8. Suppose the velocity of a falling sphere of mass m due to the gravity and the air resistance is given by v(t) = v₁(1-e⁻ᵞᵗ) with the condition that the air resistance vanishes when v = 0. The formula of the air drag force is then given by

(A) -2mγv

(B) -mγv

(C) -mγv²

(D) -mγv²/2.

9. Which of the following statements is not compatible with other 3 statements? (A) It is impossible for a heat engine that operates in a cycle to convert its heat input completely into work. (B) It is impossible for a cyclical device to transfer heat continuously from a cold body to a hot one without the input of work or other effect on the environment. (C) The change in the internal energy of the system comes from the heat input minus the work done on its surroundings. (D) The entropy change of an isolated system always stays constant or increases.

10. The rate of heat flow through a slab is R. If the slab thickness is doubled, its cross-sectional area is halved, and the temperature difference across it is doubled, then the rate of heat flow becomes (A) 2R (B) R/2 (C) 8R (D) R/8.

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.

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 conductingwire, 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.

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.

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