51. As shown in the figure on the right, a particle with charge Q is located at a small distance d above the center of a plane on a hemisphere of radius R. What is the electric flux through the circular face (of area πR²)  as δ → 0⁺? 

(A)-Q/ε₀  
(B)
(C) 0
(D)
(E) Q/ε₀ 

47. For a classical electromagnetic plane wave travelling in the x direction in a vacuum (with speed c), the electric field has the form = E0 cos(kx - wt) (V/m). Which of the following statements is true? (A) The magnetic field oscillates in the x direction with an amplitude | E0l/c (T). (B) The energy density of the electromagnetic wave is a constant everywhere in space. (C) The radiation pressure due to the electromagnetic wave shinning on a wall does not depend on its frequency. (D) The instantons power per unit area delivered by the electromagnetic wave is a constant. (E) None of the above is correct.

48. A bar magnet approaches a conducting loop from the left with its north pole directed towards the loop. Considering the effect of electromagnetic induction, the induced current in the loop has the greatest magnitude and a clockwise direction ________.(A) as the north pole of the magnet approaches the loop (B) when the north pole has passed through the loop, but the south pole has not yet passed through (C) when the north pole has passed through and the south pole is about to pass through the loop (D) as the south pole of the magnet leaves the loop (E) after the south pole of the magnet is several centimeters to the right of the loop

49. Which of the following values is closest to the wavelength (nm) of a photon with energy 1.0 eV? h = 6.6 × m²kg/s; c = 3.0 × 108 m/s (A) 1 (B) 10 (C) 100 (D) 1000 (E) 10000

50. A parallel-plate capacitor has a capacitance of 100 pF, a plate area of 100 cm², and the space between the plates is completely filled with a mica dielectric (k =5.4). At a potential difference of 50 V, which of the following values is closest to the magnitude of the electric field E in the mica? (A) 1.0 × 10⁴ V/m (B) 1.0 × 10³ V/m (C)1.0 × 102 V/m (D) 1.0 × 10¹ V/m (E) 1.0 V/m

52. As shown in the figure below, a uniform thin stick of mass M and length L is held vertically by two strings of negligible mass. What is the linear acceleration in the middle of the stick when one of the strings is cut? (Hint: The moment of inertia of the stick is I = ML²/3 for an axis through one end.) (A) 1.50 g (B) 1.0 g (C) 0.75 g (D) 0.50 g (E) 0.25 g

53. As shown in the figure below, particle 1 of mass m₁ is sliding to the right along the x-axis on a frictionless floor with velocity v₁. When it reaches x = 0, it undergoes a one-dimensional elastic collision with stationary particle 2 of mass m2. When particle 2 reaches the wall at , (＞0), it bounces off the wall  without losing velocity. What is the condition that (0 Xw particle 2 collides only twice with particle 1? (A) m2 ＜m1 (B) 1/3 ＜ m1/m2 ≤ 1 (C) 1/3 ≤ m1/m2 ≤1 (D) 1/3 ≤ m1/m2 ＜ 1 (E) None of the above.

54. Two planets of equal mass orbit a star. Planet A has a smaller orbital radius than planet B. Which of the following statements is correct? (A) Planet A and planet B have the same mechanical energy (potential energy plus kinetic energy). (B) Planet A has less kinetic energy, less potential energy, and less mechanical energy (potential energy plus kinetic energy) than planet B. (C) Planet A has more kinetic energy, less potential energy, and less mechanical energy (potential energy plus kinetic energy) than planet B. (D) Planet A has more kinetic energy, less potential energy, and more mechanical energy (potential energy plus kinetic energy) than planet B. (E) Planet A has more kinetic energy, more potential energy, and more mechanical energy (potential energy plus kinetic energy) than planet B.

55. Which of the following statements is false for one mole of monatomic ideal gas? (A) By the Equivalence Theorem, we know that the average energy of each molecule in a monatomic gas is , where the translation, rotational and vibrational motion each contribute equally to the energy . (B) The isobaric process requires absorbing more heat to increase its temperature by one unit than the isochoric process. (C) If the pressure of a gas is doubled and the volume is halved, the internal energy of the gas does not change. (D) During a reversible adiabatic process, the ideal gas law PV = nRT still holds. (E) None of the above is false.

56. Let us consider aspherical capacitor consisting of two concentric metal spherical shells of radii R1 and R2 (R1 ＜ R2), respectively. Which of the following statements is true? (A) The capacitance is increased as R₁ reduces. (B) The capacitance is increased as R2 increases. (C) The capacitance increases as R₁ and R2 increase, while the difference between R2 and R₁ remains constant. (D) The potential difference between the two metal spherical shells does not change with the stored charges. (E) None of the above.

57. Which of the following statements is not true? (A) If an external pressure is applied to a confined fluid which is incompressible, the pressure at every point within the fluid increases by that amount. (B) The magnitude of pressure exerted by an object on a given surface is equal to its weight acting in the direction perpendicular to that surface. Therefore, like the force vector, pressure is also a vector quantity. (C) 1 atm is about 14.7 psi. (D) At any depth in a static fluid, the pressure is the same in all directions at a given depth. (E) Where fluid velocity is high, pressure is low; where velocity is low, pressure is high.