51. Two objects with temperatures T1 and T2 (T2 = 2T1) are isolated from their surroundings. A small amount of heat Q is transferred without changing their temperatures. What is the total entropy change of the two objects?
(A) (1/2)·(Q/T1)
(B) (3/2)·(Q/T1)
(C) (1/3)·(Q/T2)
(D) (2/3)·(Q/T2)
(E) (1/4)·(Q/T2)

47. In a certain cyclotron a proton moves in a circle of radius 0.50 m. The magnitude of the magnetic field is 1.20 T. What is the oscillator frequency? (The mass of proton mp = 1.67×10-27 kg) (A) 1.83×107 Hz (B) 2.53×107 Hz (C) 3.62×107 Hz (D) 4.71×107 Hz (E) 5.83×107 Hz

48. A gas is at 200 K. If we wish to double the root mean square speed (vrms) of the molecules of the gas, to what value must we raise its temperature? (A) 283 K (B) 400 K (C) 500 K (D) 600 K (E) 800 K

49. In the figure, a gas enclosed within a sealed chamber follows a closed path as illustrated. What is the total amount of work performed by the gas?(A) +40 J (B) +20 J (C) 0 J (D) -20 J (E) -40 J

50. When a fixed pressure of one atmosphere is maintained, an ideal gas receives 25 J of energy in the form of heat. During this process, the gas's volume expands from 20 cm³ to 40 cm³. What is the molar specific heat of this ideal gas? (The universal gas constant R = 8.31 J/mol·K, 1 atm = 1.01×105 Pa) (A) 80 J/mol·K (B) 85 J/mol·K (C) 90 J/mol·K (D) 95 J/mol·K (E) 100 J/mol·K

52. The figure shows the configuration of a beam-expander (5x) formed by two positive lenses with focal lengthes f1 and f2. The distance between two lens is 12 cm. Wi and Wf denote the input and output laser beam diameters, respectively. What is the laser focal point in the system?(A) 2.0 cm away from the input lens (B) 4.0 cm away from the input lens (C) 6.0 cm away from the input lens (D) 8.0 cm away from the input lens (E) 10.0 cm away from the input lens

53. A police car with a 500 Hz siren is moving at 20 m/s. What is the total frequency change when the police car is approaching and then leaving the listener? (sound speed in the air is 344 m/s) (A) 32 Hz (B) 36 Hz (C) 48 Hz (D) 52 Hz (E) 58 Hz

54. A doppler flow meter transmit ultrasound of 10 MHz to measure the blood flow. If the reflected sound of 9.9 MHz is recorded by the same probe, find the speed of the blood flow. (sound speed in the tissue is 1500 m/s) (A) 5.5 m/s (B) 6.5 m/s (C) 7.5 m/s (D) 8.5 m/s (E) 9.5 m/s

55. Thin film coating is a technique for anti-reflection. How thick a thin film with the refractive index of 1.25 should be coated on a glass surface (n=1.5) to eliminate the reflection for the wavelength of 600 nm? Only consider normal incidence. (A) 120 nm (B) 150 nm (C) 300 nm (D) 500 nm (E) 600 nm

56. An acrylic cube with a volume of 8 cm³ registers a weight of 40 g on a spring scale calibrated in grams. If the same object is weighed while submerged in a liquid with a density of 4 g/cm³, what reading will the scale display? (A) 8 g (B) 16 g (C) 24 g (D) 32 g (E) 40 g

57. The net nuclear fusion reaction inside the Sun can be written as 41H → 4He + E. The rest energy of each hydrogen atom is 938.8 MeV, and the rest energy of the helium-4 atom is 3728.4 MeV. Calculate the percentage of the starting mass that is transformed to other forms of energy. (A) 0.11 % (B) 0.31 % (C) 0.51 % (D) 0.71 % (E) 0.91 %