【GR0877】 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 

---

 

61. A particle with mass m and charge q, moving with a velocity v, enters a region of uniform magnetic field B, as shown in the figure below. The particle strikes the wall at a distance d from the entrance slit. If the particle's velocity stays the same but its charge-to-mass ratio is doubled, at what distance from the entrance slit will the particle strike the wall?

 

 

⑴ answer: E

⑵ Lorentz force : F = qvB = mv² / r ⇔ r = d/2 = mv / qB 

 

 

62. Consider the closed cylindrical Gaussian surface below. Suppose that the net charge enclosed within this surface is +1 × 10^-9 C and the electric flux out through the portion of the surface marked A is -100 N∙m²/C. The flux through the rest of the surface is most nearly given by which of the following?

 

 

⑴ answer: E

⑵ Maxwell 1st law : x - 100 = Q_in / ε0 = 113 ⇔ x = 213 N∙m² / C

 

 

63. The nuclear decay below is an example of a process induced by the 

 

 

⑴ answer: D

 

 

64. Consider a single electron atom with orbital angular momentum L = √2 ℏ. Which of the following gives the possible values of a measurement of L_z, the z-component of L?

 

 

⑴ answer: D

⑵ √2 = √((±1)² + (±1)² + 0²) = √((±1)² + 0² + (±1)²) = √(0² + (±1)² + (±1)²)

 

 

65. Characteristics of the quantum harmonic oscillator include which of the following?

 

 

⑴ answer: C

 

 

66. A muon can be considered to be a heavy electron with a mass m_μ = 207 m_e. Imagine replacing the electron in a hydrogen atom with a muon. What are the energy levels E_n for this new form of hydrogen in terms of the binding energy of ordinary hydrogen E₀, the mass of the proton m_p, and the principal quantum number n?

 

 

⑴ answer: D

⑵ I'm uncertain why D is the right answer over A, but the fundamental concept seems to be this.

 

 

 

67. A large, parallel-plate capacitor consists of two square plates that measure 0.5 m on each side. A charging current of 9 A is applied to the capacitor. Which of the following gives the approximate rate of change of the electric field between the plates?

 

 

⑴ answer: D

⑵ V = Q / C = Ed

⑶ dE / dt = 1/Cd × dQ/dt = I / Cd = I / (ε₀ A / d²) = I / ε₀A = 9 / (8.85 × 10^-12 × 0.5²) = 4.07 × 10¹² V/m∙s 

 

 

68. The circuit shown in the figure below consists of eight resistors, each with resistance R, and a battery with terminal voltage V and negligible internal resistance. What is the current flowing through the battery?

 

 

⑴ answer: D

⑵ Note that there is a pair of equipotential points in the left and right circuits due to symmetry.

 

 

69. In the AC circuit below, V_i is the amplitude of the input voltage and V_o is the amplitude of the output voltage. If the angular frequency ω of the input voltage is varied, which of the following gives the ratio V_o / V_i = G as a function of ω?

 

 

⑴ answer: D

⑵ AC circuit theory : V_o = (1 / jωC) / (R + 1 / jωC) V_i = 1 / (1 + jωRC) V_i ⇔ | V_o | = 1 / √(1 + ω²R²C²) 

 

 

70. A wire loop that encloses an area of 10 cm² has a resistance of 5 Ω. The loop is placed in a magnetic field of 0.5 T with its plane perpendicular to the field. The loop is suddenly removed from the field. How much charge flows past a given point in the wire?

 

 

⑴ answer: A

⑵ Q = I Δt = VΔt / R = BA / R = 0.5 × 10 × 10^-4 / 5 = 10^-4 C

 

 

71. Two nonrelativistic electrons move in circles under the influence of a uniform magnetic field B, as shown in the figure below. The ratio r₁ / r₂ of the orbital radii is equal to 1/3. Which of the following is equal to the ratio v₁ / v₂ of the speeds?

 

 

⑴ answer: B

⑵ Lorentz force : qvB = mv² / r ⇔ v = qBr / m

 

 

72. Which of the following statements about bosons and/or fermions is true?

 

 

⑴ answer: D

⑵ boson : Does not obey the Pauli exclusion principle. 

⑶ fermion : Obeys the Pauli exclusion principle. 

 

 

73. The discovery of the J / ψ particle was especially significant because it provided evidence for which of the following?

 

 

⑴ answer: D

 

 

74. The figure below shows an object O placed at a distance R to the left of a convex spherical mirror that has a radius of curvature R. Point C is the center of curvature of the mirror. The image formed by the mirror is at 

 

 

⑴ answer: E

⑵ 1/R + 1/b = -2/R  ⇔ b = -R/3 (illusion)

⑶ Drawing is useful for determining inverted/upright.

 

 

75. A uniform thin film of soapy water with index of refraction n = 1.33 is viewed in air via reflected light. The film appears dark for long wavelengths and first bight for λ = 540 nm. What is the next shorter wavelength at which the film will appear bright on reflection?

 

 

⑴ answer: B

⑵ 2d = (m - 0.5) λ / n ⇔ λ = 2nd / (m - 0.5) = 2nd / 0.5, 2nd / 1.5, ∙∙∙

⑶ 2nd / 0.5 = 540 nm ⇔ 2nd / 1.5 = 180 nm

 

 

76. A model of an optical fiber is shown in the figure below. The optical fiber has an index of refraction, n, and is surrounded by free space. What angles of incidence, θ, will result in the light staying in the optical fiber?

 

 

⑴ answer: B

⑵ Snell's law : sin θ = n sin ϕ

⑶ total reflection : n sin (90° - ϕ) = n cos ϕ > 1 ⇔ n² - sin²θ  > 1 ⇔ θ < sin^-1(√(n² + 1))

 

 

77. A gas temperature T is composed of molecules of mass m. Which of the following describes how the average time between intermolecular collisions varies with m?

 

 

⑴ answer: C

⑵ Brownian motion

⑶ mean free path and average time

 

 

⑷ root-mean-square velocity

 

 

⑸ average time between intermolecular collision

 

 

 

78. A particle can occupy two possible states with energies E₁ and E₂, where E₂ > E₁. At temperature T, the probability of finding the particle in state 2 is given by which of the following?

 

 

⑴ answer: B

⑵ At T → 0 K, the probability should be 0.

⑶ At T → ∞ K, the probability should be 1/2.

 

 

79. Consider 1 mole of a real gas that obeys the van der Waals equation of state shown below. If the gas undergoes an isothermal expansion at temperature T0 from volume V₁ to volume V₂, which of the following gives the work done by the gas?

 

 

⑴ answer: D

⑵ W = ∫ p dV = ∫ RT / (V - b) - a / V² dV

 

 

80. A 1 kg block attached to a spring vibrates with a frequency of 1 Hz on a frictionless horizontal table. Two springs identical to the original spring are attached in parallel to an 8 kg block placed on the same table. Which of the following gives the frequency of vibration of the 8 kg block?

 

 

⑴ answer: B

⑵ simple harmonic oscillation

 

 

⑶ k' = 2k, m' = 8m → f' = f/2 

 

입력: 2023.10.07 17:23