A magnetic field of 0.1T forces a proton beam of 1.5 mA to move ina circle of radius 0.1 m. The plane of the circle is perpendicularto the magnetic field.

47. Of the following, which is the best estimate of the speed of aproton in the beam as it moves in the circle?

(A) 10-2 m/s (B) 103 m/s (C) 106 m/s (D) 108 m/s (E) 1015 m/s

52. An ideal gas is initially in a state that corresponds to point1 on the graph above, where it has presÂ¬sure p1, volume V1, andtemperature T1. The gas undergoes an isothermal process representedby the curve shown, which takes it to a final state 3 attemperature T3. If T2 and T4 are the temperaÂ¬tures the gas wouldhave at points 2 and 4, respecÂ¬tively, which of the followingrelationships is true?

(A) T1 < T3 (B) T1 < T2 (C) T1 < T4 (D) T1 = T2 (E) T1 =T4

53. The absolute temperature of a sample of monatomic ideal gas isdoubled at constant volume. What effect, if any, does this have onthe pressure and density of the sample of gas?

Pressure Density

(A) Remains the same Remains the same

(B) Remains the same Doubles

(C) Doubles Remains the same

(D) Doubles Is multiplied by a factor of 4

(E) Is multiplied by a factor of 4 Doubles

62. A sample of an ideal gas is in a tank of constant volume. Thesample absorbs heat energy so that its temperature changes from 300K to 600 K. If v1 is the average speed of the gas molecules beforethe absorption of heat and v2 is their average speed after theabsorption of heat, what is the ratio v2/ v1 ?

(A) 1/2 (B) 1 (C) (D) 2 (E) 4

63. Two people of unequal mass are initially standing still on icewith negligible friction. They then simulÂ¬taneously push each otherhorizontally. Afterward, which of the following is true?

(A) The kinetic energies of the two people are equal.

(B) The speeds of the two people are equal.

(C) The momenta of the two people are of equal magnitude.

(D) The center of mass of the two person system moves in thedirection of the less massive person.

(E) The less massive person has a smaller initial acceleration thanthe more massive person.

64. Two parallel conducting plates, separated by a distance d, areconnected to a battery of emf e. Which of the following is correctif the plate separaÂ¬tion is doubled while the battery remainsconnected?

(A) The electric charge on the plates is doubled.

(B) The electric charge on the plates is halved.

(C) The potential difference between the plates is doubled.

(D) The potential difference between the plates is halved

(E) The capacitance is unchanged.

68. A rod on a horizontal tabletop is pivoted at one end and isfree to rotate without friction about a vertical axis, as shownabove. A force F is applied at the other end, at an angle ? to therod. If F were to be applied perpendicular to the rod, at whatdistance from the axis should it be applied in order to proÂ¬ducethe same torque?

(A) L sin ? (B) L cos ? (C) L (D) L tan ? (E) L

70. A 4 ÂµF capacitor is charged to a potential differÂ¬ence of 100V. The electrical energy stored in the capacitor is

(A) 2 x 10-10 J (B) 2 x 10 8 J (C) 2 x 10 6 J (D) 2x 10-4 J (E) 2 x10-2 J