The Solution for GRE Physics Practice Test [61-80]
추천글 : 【GRE】 Solution for GRE Physics Practice Test
Questions 61-62
The equation of motion of a rocket in free space can be written
where m is the rocket's mass, v is its velocity, t is time, and u is a constant.
61. The constant u represents the speed of the
⑴ answer: E
62. The equation can be solved to give v as a function of m. If the rocket has m = m0 and v = 0 when it starts, what is the solution?
⑴ answer: E
⑵ dv = -u dm/m ⇔ v = u ln (m0 / m)
63. A point charge -q coulombs is placed at a distance d from a large grounded conducting plane. The surface charge density on the plane a distance D from the point charge is
⑴ answer: D
⑵ solution 1. You can solve it with dimension analysis at a glance.
⑶ solution 2. My initial approach, but ...
64. An alternating current electrical generator has a fixed internal impedance Rg + jXg and is used to supply power to a passive load that has an impedance Rg + jXℓ, where j = √ -1, Rg ≠ 0, and Xg ≠ 0. For maximum power transfer between the generator and the load, Xℓ should be equal to
⑴ answer: C
65. A current i in a circular loop of radius b produces a magnetic field. At a fixed point far from the loop, the strength of the magnetic field is proportional to which of the following combinations of i and b?
⑴ answer: B
⑶ When the distance is r, the magnetic field B is represented as
66. For a system in which the number of particles is fixed, the reciprocal of the Kelvin temperature T is given by which of the following derivatives? (Let P = pressure, V = volume, S = entropy, and U = internal energy.)
⑴ answer: E
⑵ dimension analysis : [S] = [Q] / [T], [U] = [Q]
67. A large isolated system of N weakly interacting particles is in thermal equilibrium. Each particle has only 3 possible nondegenerate states of energies 0, ε, and 3ε. When the system is at an absolute temperature T ≫ ε / k, where k is Boltzmann's constant, the average energy of each particle is
⑴ answer: C
⑵ When temperature is very large, the entropy is maximized. So the probability of each state is about a third.
68. If a newly discovered particle X moves with a speed equal to the speed of light in vacuum, then which of the following must be true?
⑴ answer: A
⑵ The speed of light is a maximum speed, so the rest mass of X is zero.
Questions 69-71
A car of rest length 5 meters passes through a garage of rest length 4 meters. Due to the relativistic Lorentz contraction, the car is only 3 meters long in the garage's rest frame. There are doors on both ends of the garage, which open automatically when the front of the car reaches them and close automatically when the rear passes them. The opening or closing of each door requires a negligible amount of time.
69. The velocity of the car in the garage's rest frame is
⑴ answer: C
⑵ γ = 3 / 5 = √ (1 - (v / c)2) ⇔ v = 0.8c
70. The length of the garage in the car's rest frame is
⑴ answer: A
⑵ γ × 4 = 0.6 × 4 = 2.4 m
71. Which of the following statements is the best response to the question:
⑴ answer: E
⑵ You need to draw a world line.
72. The measured index of refraction of x-rays in rock salt is less than one. This is consistent with the theory of relativity because
⑴ answer: E
73. It is necessary to coat a glass lens with a non-reflecting layer. If the wavelength of the light in the coating is λ, the best choice is a layer of material having an index of refraction between those of glass and air and a thickness of
⑴ answer: A
⑵ 2t = (n + 1/2) λ (∵ All reflecting waves are made by fixed end reflecting.)
74. Unpolarized light is incident on two ideal polarizers in series. The polarizers are oriented so that no light emerges through the second polarizer. A third polarizer is now inserted between the first two and its orientation direction is continuously rotated through 180°. The maximum fraction of the incident power transmitted through all three polarizers is
⑴ answer: B
⑵ Malus law
⑶ 1/2 × 1/2 × 1/2 = 1/8
75. The period of a hypothetical Earth satellite orbiting at sea level would be 80 minutes. In terms of the Earth's radius Re, the radius of a synchronous satellite orbit (period 24 hours) is most nearly
⑴ answer: B
⑵ Kepler's third law : T2 ∝ a3
⑶ As 24 hours is 18 times bigger than 80 minutes, the radius is (182)1/3 Re ≒ 7Re.
76. A hoop of mass M and radius R is at rest at the top of an inclined plane as shown below. The hoop rolls down the plane without slipping. When the hoop reaches the bottom, its angular momentum around its center of mass is
⑴ answer: A
77. A particle is contrained to move along the x-axis under the influence of the net force F = -kx with amplitude A and frequency f, where k is a positive constant. When x = A / 2, the particle's speed is
⑴ answer: B
78. A system consists of two charged particles of equal mass. Initially the particles are far apart, have zero potential energy, and one particle has nonzero speed. If radiation is neglected, which of the following is true of the total energy of the system?
⑴ answer: C
⑵ It is positive, because there is a net kinetic energy.
79. One of Maxwell's equations is ∇·B = 0. Which of the following sketches shows magnetic field lines that clearly violate this equation within the region bounded by the dashed lines?
⑴ answer: D
⑵ There is no magnetic monopole.
80. Which of the following electric fields could exist in a finite region of space that contains no charges? (In these expressions, A is a constant, and i, j, and k are unit vectors pointing in the x, y, and z directions, respectively.)
⑴ answer: B
⑵ Gauss' divergence theorem : div (-xy j + xz k) = ∂(-xy) / ∂y + ∂(xz) / ∂z = -x + x = 0 = net charge
입력: 2023.10.05 22:30
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