The Solution for GRE Physics Practice Test [21-40]
추천글 : 【GRE】 Solution for GRE Physics Practice Test
21. For an adiabatic process involving an ideal gas having volume V and temperature T, which of the following is constant? (γ = Cp / Cv)
⑴ answer: C
⑵ constant = PVγ = nRTVγ-1
22. An electron has total energy equal to four times its rest energy. The momentum of the electron is
⑴ answer: D
⑵ E2 = (4mec2)2 = p2c2 + (mec2)2 = 16me2c4
⑶ ∴ p = √15 mec2
23. Two spaceships approach Earth with equal speeds, as measured by an observer on Earth, but from opposite directions. A meterstick on one spaceship is measured to be 60 cm long by an occupant of the other spaceship. What is the speed of each spaceship, as measured by the observer on Earth?
⑴ answer: B
⑵ the relative velocity of a spaceship to the other : 0.8c
⑶ relativistic velocity addition
24. A meter stick with a speed of 0.8c moves past an observer. In the observer's reference frame, how long does it take the stick to pass the observer?
⑴ answer: B
⑵ length contraction : 1 m × √ (1 - (0.8c / c)2) = 0.6 m
⑶ 0.6 m / 0.8c = 2.5 ns
25. Consider a set of wave functions ψi(x). Which of the following conditions guarantees that the functions are normalized and mutually orthogonal? (The indices i and j take on the values in the set {1, 2, ∙∙∙, n}.)
⑴ answer: E
⑵ δij = 1 (if i = j) and 0 (if i ≠ j)
26. The normalized ground state wave function of hydrogen is
, where a0 is the Bohr radius. What is the most likely distance that the electron is from the nucleus?
⑴ answer: D
⑵ f(r) = 4πr2 ψ2(r)
⑶ df(r)/dr = 0 ⇔ r = a0
27. The lifetime for 2p → 1s transition in hydrogen is 1.6 × 10-9 s. The natural line width for the radiation emitted during the transition is approximately
⑴ answer: C
⑵ f = 1 / (1.6 × 10-9) = 625 MHz
28. A spring of force constant k is stretched a certain distance. It takes twice as much work to stretch a second spring by half this distance. The force constant of the second spring is
⑴ answer: C
⑵ W = 1/2 kx2 = 1/2 × 1/2 k'(x/2)2
⑶ ∴ k' = 8k
29. On a frictionless surface, a block of mass M moving at speed v collides elastically with another block of the same mass that is initially at rest. After the collision, the first block moves at an angle θ to its initial direction and has a speed v/2. The second block's speed after the collision is
⑴ answer: C
⑵ the horizontal velocity of the second block : v - v/2 cos θ (∵ momentum conservation)
⑶ the vertical velocity of the second block : -v/2 sin θ
⑷ elastic collision : θ = 60°
30. Which of the following gives Hamilton's canonical equation(s) of motion? (H is the Hamiltonian, qi are the generalized coordinates, and pi are the generalized momenta.)
⑴ answer: D
31. A layer of oil with density 800 kg/m3 floats on top of a volume of water with density 1,000 kg/m3. A block floats at the oil-water interface with 1/4 of its volume in oil and 3/4 of its volume in water, as shown in the figure below. What is the density of the block?
⑴ answer: C
⑵ ρgV = 800 × g × V × 1/4 + 1000 × g × V × 3/4
⑶ ∴ g = 800 × 1/4 + 1000 × 3/4 = 950 kg/m3
32. An incompressible fluid of density ρ flows through a horizontal pipe of radius r and then passes through a constriction of radius r/2. If the fluid has pressure P0 and velocity v0 before the constriction, the pressure in the constriction is
⑴ answer: A
⑵ continuity equation : 4πr2 × v0 = 4π(r/2)2 v'2 ⇔ v' = 4v0
⑶ Bernoulli equation : P0 + 1/2 ρv02 = P' + 1/2 ρ(v')2 = P' + 1/2 ρ × 16v02
33. A thermodynamic system, initially at absolute temperature T1, contains a mass m of water with specific heat capacity c. Heat is added until the temperature rises to T2. The change in entropy of the water is
⑴ answer: E
⑵ ΔS = ∫ dQ / T = ∫ mc dT / T = mc ln (T2 / T1)
34. Heat Q is added to a monatomic ideal gas under conditions of constant volume, resulting in a temperature change ΔT. How much heat will be required to produce the same temperature change, if it is added under conditions of constant pressure?
⑴ answer: C
⑵ Cp = Cv + R = 3/2 R + R = 5/2 R
⑶ ∴ Cp / Cv = 5/3
35. A heat pump is to extract heat from an outdoor environment at 7 ℃ and heat the environment indoors to 27 ℃. For each 15,000 J of heat delivered indoors, the smallest amount of work that must be supplied to the heat pump is approximately
⑴ answer: B
⑵ reverse Carnot cycle : QH / W = QH / (QH - QL) = TH / (TH - TL) = 320 / 20 = 16
⑶ ∴ W = 15000 / 16 = 937.5 (W)
36. The capacitor in the circuit below is charged. If switch S is closed at time t = 0, which of the following represents the magnetic energy, U, in the inductor as a function of time? (Assume that the capacitor and inductor are ideal.)
⑴ answer: A
⑵ LC circuit oscillates.
⑶ U = Q2 / 2C + 1/2 LI2, Q = Qmax at t = 0
37. A pair of electric charges of equal magnitude q and opposite sign are separated by a distance ℓ, as shown in the figure below. Which of the following gives the approximate magnitude and direction of the electric field set up by the two charges at a point P on the y-axis, which is located a distance r ≫ ℓ from the x-axis?
⑴ answer: E
⑵ 2 × 1/4πε0 × q/r2 × ℓ/2 / r (direction) = 1/4πε0 × qℓ / r3
38. Consider two very long, straight, insulated wires oriented at right angles. The wires carry currents of equal magnitude I in the directions shown in the figure below. What is the net magnetic field at point P?
⑴ answer: E
39. A beam of muons travels through the laboratory with speed v = 0.8c. The lifetime of a muon in its rest frame is τ = 2.2 × 10-6 s. The mean distance traveled by the muons in the laboratory frame is
⑴ answer: C
⑵ γ = √(1 - 0.82) = 0.6
⑶ d = 0.8c × τ / γ = 880 m
40. A paritlce of mass M decays from rest into two particles. One particle has mass m and the other particle is massless. The momentum of the massless particle is
⑴ answer: B
⑵ Two particles hava momenta of p and -p due to the law of momentum conservation.
⑶ energy-momentum formula
입력: 2023.10.06 23:32
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