51. The diagram shows a U-tube having cross-sectional area A and partially filled with oil of density . A solid cylinder, which fits the tube tightly but can slide without friction, is placed in the right arm. The system reaches equilibrium. The weight of the cylinder is:
(A) ALρg
(B) L ³ ρg
(C) Aρ(L + h)g
(D) Aρ(L – h)g
(E) None of the above.

47. Coherent light with wavelength 0.40 μm passes through two very narrow slits. The distance between these two slits is 0.20 mm. The interference pattern is shown on a screen 5.0 m from the slits. What is the width of the central interference maximum? (A) 7.5 mm (B) 5.0 mm (C) 20 mm (D) 10 mm (E) 2.5 mm

48. A cup of tea is made with 0.250 kg of C o 85.0 water. Then, the cup of tea cools down to room temperature  20.0℃ . What is the entropy change of the water while it cools? (For water,) (A) 200 J / K (B) 230 J / K (C) 1050ln(1.22) J / K (D) 1050ln(0.818) J / K (E) 190 J / K

49. A Carnot engine operates between two temperatures TH and TC. It takes in 600 J of heat from high-temperature reservoir at TH = 327℃ in each cycle and gives up 200 J to the low-temperature (TC) reservoir. What is the thermal efficiency of the cycle? (A) 67% (B) 33% (C) 75% (D)50%(E)25%

 50. When a certain rubber band is stretched a distance x, it exerts a restoring force F = ax + bx2 , where a and b are constants. The work done in stretching this rubber band from x = 0 to x = L is: (A) aL2 + bLx3 (B) aL + 2bL2 (C) a + 2bL (D) bL (E) aL2 /2 + bL3 /3 

52. A solid brass ball of mass 0.280 g will roll smoothly along a loop-the-loop track when released from rest along the straight section. The circular loop has radius R = 14.0 cm, and the ball has radius r << R. What is h if the ball is on the verge of leaving the track when it reaches the top of the loop? (A) 47.8 cm (B) 27.8 cm (C) 57.8 cm (D) 37.8 cm (E) 78.3 cm

53. The emf E = 1.2 kV, C = 6.5 μF, R1 = R2 = R3 = 0.73 MΩ. With C completely uncharged, switch S is suddenly closed (at t = 0). At t = 0, what is current i1 in resistor R1? (A) 3.3✖10-3 A (B) 3.3✖10-4 A (C) 1.1✖10-4 A (D) 1.1✖10-3 A (E) 2.2✖10-3 A

54. The following shows a rod of length L = 10.0 cm that is forced to move at constant speed v = 5.00 m/s along horizontal rails. The rod, rails, and connecting strip at the right form a conducting loop. The rod has resistance 0.400 Ω; the rest of the loop has negligible resistance. A current i = 100 A through the long straight wire at distance a = 10.0 mm from the loop sets up a (nonuniform) magnetic field through the loop. Find the emf. (μ0 = 4π10-7 T  m/A, ln 2 = 0.693, ln 10 = 2.303, ln 11 = 2.398) (A) 2.4✖10-4 V (B) 5.8✖10-3 V (C) 4.8✖10-5 V (D) 3.9✖10-4 V (E) 8.8✖10-4 V

55. If the five lenses shown below are made of the same material, which lens has the shortest positive focal length? (A) (B) (C) (D) (E)

56. For quantum model, E = hν = hc / λ, where E is photon energy in unit of eV, h is the Planck’s constant ( ), ν is the frequency (s -1 ), λ is the wavelength in meters (m), then E✖λ (eV m) is: (A)  1.24 ✖10- 3 (B)  1.24✖ 10- 4 (C) 1.24 ✖10-5 (D)  1.24✖ 10- 6 (E)  1.24✖ 10-7

57. A particle with mass m and charge q, moving with a velocity v, enters a region of uniform magnetic field B, as shown in the figure below. The particle strikes the wall at a distance d from the entrance slit. If the particle’s velocity stays the same but its charge-to-mass ratio is doubled, at what distance from the entrance slit will the particle strike the wall? (A) 2d (B) (C) d (D) (E)