【GR1775】 The Solution for GRE Physics Practice Test [41-70]

The Solution for GRE Physics Practice Test [41-70]

 

추천글 : 【GRE】 Solution for GRE Physics Practice Test 

---

 

41. A uniform solid disk starts from rest and rolls down an inclined plane without slipping. After some time, what fraction of the disk's total kinetic energy is rotational kinetic energy?

 

 

⑴ answer: B

⑵ total kinetic energy = rotational kinetic energy + translational kinetic energy

⑶ rotational kinetic energy = 1/2 × I × ω2 = 1/2 × 1/2 MR² × ω2 = 1/4 Mv² 

⑷ translational kinetic energy = 1/2 Mv² 

 

 

42. A grating spectrometer can just barely resolve two wavelengths of 500 nm and 502 nm, respectively. Which of the following gives the resolving power of the spectrometer?

 

 

⑴ answer: B

⑵ 500 / (502 - 500) = 250 

 

 

43. A gas cell with an optical path length of 10 cm is placed in one arm of a Michelson interferometer. If the light source for the interferometer is a laser with wavelength λ = 632.2 nm, then 100 fringes are counted as the gas cell is evacuated. What is the index of refraction of the original gas?

 

 

⑴ answer: B

⑵ 2 × 10 cm × (η - 1) = 100 λ = 100 × 632.2 × 10^-9 m ⇔ η = 1.00032 

 

 

44. The AC circuit shown below contains an ideal rectifying diode. If the function generator supplies ε(t) = V₀ sin ωt, which of the following describes the voltage across the resistor?

 

 

⑴ answer: B

⑵ Diode only allows for forward bias, in principle.

 

 

45. The Fourier series expansion of a function f(x) that is periodic with period 2π is 

 

 

If f(x) is given by the graph below, which of the following statements about the coefficients is true?

 

 

⑴ answer: B

⑵ The given function is even function like cosine.

 

 

46. A sample of N molecules has the distribution of speeds shown in the figure below. P(v)dv is an estimate of the number of molecules with speeds between v and v + dv, and this number is nonzero only up to 3v₀, where v₀ is constant. Which of the following gives the value of a? 

 

 

⑴ answer: B

⑵ (3v₀ + v₀) / 2 × a = N ⇔ a = N / 2v₀ 

 

 

47. Which of the following statements is (are) true for a Maxwell-Boltzmann description of an ideal gas of atoms in equilibrium at temperature T? 

 

 

⑴ answer: D

 

 

48. Low-energy electrons are accelerated between electrodes in a tube filled with a gas in the Frack-Hertz apparatus represented below. A plot of current collected versus accelerating voltage is also shown. The data provide evidence for which of the following?

 

⑴ answer: C

⑵ The electric current is quantized.

 

 

49. A particle of mass m and spin zero is in a three-dimensional isotropic well described by V(r) = 1/2 mω²r², where r² = x² + y² + z². How many states have energy 7/2 ℏω?

 

 

⑴ answer: D

⑵ This is equivalent to three one-dimensional oscillators.

 

 

⑶ The solution of the Schrödinger equation

 

 

⑷ Diophantine equation 

 

 

 

50. The operators for the total angular momentum and its three projections are Ĵ and Ĵ_x, Ĵ_y, Ĵ_z, respectively. The commutator between two operators  and B̂ is [Â, B̂] ≡ ÂB̂ - B̂Â. Which of the following is true?

 

 

⑴ answer: A

⑵ I'm not sure, but Ĵ² is similar to a scalar?

 

 

51. 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 Mg sin  θ × L/2 = Iα = 1/3 ML² × α ⇔ α = 3g/2L sin θ

 

 

52. 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 H is similar to a total energy. 

 

 

53. A magnetic field is directed perpendicular to the plane of a circular coil of area 0.2 ㎡ 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 EMF = N × dΦ_B / dt = NA ΔB / Δt = 250 × 0.2 × 0.05 / 0.25 = 10 V

 

 

54. 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.

