4. An ideal gas is allowed to undergo a free expansion. If its initial volume is V₁ and its final volume isV₂ , the change in entropy is
(A) nR ln ( V₂ /V₁ )
(B) nRT ln ( V₂ /V₁ ) 
(C) nk ln ( V₂ /V₁ ) 
(D) 0
(E) nR

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1. Carts A and B have equal masses and travel equal distances D on side-by-side straight frictionless tracks while a constant force F acts on A and a constant force 2F acts on B. Both carts start from rest. The velocities vA  and  vB of the bodies at the end of distance D are related by (A) (B) (C) (D) (E)

2. A solid sphere, spherical shell, solid cylinder and a cylindrical shell all have the same mass m and radius R. If they are all released from rest at the same elevation and roll without slipping, which reaches the bottom of an inclined plane first? (A) solid sphere (B) spherical shell (C) solid cylinder (D) cylindrical shell (E) all take the same time

3. Cubical blocks of mass m and side l are piled up in a vertical column. The total gravitational potential energy of a column of three blocks is (A) 2.5 mg (B) 3 mg (C) 4.5 mg (D) 6 mg (E) 9 mg

5. A parallel plate capacitor of capacitance C0 has plates of area A with separation d between them. When it is connected to a battery of voltage V0 , it has charge of magnitude Q0 on its plates. While it is connected to the battery, the space between the plates is filled with a material of dielectric constant 3. After the  dielectric is added, the magnitude of the charge on the plates and the potential difference between them are (A) (B) (C) (D) (E)

6. To decrease the intensity of the sound you are hearing from your speaker system by a factor of 36, you can (A) reduce the amplitude by a factor of 18 and increase your distance from the speaker by a factor of 2. (B) reduce the amplitude by a factor of 4 and increase your distance from the speaker by a factor of 3. (C) reduce the amplitude by a factor of 2 and increase your distance from the speaker by a factor of 3. (D) reduce the amplitude by a factor of 3 and increase your distance from the speaker by a factor of 12. (E) reduce the amplitude by a factor of 3 and increase your distance from the speaker by a factor of 4.

7. If an R = 1 kΩ resistor, a C = 1 µF capacitor, and an L = 0.2 H inductor are connected in series with a V = 150 sin (377t) volts source, what is the maximum current delivered by the source? (A) 0.007 A (B) 27 mA (C) 54 mA (D)0.0308mA(E)0.34A

8. In which process will the internal energy of the system NOT change? (A) An adiabatic expansion of an ideal gas. (B) The evaporation of a quantity of a liquid at its boiling point. (C) An isothermal compression of an ideal gas. (D) An isobaric expansion of an ideal gas. (E) The freezing of a quantity of liquid at its melting point. 

9. Two balls, projected at different times so they don’t collide, have trajectories A and B, as shown below. Which statement is correct? (A) v 0B must be greater than v 0A. (B) Ball B is in the air for a longer time than ball A. (C) Ball A is in the air for a longer time than ball B. (D) Ball B has a greater acceleration than ball A. (E) Ball A has a greater acceleration than ball B.

10. A binary star system in the constellation Orion has an angular separation between the two stars of 1.2 × 10-5radians. If λ = 5 × 10–7 m, what is the smallest aperture (diameter) telescope that may be used to resolve the two stars? (A) 10 cm (B) 5 cm (C) 50 cm (D) 1 m (E) 4 m