6. A thin uniform rod of length L is pivoted about a horizontal axis at one end. What is the angular frequency when it does small-angle oscillations? Assume that the acceleration of gravity is g.
(A)
(B)
(C)
(D)
(E) none of the above

7. The figure shows a gyroscope, consisting of a solid disk and a weight mounted on a shaft. The disk spins about the shaft freely. The shaft is mounted on a stand and can pivot freely. The position of the weight is adjusted, so the weight balances the disk. The spinning direction of the disk is as indicated. If you gently push the end of the shaft upward as shown in the figure, the end of the shaft will move (A) toward you (B) away from you (C) downward (D) upward (E) the disk does not move

8. A 2-m-long string is clamped at both ends. If the wave speed on the string is 60 m/s, what is the lowest standing-wave frequency? (A) 7.5 Hz (B) 10 Hz (C) 15 Hz (D) 20 Hz (E) 30 Hz

9. The pressure of an ideal gas becomes three times of its initial pressure during an adiabatic process. What is the ratio of its final volume to its initial volume? γ is the ratio of the constant-pressure specific heat to the constant-volume specific heat of this. (A) 1/3 (B) 3-γ (C) 3γ (D) 3-1/γ (E)  31/γ

10. An ideal gas is slowly compressed to one-half its original volume with no change in pressure. If the original root-mean-square speed of the gas molecules was v, the new speed after the compression is (A) v (B) 2v (C) v (D) v/2 (E) v/

11. When n moles of a monatomic ideal gas doubles its volume at constant temperature, how much does its entropy change? R is the universal gas constant. (A) nRln2 (B) nR (C) nR (D) 2nR (E) nR

12. A Carnot engine operates between reservoirs at 500 K and 300 K. When it discharges 150 J to the lower-temperature reservoir, how much is the work done? (A) 50 J (B) 100 J (C) 150 J (D) 200 J (E) 250 J

13. When an ideal gas undergoes an adiabatic free expansion, what remains unchanged during the process? (A) volume (B) temperature (C) pressure (D) entropy (E) density

14. Consider a large open tank with a small hole at its bottom. The tank is filled with water to a height of 1.25 m. What is the speed at which the water exits the tank through the hole? The acceleration of gravity is 10 m/s². (A) 1.25 m/s (B) 3.53 m/s (C) 5 m/s (D) 12.5 m/s (E) 25 m/s

15. An electric dipole with a dipole moment p is within a uniform electric field E. If the electric dipole is at an angle of 60° to the electric field, what is the external work needed to rotate the electric dipole to be perpendicular to the electric field? (A) pE (B) -pE (C)pE(D) -pE (E) (1-)pE

16. Consider a system consisting of a conducting sphere and a conducting spherical shell that are concentric. The radius of the sphere is a； the radii of the inner and outer surfaces of the shell are 2a and 3a, respectively, as shown in the figure. If the sphere carries a net charge of -Q and the shell carries a net charge of +2Q, what is the electric potential at a distance of a/2 from the center when the system is in electrostatic equilibrium? Assume that the zero of potential is at infinity. k is the Coulomb's constant. (A) -kQ/a (B) -2kQ/a (C) 2kQ/a (D) kQ/3a (E) -kQ/6a

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