【GR1776】 The Solution for GRE Physics Practice Test [21-40]

The Solution for GRE Physics Practice Test [21-40]

 

추천글 : 【GRE】 Solution for GRE Physics Practice Test 

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21. 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 

 

 

 

22. 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 wavelengths are 

 

 

⑴ answer: A

⑵ Bohr's model can be used here.

 

 

 

23. In an atom of hydrogen, the electron is bound to a proton. In an atom of positronium, the electron is bound to a positron 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)

 

 

 

24. Which of the following gives the total spin quantum number of the electrons in the ground state of neutral nitrogen (Z = 7) ?

 

 

⑴ answer: C

⑵ Hund's rule : 1/2 for each spin × 3 = 3/2

 

 

 

25. Consider a Hermitian operator  with the property Â⁴ = 1. Which of the following is an allowed pair of eigenvalues of  ?

 

 

⑴ answer: B

⑵ Since the eigenvalues of a quantum mechanical operator correspond to measurable quantities, the eigenvalues must be real. (link)

 

 

26. Consider the kinetic energy operator T and the Hamiltonian operator Ĥ above. Which of the following pairs of observables can be measured simultaneously with no restriction on their precision?

 

 

⑴ answer: E

⑵ uncertainty principle : It is impossible to know the momentum and the position at the same time.

⑶ Even if so, it is possible to know the kinetic energy and the momentum, with the following formula.

 

 

 

27. Electromagnetic radiation emitted from a nucleus is most likely to be in the form of 

 

 

⑴ answer: A

⑵ Gamma ray is generated due to the change of the state of a nucleus.

 

 

28. A sample of nitrogen gas undergoes the cyclic thermodynamic process shown below. Which of the following gives the net heat transferred to the system in one complete cycle 1 → 2 → 3 → 1 ?

 

 

⑴ answer: C

⑵ Q = U + W = W (∵ no state change)

⑶ W = ∫ P dV = (1/2) × (0.03 - 0.01) × (6000 - 2000) = 40 (J)

 

 

29. For an ideal gas, consider the three thermodynamic processes - labeled 1, 2, and 3 - shown in the PV diagram below. Each process has the same initial state and the same final volume. One process is adiabatic, one is isobaric, and one is isothermal. Which of the following correctly identifies the three processes?

 

 

⑴ answer: D

⑵ adiabatic process : PV^γ = constant, γ = C_P / C_V > 1 (less change in V when compared to isothermal process)

⑶ isbaric process : P = constant

⑷ isothermal process : PV = constant (more change in V when compared to adiabatic process)

 

 

30. The driver of a police car hears an echo of the car's siren from a wall toward which the car is moving with a speed of 3.5 m/s. If the speed of sound is 350 m/s and the frequency of the siren is 600 Hz, the driver hears the echo at a frequency nearest to which of the following?

 

 

⑴ answer: E

⑵ situation : The car is moving toward the wall, ringing the siren.

⑶ doppler effect

 

 

 

31. The first five harmonics produced by an organ pipe open at both ends are 50 Hz, 100 Hz, 150 Hz, 200 Hz, and 250 Hz. Which of the harmonics, if any, will survive once the pipe is closed at one end?

 

 

⑴ answer: E

⑵ standing wave 

⑶ open at both ends : λ_n = 2L / n, where L is the length of the pipe and n is 1, 2, ···.

⑷ closed at one end : λ_m = 4L / (2m-1), where L is the lendgh of the pipe and m is 1, 2, ···.

⑸ λ_n cannot be the same with λ_m. 

 

 

32. A refracting telescope consists of two converging lenses separated by 100 cm. The eye-piece lens has a focal length of 20 cm. The angular magnification of the telescope is 

 

 

⑴ answer: A

⑵ telescope

 

 

 

33. The best type of laser with which to do spectroscopy over a range of visible wavelength is 

 

 

⑴ answer: A

 

 

34. A rod measures 1.00 m in its rest system. How fast must an observer move parallel to the rod to measure its length to be 0.80 m?

 

 

⑴ answer: B

⑵ length contraction 

 

 

 

35. A particle decays in 2.0 μs in its rest frame. If the same particle moves at v = 0.60c in the lab frame, how far will it travel in the lab before decaying?

 

 

⑴ answer: D

⑵ time dilation 

 

 

 

36. The rest mass of a particle with total energy 5.0 GeV and momentum 4.9 GeV/c is approximately

 

 

⑴ answer: D

⑵ The relationship between the momentum and total energy in the theory of relativity 

 

 

 

37. If charge +Q is located in space at the point (x = 1 m, y = 10 m, z = 5 m), what is the total electric flux that passes through the yz-plane?

 

 

⑴ answer: D

⑵ Maxwell's 1st law

 

 

⑶ About half of the total flux goes up and about half of the total flux goes down.

 

 

38. A point charge Q is placed at the center of a hollow, conducting spherical shell of inner radius a and outer radius b, as shown below. A net charge q is placed on the conducting shell. If the electric potential is assumed to be 0 at infinity, the magnitude of the electric potential at r, where a < r < b, is

 

 

⑴ answer: E

⑵ As the shell consists of conducting material, the intensity of the electric field at r, where a < r < b, is 0.

⑶ Thus, the electric potential V = ∫ E · ds at r, where a < r < b, is the same with the value at a. 

 

 

39. The figure below shows three arrangements of one electron (e) and two protons (p). Which of the following is true about the magnitude F of the net electrostatic force acting on the electron due to the protons?

 

 

⑴ answer: C

⑵ F₁ : synergism

⑶ F₃ : orthogonality

⑷ F₂ : antagonism 

 

 

40. A series AC circuit with impedance Z consists of resistor R, inductor L, and capacitor C, as shown below. The ideal emf source has a sinusoidal output given by ε = ε_max sin ωt , and the current is given by I = I_max sin(ωt - ϕ). What is the average power dissipated in the circuit? ( I_rms is the root-mean-square current.)

 

 

⑴ answer: A

⑵ For this reason, there is an aspect in which the root-mean-square current was introduced.

 

 

입력 : 2022.12.27 01:21