3. A uniform sphere of radius R has a spherical hole of radius R/2 removed. The center of the sphere and the hole are located at x = 0 and x = -R/2, as shown in the figure. Where is the center of the mass of this system?

(A) x = 0
(B) x = R
(C) x = R
(D) x = R
(E) x = R

4. Consider an infinite wire carrying a current I as shown in the figure. The curve is a semicircle of radius a. What is the magnetic field at the center of the semicircle P? μ₀ is the vacuum permeability. (A)(π + 1) (B)(π + 2) (C)(2π + 1) (D)(2π + 2)(E) none of the above

5. Two blocks m₁(5 kg) and m₂(1 kg) are connected with a string via a pulley. The block m₂ is on a frictionless incline of θ = 30°, as shown in the figure. What is the tension of the string? The acceleration of gravity is 10 m/s².(A) 4.2 N (B) 8.3 N (C) 12.5 N (D) 15.6 N (E) 18.8 N

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

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