 

 

55. 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

 

 

 

56. The binding energy per nucleon is greatest for which of the following nuclei?

 

 

⑴ answer: C

 

 

 

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

 

 

⑴ answer: E

⑵ Both are leptons and negatively charged.

 

 

 

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

 

 

⑴ answer: A

⑵ example of lepton : electron

⑶ example of baryon : proton, neutron

 

 

59. A beam of positive ions is initially moving in the +x-direction with nonrelative 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

 

 

60. 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

 

 

 

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

 

 

⑴ answer: B

⑵ This is the same principle with the antenna.

 

 

62. 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 

 

 

⑴ answer: C

⑵ a = m₂g / (m₁ + m₂)

⑶ T = m₁a = m₁m₂g / (m₁ + m₂) ＜ m₁m₂g / m₁ = m₂g 

 

 

63. As represented in the figure below, a light ray refracts from air into a rectangular block of plastic with an index of refraction n ＞ 1. At a point on the side of the block, the ray partly reflects (at an angle of 60°) and partly refracts. The value of the angle α is 

 

 

⑴ answer: D

⑵ the law of reflection : θ = 30° 

⑶ partly reflection = critical point : n sin 60 ° = 1 ⇔ n = 2 / √3

⑷ Snell's law : n sin θ = 1 / √3 = sin α 

 

 

64. The hydrogen lines observed in the spectrum of the quasar 3C9 are shifted so far into the red that their wavelengths are three times as long as those observed in the light from hydrogen atoms at rest in a laboratory on Earth. If it is assumed that the shift is entirely due to the relative motion of 3C9 and Earth, the relative speed of the quasar is 

 

 

⑴ answer: C

⑵ Red bias due to cosmological Doppler effect (ref1, ref2) : z = 2

 

 

 

65. Protons used in cancer therapy are typically accelerated to about 0.6c. How much work must be done on a particle of mass m in order for it to reach this speed, assuming it starts at rest?

 

 

⑴ answer: A

⑵ γ = 1 / √(1 - 0.6²) = 1/0.8 = 1.25

⑶ W = (γ - 1)mc² = 0.25 mc² 

 

 

66. The sign of the charge carriers in a doped semiconductor can be deduced by measuring which of the following properties? 

 

 

⑴ answer: E

⑵ Hall effect 

 

 

67. An airplane drops a payload while traveling due north, parallel to the ground, at a constant speed of 100 m/s. If air resistance is neglected, what is the velocity of the payload relative to the plane 4.0 s after it is released?

 

 

⑴ answer: B

⑵ v = gt = 10 × 4 = 40 m/s

 

 

68. Two balls, identical in every way except that one has twice the mass of the other, are dropped from rest from the same height so that they both reach terminal speed before hitting the ground. If it is assumed that the drag force varies like the speed squared, what is the ratio of the terminal speeds of the balls? (Note: The subscripts h and l denote the heavy and light masses, respectively.)

 

 

⑴ answer: B

⑵ 2mg = Cv_h² ⇔ v_h = √ (2mg / C)

⑶ mg = Cv_l² ⇔ v_l = √ (mg / C)

 

 

69. One end of a horizontal, massless spring is attached to a wall. A mass of 0.30 kg is attached to the other end of the spring and rests on a table. The mass is displaced 0.030 m from its equilibrium position and released. It has a speed of 0.040 m/s as it passes through its equilibrium position. In the absence of friction, what is the total mechanical energy of the system?

 

 

⑴ answer: A

⑵ E = 1/2 × k × 0.030² = 1/2 × 0.30 × 0.040² = 0.24 mJ

 

 

70. The diagram below shows a Carnot cycle for an ideal air conditoner, which is to cool a house on a hot summer day. The air conditioner absorbs heat at the lower temperature inside and pumps it to the environment at the higher temperature outside. Which of the following gives the ratio of the heat Q_bc absorbed in house (i.e., between points b and c on the cycle) to the work don during the cycle?

 

 

 

⑴ answer: E

⑵ Q_bc / W = T_L / (T_H - T_L) = 295 / 10

 

입력: 2023.09.24 11:11