【GR1776】 The Solution for GRE Physics Practice Test [61-80]

The Solution for GRE Physics Practice Test [61-80]

 

추천글 : 【GRE】 Solution for GRE Physics Practice Test 

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61. Excited states of the helium atom can be characterized as para- (antiparallel electron spins) and ortho- (parallel electron spins). The observation that an ortho- state has lower energy than the corresponding para- state can be understood in terms of which of the following?

 

 

⑴ answer: B

⑵ Pauli exclusion principle : The ground state has the largest sum of spins.

 

 

62. A particle of mass m and spin zero is in a three-dimensional isotropic well described by V(r) = 0.5mω²r², where r² = x² + y² + z². How many states have energy 3.5 ℏω?

 

 

⑴ answer: D

⑵ This is equivalent to three one-dimensional oscillators.

 

 

⑶ The solution of the Schrödinger equation

 

 

⑷ Diophantine equation 

 

 

 

63. The operators for the total angular momentum and its three projections are J and J_x, J_y, J_z respectively. The commutator between two operators A and B is [A, B] ≡ AB - BA. Which of the following is true?

 

 

⑴ answer: A

⑵ total angular momentum operator

 

 

 

64. The suspension cable of a 1,000 kg elevator snaps, sending the elevator moving downward through its shaft. The emergency brakes of the elevator stop the elevator shortly before it reaches the bottom of the shaft. If the elevator fell a distance of 100 m starting from rest, the heat that the brakes must dissipate to bring the elevator safely to rest is

 

 

⑴ answer: E

⑵ Q = mgh = 1000 × 10 × 100 = 1000000 (J)

 

 

65. A uniform rod of length L and mass M is released from rest at θ = 0 and rotates about a horizontal axis through its base, as shown in the figure below. What is the angular acceleration of the rod as a function of θ? (Ignore the effects of friction and air resistance.)

 

 

⑴ answer: D

⑵ the definition of angular acceleration 

 

 

 

66. Two identical, ideal springs, each with force constant k, are attached in series and hung vertically. When a block of mass m is attached to the two-spring system, the block moves down a distance x from the relaxed state, as shown in the figure below. Which of the following gives the angular frequency of the block when it oscillates vertically?

 

 

 

⑴ answer: C

⑵ simple harmonic oscillation 

 

 

⑶ composite elastic coefficient in series

 

 

 

67. A block attached to a spring is moving along the x-axis on a frictionless horizontal surface. What is the Hamiltonian for the block?

 

 

⑴ answer: E

⑵ Hamiltonian operator : It represents energy terms.

⑶ kinetic energy : p² / 2m 

⑷ elastic energy : kx² / 2 

 

 

68. A conducting sphere is solid except for three spherical cavities inside. Cavity A contains a point charge of +2q, cavity B contains a point charge of -4q, and cavity C is empty, as shown below. What charges are induced on the inner surfaces of the spherical cavities?

 

 

⑴ answer: A

⑵ Free charge moves freely within the conductor, resulting in zero electric field strength within the conductor. If the strength is not zero,  the free charge moves easily, making the strength zero.

 

 

69. A magnetic field is directed perpendicular to the plane of a circular coil of area 0.2 m² and 250 turns. If the magnetic field is increased from 0.01 T to 0.06 T during a time interval of 0.25 s, the average induced EMF in the coil is

 

 

⑴ answer: D

⑵ Maxwell's 4^th law  

 

 

 

70. The figure below depicts a step potential with 

 

 

A beam of particles with E > 0 is incident from the left. The momentum of the particle in each region has the form ℏk. The reflection coefficient R for the interface at x = 0 is 

 

 

⑴ answer: D

⑵ The reflection coefficient of electromagnetic wave (η : intrinsic impedance)

 

 

⑶ The reflection coefficient of a material wave must be similar to the reflection coefficient of an electromagnetic wave by symmetry.

 

 

71. Consider the Pauli spin matrices σ_x, σ_y and σ_z. The product σ_xσ_y is equal to which of the following?

 

 

⑴ answer: E

⑵ Pauli matrices

 

 

 

72. The binding energy per nucleon is greater for which of the following nuclei?

 

 

⑴ answer: C

⑵ ⁵⁶Fe has the largest binding energy per nucleon among all nuclei.

 

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73. The negative muon, μ^-, has properties most similar to which of the following?

 

 

⑴ answer: E

⑵ Electrons and muons are classified as leptons.

⑶ Electrons and negatively charged muons have an equivalent negative charge per particle.

 

 

74. Which of the following correctly gives the quark and antiquark content of a lepton and a baryon?

 

 

⑴ answer: A

⑵ by definition

 

 

75. Under certain conditions, a beam of electrons impinging on a crystal surface will diffract and a scattering pattern of the beam can be obtained. What is the approximate kinetic energy of the electrons needed in order to see the pattern? (Assume the lattice spacing of the crystal to be 0.4 nm.)

 

 

⑴ answer: C

⑵ related to Bloch electron in a periodic potential 

 

 

76. A beam of positive ions is initially moving in the +x-direction with nonrelativistic velocity. The beam enters a velocity selector in which the electric field E is oriented along the +y-direction and the magnetic field B is oriented along the +z-direction, as shown below. Which of the following gives the critical speed v_c at which the ion beam is not deflected as it moves through the velocity selector? 

 

 

⑴ answer: E

⑵ equilibrium between the electric force and the Lorentz force

 

 

 

77. Under ideal conditions, the electric and magnetic fields inside a superconductor are zero. Maxwell’s equations imply that which of the following must be true just outside the surface of the superconductor?

 

 

⑴ answer: C

⑵ Meissner effect and diamagnetism 

 

출처 : 이미지 클릭

 

 

78. A positive charge, +q, oscillates up and down, as represented in the figure below. What is the direction of the Poynting vector S at point P? (Assume P is located far to the right of +q.)

 

 

⑴ answer: B

⑵ The oscillation of the positive charge is similar to the electrical current along a wire.

⑶ Poynting vector : Electrical 

 

 

 

79. A block with mass m₁ that slides on a frictionless table is attached by a massless string over a massless, frictionless pulley to a hanging ball with mass m₂, as shown in the figure below. The tension in the string must be

 

 

⑴answer: C

 

 

 

80. Two planets of mass m revolve around a star of mass M in a circle of radius r, as shown in the figure below. The two planets are always on opposite sides of the star. The orbital period T of the planets is of the form

 

 

What is the value of M'?

 

 

⑴ answer: D

 

 

입력: 2022.12.30 01:46