【GR1775】 The Solution for GRE Physics Practice Test [01-20]

The Solution for GRE Physics Practice Test [01-20]

 

추천글 : 【GRE】 Solution for GRE Physics Practice Test 

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1. Two objects sliding on a frictionless surface, as represented below, collide and stick together. How much kinetic energy is converted to heat during the collision?

 

 

⑴ answer: E

⑵ v_f,x = 2 m/s × 0.5 kg / (1 kg + 0.5 kg) = 2/3 m/s

⑶ v_f,y = 1 m/s × 1 kg / (1 kg + 0.5 kg) = 2/3 m/s

⑷ Q = ΔK = 1/2 × 0.5 × 2² + 1/2 × 1 × 1² - 1/2 × 1.5 × ((2/3)² + (2/3)²) = 5/6 J

 

 

2. Two simple pendulums A and B consist of identical masses suspended from strings of length L_A and L_B, respectively. The two pendulums oscillate in equal gravitational fields. If the period of pendulum B is twice the period of pendulum A, which of the following is true of the lengths of the two pendulums?

 

 

⑴ answer: E

⑵ T_B = 2π √ (L_B / g)  = 2 T_A = 2 × 2π √ (L_A / g)

⑶ ∴ L_B = 4 L_A  

 

 

3. For the circuit shown in the figure below, what is the current i through the 2 Ω resistor?

 

 

⑴ answer: B

⑵ total current = 20 / (1 + (1^-1 + 2^-1)^-1) = 12 A

⑶ i = 12 / 3 = 4 A

 

 

4. By definition, the electric displacement current through a surface S is proportional to the 

 

 

⑴ answer: E

 

 

 

5. The electric field of a plane electromagnetic wave of wave number k and angular frequency ω is given by E = E₀ (e_x + e_y) sin (kz - ωt). Which of the following gives the direction of the associated magnetic field B?

 

 

⑴ answer: B

⑵ point 1. B is placed on x-y plane

⑶ point 2. B is perpendicular to E

⑷ point 3. Poynting vector equation can indicate the direction of B

 

 

 

6. Which of the following is true about any system that undergoes a reversible thermodynamic process?

 

 

⑴ answer: C

⑵ reversible thermodynamic process : q = 0

 

 

7. For which of the following thermodynamic processes is the increase in the internal energy of an ideal gas equal to the heat added to the gas?

 

 

⑴ answer: B

⑵ q = u + w = u ⇔ w = ∫ P dv = 0

 

 

8. Light of variable frequency ν shines on the metal surface of a photoelectric tube. Einstein's theory of the photoelectric effect predicts that the 

 

 

⑴ answer: D

⑵ E = hν = Φ + ΔV 

⑶ Work function (Φ) is constant.

 

 

9. Characteristic X rays, appearing as sharp lines on a continuous background, are produced when high-energy electrons bombard a metal target. Which of the following processes results in the characteristic X rays?

 

 

⑴ answer: C

⑵ characteristic X-ray

 

 

10. A single-electron atom has the electron in the ℓ = 2 state. The number of allowed values of the quantum number m_ℓ is

 

 

⑴ answer: E

⑵ m_ℓ = {-ℓ, ···, -1, 0, 1, ···, ℓ} = {-2, -1, 0, 1, 2}

 

 

11. A particle of mass m is confined inside a one-dimensional box (infinite square well) of length a. The particle's ground state energy is which of the following?

 

 

⑴ answer: D

⑵ E = n²h² / 8ma² = h² / 8ma² (∵ ground state) = ℏ²π² / 2ma² (∵ ℏ = h / 2π)  

 

 

12. The Planck length is the only combination of the factors G (Newton's gravitational constant), ℏ (Planck's constant  / 2π), and c (the speed of light) that has units of length. Which of the following gives the Planck length?

 

 

⑴ answer: A

⑵ dimension analysis

 

 

13. The speed of light inside of a nonmagnetic dielectric material with a dielectric constant of 4.0 is 

 

 

⑴ answer: C

⑵ c = 1 / √ με

⑶ ε_r = ε / ε₀ 

 

 

14. Consider two identical systems, 1 and 2, each consisting of a planet in circular orbit about a much heavier star. For system 1 the radius of the orbit is a, and for system 2 the radius of the orbit is 4a. Which of the following gives the ratio, T₁ / T₂, of the period of system 1 to the period system 2?

 

 

⑴ answer: D

⑵ Kepler 3rd law : T² ∝ a³. ∴ T₁ / T₂ = 1 / 4^3/2 = 1 / 8

 

 

15. Two identical satellites, A and B, are in circular orbits around Earth. The orbital radius of A is twice that of B. Which of the following gives the ratio of the angular momentum of A to the angular momentum of B?

 

 

⑴ answer: C

⑵ mv² / r = GMm / r² ⇔ v = √ (GM / r)

⑶ L_A : L_B = r_A m v_A : r_B m v_B = √ r_A : √ r_B = √ 2 : 1

 

 

16. A 10 kg box slides horizontally without friction at a speed of 1 m/s. At one point, a constant force is applied to the box in the direction of its motion. The box travels 5 m with the constant force applied. The force is then removed, leaving the box with a speed of 2 m/s. Which of the following gives the magnitude of the applied force?

 

 

⑴ answer: C 

⑵ F × 5 = 1/2 × 10 × (2² - 1²) = 15 ⇔ F = 3 N

 

 

17. What is the magnitude of the magnetic field at the center of a circular conducting loop of radius a that is carrying current I?

 

 

⑴ answer: D

 

 

18. Let ω_p, ω_d, and ω_α be the cyclotron frequencies of protons, deutrons, and alpha particles, respectively, in the same magnetic field. The frequencies are related by which of the following? (Assume that the particle masses are in the ratio 1 : 2 : 4.)

 

 

⑴ answer: E

⑵ Lorentz force : QvB = mrω² = QBrω ⇔ ω = QB / m

⑶ ω_p : ω_d : ω_α = 1/1 : 1/2 : 2/4 

 

 

19. The emission spectrum of the doubly ionized lithium atom Li⁺⁺ (Z = 3, A = 7) is identical to that of a hydrogen atom in which all the wavelength are 

 

 

⑴ answer: A

⑵ E = hf = hc / λ ∝ 1 / n² 

 

 

20. In an atom of hydrogen, the electron is bound to a proton. In an atom of positronium, the electron is bound to a position instead of a proton. Which of the following gives the approximate Rydberg constant for positronium? (For a nucleus of infinite mass, R_∞ = m_ee⁴ / 8ε₀²ch³.)

 

 

⑴ answer: B

⑵ hydrogen atom = 1 proton + 1 electron

⑶ positronium = 1 positron + 1 electron

⑷ the common center of masses ~ the electron or the positron = 1/2 × (the proton ~ the electron)

 

입력: 2023.09.24 08:55