53. A 30-turn circular coil of radius 1 m and resistance 1 Ω is placed in a magnetic field directed perpendicular to the plane of the coil. The magnitude of the magnetic field varies in time according to the expression B = 0.1 t + 0.04 t² , where B is in tesla and t is in second. Calculate the induced emf in the coil at t = 5 s.
(A) 27 V
(B) 37 V
(C) 47 V
(D) 57 V
(E) 67 V

49. A cylinder contains n mol of helium gas (ideal monatomic gas) at a temperature of 300 K. The universal gas constant is R (R=) , where is Avogadro’ number and is Boltzmann’s constant. If the gas is heated at constant pressure, how much energy must be transferred by heat to the gas after it is heated to 500 K? (A) 200n? (B) 300nR (C) 500nR (D) 800nR (E) 1000nR

50. The switch is connected to position a for a long time interval as shown in the figure. At t = 0, the switch is thrown to position b. After this time, what are the frequency of oscillation of the LC circuit? (A) 159 Hz (B) 359 Hz (C) 559 Hz (D) 759 Hz (E) 959 Hz

51. An infinite long wire is charged uniformly with line charge density λ. What is the electric field at a point with a distance y from the stick? (Electric constant is ε0) (A) (B)(C) (D) (E)

52. A charge +q is at the position a and a second charge –q is placed at –a as shown in the figure. What is the limiting form of the electric field for x ≫ a? (Coulomb’s constant is ) (A) (B) (C) (D) (E)

54. Electric currents I1 and I2 are flowing through two parallel electric wires which are separated apart by a distance R. What is the force per unit length between the two parallel wires? (Magnetic constant is μ0) (A) (B) (C) (D) (E)

55. While you are under water in a pool, you look up and see objects above water in a circle of light with a radius ?. The rest of your vision is the color of the sides of the pool. Assume that the index of refraction of air is 1 and that of water is n. How deep are you in the pool? (A)(B) (C) (D) Rn (E)

56. The pupil of a cat’s eye narrows to a vertical slit of width 0.5 mm in daylight. Assume the average wavelength of the light is 500 nm. What is the angular resolution for horizontally separated mice? (A)rad (B)rad (C)rad (D)rad (E) rad

57. The focal length of a spherical, concave mirror is 8 cm. An object is placed at a distance of 24 cm in front of the mirror. How fast does the image move if the object starts to move at speed toward the concave mirror? (A) (B) 0.50 (C) 0.25 (D) 0.20 (E) 0.18

58. In a lecture demonstration of single-slit diffraction, a laser beam of wavelength λ passes through a vertical slit of a wide a and hits a screen at a distance of L away. What is the width of the central diffraction maximum on the screen? (A) (B) (C) (D) (E)

59. An AC voltage source is connected to a capacitor. There is a phase difference between the voltage across the capacitor and the current passing it. Which of the following statement is correct? (A) The phase of the current leads the voltage by π/2. (B) The phase of the current leads the voltage by π/4. (C) The phase of the current lags the voltage by π/2. (D) The phase of the current lags the voltage by π/4. (E) None of the above.