) V/R1
C) V/R2
D) V(R1 + R2)/R1R2
E) zero
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Page 154
Multiple Choice 1993 C
Page 155
Questions 59-61 relate to the following circuit in
which the switch S has been open for a long time.
(D)
i
O
(E)
59. What is the instantaneous current at point X
immediately after the switch is closed?
A) 0
B) /R
C) /2R
D) /RL
E) L/2R
t
i
O
t
60. When the switch has been closed for a long time
what is the energy stored in the inductor?
A) L/2R
B) L2/2R2
C) L2 /4R2
2
2
2 2
D) LR /2
E)  R /4L
61. After the switch has been closed for a long time,
it is opened at time t = 0. Which of the
following graphs best represents the subsequent
current i at point X as a function of time t ?
(A)
i
O
t
(B)
i
O
(C)
62. A 30-ohm resistor and a 60-ohm resistor are
connected as shown above to a battery of emf 20
volts and internal resistance r. The current in
the circuit is 0.8 ampere. What is the value of r
?
A) 0.22 
B) 4.5 
C) 5 
D)
16
E) 70 
t
i
O
t
63. A square loop of wire 0.3 meter on a side carries
a current of 2 amperes and is located in a
uniform 0.05-tesla magnetic field. The left side
of the loop is aligned along and attached to a
fixed axis. When the plane of the loop is parallel
to the magnetic field in the position shown
above, what is the magnitude of the torque
exerted on the loop about the axis?
A) 0.00225 Nm
B) 0.0090 Nm
C)
0.278 Nm
D) 1.11 Nm
E) 111 Nm
64. A solid nonconducting sphere of radius R has a
charge Q uniformly distributed throughout its
volume. A Gaussian surface of radius r with r <
R is used to calculate the magnitude of the
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Multiple Choice 1993 C
Page 156
electric field E at a distance r from the center of
the sphere. Which of the following equations
results from a correct application of Gauss's law
for this situation?
A) E(4R2) = Q/o
B) E(4r2) = Q/o
2
3
C) E(4r ) = (Q3r )/(o4R)
D) E(4r2) = (Qr3)/(oR3)
E) E(4r2) = 0
65. Two long parallel wires are a distance 2a apart,
as shown above. Point P is in the plane of the
wires and a distance a from wire X. When there
is a current I in wire X and no current in wire Y,
the magnitude of the magnetic field at P is Bo.
When there are equal currents I in the same
direction in both wires, the magnitude of the
magnetic field at P is
A) 2Bo/3
B) Bo
C) 10Bo/9
D) 4Bo/3
E) 2 Bo
66. In the figure above, the north pole of the magnet
is first moved down toward the loop of wire,
then withdrawn upward. As viewed from above,
the induced current in the loop is
A) always clockwise with increasing magnitude
B) always clockwise with decreasing magnitude
C) always counterclockwise with increasing
magnitude
D) always counterclockwise with decreasing
magnitude
E) first counterclockwise, then clockwise
68. The point charge Q shown above is at the center
of a metal box that is isolated, ungrounded, and
uncharged. Which of the following is true?
A) The net charge on the outside surface of the
box is Q.
B) The potential inside the box is zero.
C) The electric field inside the box is constant.
D) The electric field outside the box is zero
everywhere.
E) The electric field outside the box is the same
as if only the point charge (and not the box) were
there.
69. Which of the following capacitors, each of which
has plates of area A, would store the most charge
on the top plate for a given potential difference V
?
67. A variable resistor is connected across a constant
voltage source. Which of the following graphs
represents the power P dissipated by the resistor
as a function of its resistance R ?
Copyright © 1988-2002 by College Entrance Examination Board. All rights reserved.
College Board, Advanced Placement Program, AP, SAT, and the acorn logo are registered trademarks of the College Entrance Examination Board.
Multiple Choice 1993 C
70. If the ammeter in the circuit above reads zero,
what is the resistance R ?
A) 1.5 
B) 2
C) 4 
D) 5 
E) 6
Copyright © 1988-2002 by College Entrance Examination Board. All rights reserved.
College Board, Advanced Placement Program, AP, SAT, and the acorn logo are registered trademarks of the College Entrance Examination Board.
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