8. What is the entropy change for one mole ideal gas that expands from volume V to 4V in a free expansion process?
(A) 4 R
(B) 2 R
(C) (ln4) R
(D) (ln2) R
(E) R

4. A circular track of radius 1000 meters is banked at 30 degrees without any friction. What is required speed for a car to keep running on the circular track? (A) about 30 m/s (B) about 45 m/s (C) about 55 m/s (D) about 65 m/s (E) about 75 m/s

5. Two point masses 1 kg and 2 kg are on a massless bar with axis of rotation through the center of length 2 meters, and a sphere of radius 10 cm and of mass 100 kg is on the center of the bar, as shown below. What is the moment of inertia (kg∙m2 )? (A) 3.33 (B) 3.4 (C) 3.5 (D) 3.67 (E) 4

6. The disk A with moment of inertia I1 rotates with angular speed ω1 about a vertical frictionless axle. A second disk B with moment of inertia I2 rotates with angular speed ω2 drops on the disk A. Since two disks are rough and two disks eventually reach the same angler speed ω, what is the final angular speed ω? (A) (I1ω1+ I2ω2)/I1 (B) (I1ω1)/(I1+ I2) (C) (I1ω1+ I2ω2)/( I1+ I2) (D) (I2ω2)/( I1+ I2) (E) (I1ω1− I2ω2)/( I1+ I2)

7. The same force F is applied horizontally to bodies 1, 2, 3, and 4, of masses m, 2m, 3m, and 4m, initially at rest and on a frictionless surface, until each body has traveled distance d. The correct listing of the magnitudes of the velocities of the bodies, are . (A) (B) (C) (D) (E)

9. The superposition of two wavesand at the location x = 0 in space results in (A) Beats at a beat frequency of 6 Hz in a 153 Hz tone. (B) A tone at a frequency of 156 Hz, as well as beats at a beat frequency of 6 Hz in a 153 Hz tone. (C) Beats at a beat frequency of 3 Hz. (D) A pure tone at a frequency of 153 Hz. (E) A pure tone at a frequency of 156 Hz.

10. A diver swims from 2 meters to 10 meters below the surface of a lake. What is the pressure difference? (A) 54.5 kPa (B) 62.1 kPa (C) 78.4 kPa (D) 82.8 kPa (E) 98.2 kPa

11. A Carnot engine takes 2000 J of heat from a reservoir at 500 K, does some work, and discards some heat to reservoir at 300 K. What is its efficiency? (A) 0.2 (B) 0.3 (C) 0.4 (D) 0.5 (E) 0.6

12. A series of 3 uncharged concentric spherical conducting shells surround a small central charge q. The potential at a point outside the third shell, at distance r from the center, and relative to V = 0 at ∞, is (A) −3keq/r (B) +3keq/r (C) − (ln 3)keq/r (D) + (ln 3)keq/r (E) +keq/r

13. A conductor of radius r, length ℓ , and resistivity ρ has resistance R. It is melted down and formed into a new conductor, also cylindrical, with one fourth the length of the original conductor. The resistance of the new conductor is . (A) R (B) R (C) R (D) 4 R (E) 16 R

複選題14. There is an electric dipole in an electric field, as shown below. Which of the following statement is incorrect? (A) The dipole rotates clockwise. (B) The torque on +q points up. (C) The electric dipole moment is proportional to the distance from –q to +q. (D) The dipole has a max potential energy when it is perpendicular to E. (E) The electric dipole moment points from –q to +q.