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

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)

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

9. Which of the following statement is correct?(A) The law of thermodynamics states that two systems in thermal contact always reach thermal equilibrium in the end. (B) The entropy of any macroscopic system never decreases over time. (C) The entropy of an idcal gas is doubled if its volume is doubled at the same temperature. (D) Any irreversible engine always has a smaller efficiency than any reversible engine. (E) By choosing a suitable definition of Kelvin, the Boltzmann constant has an exact value that does not have to be determined by experiments.

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