6. A solid spherical marble starts from rest and rolls without slipping on the loop-the-loop track in fgure 1. What is the minimum starting height h from which the marble will remain on the track through the loop. Assume the marbles radius is small compared with R.
(A) 2.5R；
(B) 2.7R；
(C)2.9R；
(D) 3.1R；
(E) 3.3R.
 (Note: the moment of inertial for a solid spherical object is, where m is the mass of the object and r is its radius.) Figure 1: Figure for problem 6. Figure 2: Figure for problem 7.

7. What is the moment of inertia related to central axis A of a uniform solid pyramid of mass M and height h, with a square bottom of side L, as shown in figure 2. (A) 0.4MI3/h； (B) 0.2MLh； (C)0.1ML2, (D) 0.1MLh； (E) 0.2ML2.

8. A thin circular disk of radius R carries a total charge Q uniformly distributed on its surface. Assuming symmetric electric field on the two sides of the disk, which of the following expressions is a good approximation of the electric feld strength at a distance r above the center of the disk, where r << R?(A) (B) (C) (D)(E)

9. Same setting as in prablem 8, but with r ＞＞ R. Which of the following is a good approximation of the electric field strength?(A) (B) (C) (D) (E)

10. A piston system containing 1 mole of ideal gas in a 10 liter volume initially. The system is put in thermal contact with the environment at 20℃ and 1 atm of pressure. The piston is then released and the volume expands slowly in a quasi-static manner. The temperature is maintained at 20℃ during the whole process. The expansion stops when the pressure inside the piston reaches 1 atm. What is the volume of the gas chamber after the expansion? (The universal ideal gas constant, R, is 0.082 Liter-atm/K/mole.)(A) 24.1 liter； (B) 22.1 liter； (C)18.4 liter； (D) 16.9 liter； (E) 12.3 liter.

11. Same setting as problem 10, what is the work done by the piston during the expansion process?(A) 24 J； (B) 21 J； (C)18 J； (D) 16 J； (E) o J.

12. Same initial condition as in problem 10, but this time we insulate the system from the environment such that the expansion process is quasi-static and adiabatic. Starting with 20℃ and 10 liter, what is the volume of the chamber when the pressure reaches 1 atm? Assuming the specific heat are and (A) 24 liter； (B) 22.1 liter； (C)18.4 liter； (D) 16.9 liter； (E) 12.3 liter.

13. Same as problem 12, what is the change of entropy during this process?(A) 24 J/K； (B) 21 J/K； (C)18 J/K； (D) 16 J/K；(E)0 J/K.

14. In electrostatic equilibrium, the electric field just outside any charged con- ductor is(A) always zero； (B) always perpendicular to the surface of the conductor； (C)always parallel to the surface of the conductor, along the gra- dient of the surface charge distribution； (D) always parallel to the surface, but perpendicular to the gradient of the surface charge distribution, (E) of no particular direction.

15. A string of length L and linear density λ is stretched to a tension T. What is the expression of its resonance frequencies of standing waves?(A) (B)(C)(D)(E),where n is any positive integer. (Hint: Wave equation of small displacement y is )

16. Two parallel infinite wires 2cm apart carry currents of 1A and 8A, separately. What is the force per meter between them?(A) (B) N/m； (C)(D) (E)

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