37. A neutron has a mass of 1.67 × kg. The de Broglie wavelength is 1.4 × m. What is the velocity of the neutron? (Plank's constant h = 6.63 × J.s)
(A) 1.55 × 10² m/s
(B) 7.01 × 10² m/s  
(C) 2.99 × 10⁶ m/s
(D) 2.83 × 10³ m/s
(E) 3.53 × 10³ m/s

33. The wave function of a transverse wave propagating on a rope is y(x, t) = 5sin(πχ 4πt), where x and y are measured in meters and t is in seconds. What is the velocity (m/s) of a particle on the rope at x = 2 m and t = 0.5s? (A) 0 (B) -4 (C) 5π (D) 10π (E) 20π

34. A conductor of radius r, length 1, and resistivity p has resistance R. Assume that the volume of this conductor is conserved. What is the new resistance if it is stretched to double its original length? 1 (A) (B)(C) R (D) 2R (E) 4R

35. The molar specific heat at constant volume is , and the molar specific heat at constant pressure is . For an ideal gas at a fixed temperature, which of the following statements is true? (A) is always greater than , because part of the absorbed heat is used to do work to the environment. (B) is always greater than , because the environment absorbs additional heat. (C) is always less than , because part of the absorbed heat is used to do work to the environment. (D) is always less than , because the environment absorbs additional heat. (E) There is no certain relation between and .

36. Which of the following statements about the specific heat of an ideal gas is correct? (A) The specific heat at constant pressure is greater than the specific heat at constant volume because work is done by the gas at constant volume. (B) The specific heat at constant pressure is greater than the specific heat at constant volume because work must be done by the gas at constant pressure. (C) The specific heat is greater for a more massive gas. (D) The specific heat is greater at lower temperature. (E) The specific heat is proportional to the absolute temperature.

38. For designing an anti-reflective coating for a glass surface in an optical device at a free-space wavelength of 552 nm. The refractive index of the glass is 1.50. Determine the minimum thickness (nm) of the optical coating with a refractive index of 1.38. (A) 276 (B) 184 (C) 138 (D) 100 (Ε) 92.0

39. A coin of mass m and radius R rolls steadily without slipping on a moving pad. Assume that the coin's face orientation remains fixed and its density is uniform. The coin rolls counter-clockwise and moves in the x-direction as shown in the figure. Suppose the pad is accelerating along the +x-direction with a constant acceleration a0 with respect to the inertial frame. What is the linear acceleration of the coin with respect to the inertial frame?  (A)+a0/3(B)-a0/3(C) +a0/2 (D) -a0/2 (E) 0 

40. What is the capacitance C of an isolated conductive spherical shell of radius R in free space with total charge Q uniformly distributed over its surface? (You can think of the second conductor as a hollow conducting shell of infinite radius.) (A) 0 (B) 4 πρ² Q (C) 2πε0RQ (D) 2 πε0Ρ (E) 4 πε0Ρ

41. A long, straight conductor carries 1.0 A of current. At what distance from the axis of the conductor is the magnetic field caused by the current equal to the Earth's magnetic field (about 0.5 Gauss)? μ0 = 4π × T·m/A (A) 200 mm (B) 40 mm (C) 20 mm (D) 4 mm (E) 1 mm

42. Which of the following statements is true for one mole of ideal monatomic gases? (A) For the isobaric process, the change in the internal energy is linearly proportional to the change in the temperature. (B) For the gas undergoing the adiabatic process, the temperature of the gas remains constant. (C) For the gas undergoing the isothermal expansion, the internal energy of the gas increases. (D) For the gas undergoing the adiabatic free expansion process, the temperature of the gas drops. (E) For the gas undergoing the adiabatic free expansion process, the internal energy of the gas increases.

43. For a monatomic ideal gas undergoing the following three consecutive thermodynamic processes. First, an isochoric process from (P0, V0) to (2P0, V0). Second, an adiabatic free expansion from (2P0, V0) to (P0, 2V0). Finally, an isobaric process from (P0, 2V0) to (P0, V0). Which of the following statements is true? (A) The entropy of the gas and the entropy of the surroundings increase. (B) The entropy of the gas increases during the isochoric process. (C) The entropy of the gas increases during the isobaric process. (D) The entropy of the gas increases after one cycle is unknown since the gas undergoes the adiabatic free expansion process. (E) None of the above is true.