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

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

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

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.

60. MRI machine probes the concentration distribution of water molecules by detecting the magnetic resonance between the nucleus of hydrogen atoms, placed in a strong static magnetic field B, and a small alternating magnetic field of frequency f. If B is 2T and the z-component of the proton magnetic moment is J/T. What is the frequency f of the alternating magnetic field? (Plank constant is J/s) (A) 43 MHz (B) 85 MHz (C) 170 MHz (D) 340 MHz (E) 680 MHz

61. When a certain atom emits a photon of light at 232 nm, what is the frequency of this light? (A) (B) (C) (D) (E) None of the above.

62. Given a cylinder of fixed volume filled with 1 mol of argon gas, which of the following is correct? (Assume all gases obey the ideal gas law.) (A) If the temperature of the cylinder is changed from 25°C to 50°C, the pressure inside the cylinder will remain the same. (B) If a second mole of argon is added to the cylinder, the ratio of T/P would decrease. (C) A cylinder of identical volume filled with the same pressure of helium must contain more atoms of gas, because helium has a smaller atomic radius than argon. (D) Two of the above. (E) None of the above.

63. Which of the following statements is true? (A) The energy of electromagnetic radiation increases as its frequency decreases. (B) An electron in the n = 4 state in the hydrogen atom can go to the n = 2 state by absorbing electromagnetic radiation at the appropriate frequency. (C) The frequency and wavelength of electromagnetic radiation are proportional to each other. (D) The energy of an atom is increased when electromagnetic radiation is emitted from it. (E) An excited atom can return to its ground state by emitting electromagnetic radiation.