【GR1775】 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. 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 # of unpaired electrons = 3

 

 

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

 

 

⑴ answer: B

 

 

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

 

 

⑴ answer: E 

⑵ Only H and T cannot be observed at the same time, but T and its simple computational result, p, can be observed at the same time.

 

 

24. 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 Δ = 1/2 × (6000 - 2000) × (0.03 - 0.01) = 40 J

 

 

25. 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 : PV^γ = constant, γ ＞ 1

 

 

26. 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

 

 

 

27. 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 open at both ends : λ_n = 2L / n, f_n = v / λ_n = nv / 2L (cf. v is the velocity of sound)

⑶ intermediate conclusion : v / 2L = 50 (Hz)

⑷ closed at one end : λ_m = 4L / (2m-1), f_m = v / λ_m = (2m-1)v / 4L = (2m-1) / 2 × 50 = 25, 75, 125, 175, ··· Hz

 

 

28. 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

 

 

 

29. 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

 

 

 

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

 

 

⑴ answer: D

⑵ E² = (pc)² + (mc²)²

⑶ (mc²)² = E² - (pc)² = 9.9 × 0.1 = 0.99 ⇔ mc² ≒ 1 GeV

 

 

31. 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

 

 

32. 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 Since the electric field inside the conductor is zero, the potential inside the conductor is equal to the potential on the outer surface of the conductor.

 

 

33. 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

 

 

34. A series AC circuit with impedence 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 Only resistance contributes to power.

 

 

35. The quantum efficiency of a photon detector is 0.1. If 100 photons are sent into the detector, one after the other, the detector will detect photons

 

 

⑴ answer: E

⑵ binomial distribution

⑶ average = np = 100 × 0.1 = 10

⑷ variance = np(1 - p) = 100 × 0.1 × 0.9 = 9

 

 

36. Two students perform an experiment in which they drop a ball from rest from a known height above the ground and measure the speed of the ball just before it strikes the ground. From repeated measurement, the students estimate the uncertainty in the measured speed of the ball to be 10 percent. Which of the following gives the uncertainty in the kinetic energy of the ball? (Assume the uncertainty in the ball's mass is negligibly small.)

 

 

⑴ answer: D

⑵ Taylor expansion

 

 

 

37. A particle in an infinite square well has as its initial wave function an equal mixture of the first three orthonormal stationary states: 

 

 

The value of the normalization constant A is equal to which of the following?

 

 

⑴ answer: A

⑵ ∫ ΨΨ* = A²(1+1+1) = 1 

 

 

38. A matter wave of energy E ＞ 0 and wave number k is incident from the left on a potential well of width L and depth V₀. The top of the well is at zero energy and the bottom of the well is at -V₀, as shown in the figure below. The spatial part of the wave function in region 3 has which of the following forms? (A is a constant.)

 

 

⑴ answer: A

⑵ time-independent Schrödinger equation

 

 

⑶ point 1. Ψ is exponential functoin.

⑷ point 2. Ψ should have exponents which are imaginary.

 

 

39. Spring 1 has force constant k₁ and spring 2 has force constant k₂, where k₁ > k₂. If the same external force is applied to both springs, which of the following is true about the extensions (Δx₁ and Δx₂) and the stored potential energies (U₁ and U₂) of the two springs?

 

 

⑴ answer: A

⑵ Δx = F / k

⑶ U = 1/2 kx² = F² / 2k

 

 

40. A stone is glued to the top of a light wooden block that floats in a pool of water, as shown in Figure 1 below. Assume that exactly 50 percent of the block is under water, and that the stone has half the weight of the block. If the block and stone are flipped over, as shown in Figure 2, and replaced in the pool, the amount of the block under water will be 

 

 

⑴ answer: A

⑵ (m_Stone + m_Block)g = ρ_BlockgV_Block × 0.5 = ρ_StonegV_Stone + ρ_BlockgV_Block × η

⑶ ∴ η ＜ 0.5 

 

입력: 2023.09.24 11:11