15. A metal sphere of radius 2R stores an amount of charge Q initially.
It then connects to another metal sphere of radius R by a conducting
wire, which is removed after the charge is redistributed. Suppose the two spheres are far away apart.
The ratio of the electric-field strength just outside the surface of the larger sphere to that of the smaller spheres is
(A) 2:1
(B) 3:2
(C) 1:3
(D) 1:2.

11. A molar monatomic ideal gas does adiabatic free expansion from an initial state of pressure P and volume V/2 to volume 2V, and then raise the pressure to 2P while keeping constant volume. Find the change of entropy: (A)Rln2(B)Rln2(C)Rln 2 (D) Rln 2.

12. The temperature of low-pressure hydrogen is reduced from 127°C to 47°C. The rms speed of its molecules decreases by approximately (A) 5% (B) 10% (C) 15 % (D) 20%.

13. Which of the following statements about the Carnot engine is not correct? (A) The efficiency of a Carnot engine operating between temperatures T₁ and T2 (T₁ ＞ T2) is 1 – T2/T1. (B) The efficiency of any reversible engine is identical to that of a Carnot engine for given two heat reservoirs. (C) A Carnot engine has the best efficiency for given two heat reservoirs. (D) The entropy of a Carnot engine during a cycle remains constant.

14. Consider a partial circuit shown in the figure. Suppose every resistor is of identical resistance R. Find the effective resistance between A and B: (A) R (B) R/2 (C) 2R/3 (D) R/6.

16. A henry (H) is the same as (A) J/V (B) C/J (C) J/V2 (D) J/A2.

17. A negatively charged particle of mass m and charge q＜ 0 is restricted to move freely along the axis of a circular ring of radius R. A positive charge is uniformly distributed over the ring with a charge density (charge per unit length) λ＞ 0. Suppose the vertical coordinate of the particle relative to the center of the circular ring is y and y << R. Find the period of oscillation for small y: (A)2πR (B) 2πR (C) 2πR(D)πR

18. Suppose H+ and He2+ particles are injected into the device as shown in the figure from the left hole. Once they come out from the right hole, they immediately enter a region of another 9 uniform magnetic field B'perpendicular to their velocities. What is the ratio of radii of their circular motion rH+/rHe2+ under the field B'? (A) 2 (B) 1/2 (C) 1/(D) 4.

19. In an experiment on Newton's rings as shown in the figure, where we consider a lens of maximum thickness t and refractive index n. The radius of curvature of the spherical surface is R. When a light of wavelength A is incident from the top, the observed radius of the 3th bright fringe is given by (A) (B) (C) (D) 2Rλ/t.

20. A Rydberg atom is an atom with one of its electrons being excited to a state of a very large principle quantum number n, called a Rydberg state. For a Rydberg hydrogen atom whose diameter is approximately 1 µm, estimate the corresponding principle quantum number n: (Hint: For the ground state, n = 1, the diameter of a hydrogen atom is approximately 1 Å.)(A) 80 (B) 100 (C) 120 (D) 140.

21. Alice is initially on the moon and takes a rocket of speed 0.8 c to the earth. How long does it take for Alice to arrive at the earth according to Alice's watch supposing the moon-to-earth distance is approximately 4 × 10⁵ km? (A) 0.01 s (B) 0.1 s (C) 1 s (D) 10 s.