6. A disk rolls down a 30-degree slope without slipping. Given the inertial moment of a disk (mass M and radius R) I = MR²/2, please find the frictional force for the disk during rolling down:
(A) 1 Mg
(B) 1/2 Mg
(C) 1/3 Mg
(D) 1/6 Mg
(E) 2/3 Mg

7. Connect three disks as shown in the following figure. Their centers form a regular triangle. Each disk of mass M, radius R has an inertial moment I = MR²/2 when rotating about the disk center. Calculate the total inertial moment of the three disks when rotating about the center of triangle (in unit of MR²). (A) 1.5 (B) 2.5 (C) 3.5 (D) 4.5 (E) 5.5

8. The intensity from a sound source is I. If another identical but independent sound source is placed next to it, what will be the change of intensity level? (A) 2 dB (B) 3 dB (C) 4 dB (D) 5 dB (E) 6 dB

9. Which of the following is a consequence of (or is implied by) the second law of thermodynamics: (A) for all cyclic processes we have ΔQ/T ＜ 0 (B) work cannot be completely converted to heat energy (C) heat energy cannot be completely converted to work (D) the reason all heat engine efficiencies are less than 100% is friction, which is unavoidable (E) in the Carnot engine, ΔS ＞ 0 for each cycle

10. As shown in the following, two large insulating parallel plates carry positive charge of equal magnitude, one positive and the other negative, that is distributed uniformly over their inner surfaces. Rank the points 1 through 5 according to the magnitude of the electric field at the points, least to greatest. (A) 1, 2, 3, 4, 5 (B) 5, 4, 3, 2, 1 (C) 1= 4 = 5, 2 = 3 (D) 2 = 3, 1 = 4 = 5 (E) 2 = 3, 1, 4 = 5

11. According to Hubble's Law the velocity of v of a galaxy moving away from Earth is proportional to its distance from Earth. Consider two galaxies one of which is twice as far away as the other from Earth at some instant of time. At subsequent times, the ratio of their distances to Earth will be: (A) 2 to 1. (B) greater than 2 to 1. (C) less than 2 to 1. (D) it depends on the specific time. (E) it depends on the positions of galaxies.

12. A person sits on a swing. When the person sits still, the swing oscillates back and forth at its natural frequency ω₀. If, instead, two people sit on the swing, the new natural frequency of the swing is (A) 4ω₀. (B) 3ω₀. (C) 2ω₀. (D) ω₀. (E) ω₀/2.

13. If the inertial mass and gravitational mass were not equal, which of the following principles would change? (A) Kepler's third law. (B) Principle of least action. (C) The inverse-square law of gravitation. (D) Newton's second law. (E) Nothing has changed.

14. An electron (mass m, charge −e) is accelerated from rest through a potential difference V and then deflected by a magnetic field B that is perpendicular to its velocity. The radius of the resulting electron trajectory is: (A) (B) (C) (D) (E) none of these

15. Eight identical spherical conducting raindrops are each at a potential V, relative to the potential far away. They coalesce to make one spherical raindrop whose potential is: (A) V/8 (B) V/2 (C) 2V (D) 4V (E) 8

16. An electron has velocity v = (32 i + 40 j) km/s as it enters a uniform magnetic field B = (60 i) μT. (A) The radius of the helical path taken by the electron is 0.38 m. (B) The pitch of that path is 1.9 m. (C) The period of the revolution is 60 μs. (D) To an observer looking into the magnetic field region from the entrance point of the electron, the electron spirals counterclockwise as it moves. (E) The magnetic force points in the +k direction.

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