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1. Torque is the rotational analogue of(A) kinetic energy (B) linear momentum (C) acceleration (D) force (E) mass
2. 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
(A) s (B) s (C) s (D) 2 s
(E) s
3. 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
(A) T (B) T (C) T (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.
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
7. 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
8. 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
9. 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
Questions 10-12A 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
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
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?
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?
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
(A) (B) (C) (D)
(E) vo
18. Which of the following is true for a system con-sisting 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 maxi-mum 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
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
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?
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?
(A) m (B) (C)
(D) (E) 1m
24. At what time after release will the block first return to its initial position?
(A) (B) (C) (D)
(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)= Cost (C) v(t) = -2cost (D) v(t) =-4 sint (E) v(t) = - 4sint
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)
(E)
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
(A) (B) (C)
(D) (E)
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
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
(A) ( B) (C)
(D) (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
(A) (B) (C) (D)
(E)
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
38. If i is current, t is time, E is electric field
intensity, and x is distance, the ratio of to
may be expressed in (A) coulombs (B) joules (C) newtons (D) farads (E) henrys
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 (E) 6Ea2
41. In the circuit shown above, what is the resistance R ? (A) 3 (B) 4 (c) 6 (D) 12 (E) 18
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
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
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
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
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
Questions 54 - 56
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)
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 (D) 9 F (E) 18 F
61. The energy stored in each capacitor is(A) 4 J (B) 6 J (C) 12 J (D) 18 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
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
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
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
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 ?
1. 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?
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.
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) S m
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
8. 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 (B) (C) D)
(E)
9. A piece of wire of uniform cross section is bent in the shape shown above. What are the coordinates
of the center of mass?(A) (15/14, 6/7) (B) (6/7, 6/7) (C) (15/14, 8/7) (D) (1,1) (E) (1,6/7)
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 non-constant 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
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?
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
(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) 6 m/s2 (E) 8 m/s2
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
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) (B) (C) ½gL (D) gL (E) 2gL
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.
Questions 18-19 refer to the graph below of the displacement x versus time t for a particle in simple harmonic motion.
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?
19. Which of the following graphs shows the kinetic energy K of the particle as a function of its displacement x ?
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?
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) (E) Re2
22. Two artificial satellites, 1 and 2, orbit the Earth in circular orbits having radii R1 and R2, respec-tively, as shown above. If R2 = 2R1, the accelera-tions 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
(A) (B) (C)
(D) (E)
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
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?
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
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 (D) 9 m/s2 (E) 11 m/s2
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) (B) (C)
(D) (E)
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.)
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 + 3The 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
(A) (B) (C) vo
(D) (E) 2vo
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(D) 8 x 104 J (E) 12 x 104 J
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
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
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.
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?
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
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 ?
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.
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
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?
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
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?
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.
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
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
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 ?
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 ?
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?
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.
61. Which of the following equations implies that it is impossible to isolate a magnetic pole?
(A)
(B)
(C)
(D) (E) None of the above
Questions 62 - 63 refer to the diagram below of two conducting loops having a common axis.
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
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
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
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?
(A) (B)
(C) (D)
(E)
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.
1. 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) v v1
22
2 (E) v v1 22 2
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?
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
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.
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.
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
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
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?
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) m2r (C) m2r2 + mg (D) m2r - mg (E) m2r + 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
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 (B) 2 (C) 4 (D)2 (E) 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
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) 2
2R (C) 2 R
(D) 2R (E) 4RQuestions 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?
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
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 ?
(E) There is no acceleration of the ball at point Q.
28. Which of the following best indicates the direction of the net force on the ball at point P ?
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
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?
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?
(A) rr
v1
21 (B)
rr
v2
11
(C) r r v2 2 1 (D) r r
v1 212
(E)r rr r
v2 1
1 21
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
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) M M1 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.
38. The net electric flux through a closed surface is
A) infinite only if there are no charges enclosed by the surfaceB) infinite only if the net charge enclosed by the surface is zeroC) zero if only negative charges are enclosed by the surfaceD) zero if only positive charges are enclosed by the surfaceE) zero if the net charge enclosed by the surface is zero
Questions 39 - 40 refer to the system of six 2-microfarad capacitors shown below.
39. The equivalent capacitance of the system of capacitors isA) 2/3F 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 FieldA) Zero ZeroB) Zero 2Eo
C) 2 Vo 4Eo
D) 4 Vo ZeroE) 4 Vo 2Eo
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.
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
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 isA) 1 B) 2 C) 3 D) 4 E) 6
46. The potential difference between points X and Y isA) 1.2 V B) 6.0 V C) 8.4 V D) 10.8 V E) 12.2 V
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 nearlyA) 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 E) 2ar-3
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 toA) 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 toA) Q1/r2 B) (Q1 + Q2)/r2 C) (Q1 + Q2)/r D) Q1/r1 + Q2/r E) Q1/r + Q2/r2
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?
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 linesE) directed to the left, but its magnitude cannot be determined without knowing the distance between the 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 YA) Zero Zero B) Negative NegativeC) Negative PositiveD) Positive NegativeE) 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 =
( / )kq R dqQ
0 D) W = ( / )kq R dqQ 2
0E) W = ( / )kq R dq
Q 2
0
Questions 57-58
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 isA) V/(R1 + R2) B) V/R1 C) V/R2 D) V(R1 + R2)/R1R2 E) zero
Questions 59-61 relate to the following circuit in which the switch S has been open for a long time.
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
60. When the switch has been closed for a long time what is the energy stored in the inductor?
A) L/2R B) L2/2R2 C) L2 /4R2 D) LR2/22 E) 2R2/4L
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 ?
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
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 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(4R2) = Q/o B) E(4r2) = Q/o C) E(4r2) = (Q3r3)/(o4R) D) E(4r2) = (Qr3)/(oR3) E) E(4r2) = 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 isA) 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 isA) 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
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 ?
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 ?
