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

43. A heart surgeon monitors the flow rate of blood through an artery using an electromagnetic flowmeter as shown in the figure. Electrodes A and B make contact with the outer surface of the blood vessel, which has a diameter of 3.0 mm. For a magnetic field magnitude of 0.04 T, an emf of 160 μV appears between the electrodes. Calculate the speed of the blood.(A) 1.33 m/s (B) 2.33 m/s (C) 3.66 m/s (D) 4.66 m/s (E) 6.66 m/s

44. A rectangular coil with 1000 turns has a length and width of 10 cm and 20 cm respectively and carries a counterclockwise current of 10 A. When the magnetic dipole moment makes an angle of 60° with a magnetic field of 0.5 T, what is its potential energy? (A) -50 J (B) -87 J (C) -100 J (D) 50 J (E) 100 J

45. A rectangular conductor coil has width L = 10 cm, resistance R = 0.3 Ω, and mass m = 100 g. Ignoring the air drag, when the coil falls in a uniform magnetic field B = 10 T, the final terminal velocity value of the coil is: (Gravitational acceleration g = 10 m/s2 )(A) 0.3 m/s (B) 0.5 m/s (C) 0.7 m/s (D) 3.0 m/s (E) 5.0 m/s

46. A 5 µF capacitor is linked to an electromotive force experiencing uniform increment at a rate of 100 V/s over time. The displacement current between the plates is: (A) 0 (B) 5 A (C) 5×10-2 A (D) 5×10-4 A (E) 5×10-6 A

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

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)

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