12. Work done in an isobaric process by an ideal gas is
(A)\( nRT₂\ln(V₂/V₁)
(B)\( nRT_1(1-V₁/V₂)
(C)\( nRT_1\lnV₁/V₂)
(D)\( nRT_1(1-V₂/V₁)

4. Where is the center of mass of the thin semicircular ring (mass M)? (A) (0, (B)\( (0,) (C)\( (0,) (D)\( (0,) (E)( π0,)

5. A dumbbell has a massless rod and a rod length of 2a. It is placed next to a solid sphere. What is the force difference (the tidal force) between the two particles? (A)\( \frac{4GMa}{5r^3} \) (B)\( \frac{4GMa}{r^3} \) (C)\( \frac{GMa}{r^3} \) (D)\( \frac{GMm}{r^3} \) (E)\( \frac{4GMma}{r^3} \)

6. A small disk of radius \( R_1 \) is fastened coaxially to a larger disk of radius \( R_2 \). The combination is free to rotate on a fixed axle, which is perpendicular to a horizontal frictionless table top, as shown in the overhead view below. The rotational inertia of the combination is I. A string is wrapped around the larger disk and attached to a block of mass m, on the table. Another string is wrapped around the smaller disk and is pulled with a force \( \overrightarrow{F} \) as shown in fig. below. The tension in the string pulling the block is: (A)\( \frac{mR_1F}{R_2} \) (B)\( \frac{mR_1R_2F}{I - mR_2^2} \) (C)\( \frac{mR_1R_2F}{I + mR_2^2} \) (D)\( \frac{mR_1R_2F}{I - mR_1R_2} \) (E)\( \frac{mR_1R_2F}{I + mR_1R_2} \)

7. A satellite is in elliptical orbit around Earth as shown. If L denotes the magnitude of its angular momentum and K denotes kinetic energy: (A)\( L_2 ＞ L_1 \) and \( K_2 ＞ K_1 \) (B)\( L_2 ＞ L_1 \) and \( K_2 = K_1 \) (C)\( L_2 = L_1 \) and \( K_2 = K_1 \) (D)\( L_2 ＜ L_1 \) and \( K_2 = K_1 \) (E)\( L_2 = L_1 \) and \( K_2 ＞ K_1 \)

8. A simple pendulum is suspended from the ceiling of an elevator. The elevator is accelerating upwards with acceleration a. The period of this pendulum, in terms of its length L, g and a is: (A)\( 2\pi\sqrt{L/g} \) (B)\( 2\pi\sqrt{\frac{L}{g+a}} \) (C)\( 2\pi\sqrt{\frac{L}{g-a}} \) (D)\( 2\pi\sqrt{La} \) (E)\( \frac{1}{2\pi}\sqrt{g/L} \)

9. A point source emits sound waves with a power output of 100 watts. What is the sound level (in dB) at a distance of 10 m? (A)139 (B)119 (C)129 (D)109 (E)10

10. Two harmonic waves traveling in opposite directions interfere to produce a standing wave described by \( y = 2\sin(\pi x)\cos(3\pi t) \) where x is in m and t is in s. What is the distance (in m) between the first two antinodes? (A)8 (B)2 (C)4 (D)1 (E)0.5

11. The temperature of n moles of an ideal monatomic gas is increased by T at constant pressure. The energy Q absorbed as heat, change \( E_{int} \) in internal energy, and work W done by the environment are given by: (A)\( Q = \frac{5}{2}nRT \), \( E_{int} = 0 \), \( W = -nRT \) (B)\( Q = \frac{5}{2}nRT \), \( E_{int} = \frac{5}{2}nRT \), \( W = -\frac{3}{2}nRT \) (C)\( Q = \frac{5}{2}nRT \), \( E_{int} = \frac{5}{2}nRT \), \( W = 0 \) (D)\( Q = \frac{3}{2}nRT \), \( E_{int} = 0 \), \( W = -nRT \) (E)\( Q = \frac{5}{2}nRT \), \( E_{int} = \frac{3}{2}nRT \), \( W = -nRT \)

13. During a reversible adiabatic expansion of an ideal gas, which of the following is NOT true? (A)\( pV^{\gamma} = \text{constant} \) (B)\( pV = nRT \) (C)\( TV^{\gamma-1} = \text{constant} \) (D)\( W = -pdV \) (E)\( pV = \text{constant} \)

14. Positive charge Q is placed on a conducting spherical shell with inner radius \( R_1 \) and outer radius \( R_2 \). A point charge q is placed at the center of the cavity. The magnitude of the electric field at a point outside the shell, a distance r from the center, is: (A) (B) (C)(D)(E)

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