12. Capacitance( C ):
(A)2πε₀a
(B) πε₀a 
(C) 4πε₀a 
(D)8πε₀a 
(E)πε₀a/2

19. What is the water temperature? (A) 4 ℃ (B) -10℃ (C)0℃ (D)-5℃ (E) unknown

20. Please calculate the rate of ice formation (in centimeters per hour) on the bottom of the ice slab. Take the thermal conductivity of icc to be 0.004 cal/sㆍ cm ㆍ℃, the latent heat of fusion of water to be 80 cal/g, and density of ice to be 0.92 g/cm3； here we assume no heat transfer through the tank walls or bottom. (A) 0.55 cm/r (B) 0.39 cm/hr(C)0.62 cm/hr(D)0.24cm/hr (E) 0.12 cm/hr

1. What isis natural fequency?(A)(B)(C)(D)

2. Following the previous question, what is the Lagrangian of the simple harmonic oscillator?(A)(B) (C) (D) (E) L=mv2+kx

複選題3. Which of the following is correct?(A) Given physical quantities A and B of the same dimension (e.g. they are both the lengths of something), and quantities C and D of the same dimension, if D is uniquely determined by A, B, and C, there must be some num nerical constants k and n (of no dimension) such that D = kC(A/B)n. (B) The moon is orbiting around the earth with roughly the samne period as that for its spinning around its own axis. (C) The gravitational potential energy for N point masses is the distance between particle i and particle j, and G is the Newton constant. (D) As the kinetic energy is given by a diffcrent formula, the total energy of an isolated system is not conserved in special relativity. (E) The friction is a conservative force. GMMI

4. What is the center-of-mass velocity of the system? (A) (B) (C)(D) = 2V/3 (E)

5. What is the moment of inertia I of the system around its center-of-mass? (A) (B) (C)I= (D)(E)

6. What is the magnitude of the total angular momentum of the system around its center of mass?(A)(B) (C) (D) (E)

7. Which of the following is wrong? (A) Divide a uniform spring of spring constant k into two identical halves. The spring constant of each half is 2k. (B) Fix one endpoint of a rope on the edge of a cliff, and release the other endpoint from equal height. At the moment when the free endpoint falls a distance h below the other endpoint, its velocity v is smaller than for any h ＞ 0. (See Fig. B above.)(C) Newton'slaw is necessary for the momentum conservation of physical systems.(D) Given arbitrary 3-dimensional vectors A, B, and C, the following identity bolds: A X(BXC = B(AㆍC) - C(AㆍB)(E) The angular momentum of a point mass in linear motion at constant velocity can be non-zero.

8. The change in entropy for an ideal gas over a reversible isothermal process at the temperature T from the initial pressure P and volume V to the final pressure P/2 and volume 2Vis(A) PVlog(1/2)(B) PVlog(2) (C) PVlog(1/2)T (D) PV 10g(2)/T (E) 2PVlog(2)/T

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