47. A planet orbits a star in an elliptical path under a central gravitational force. The length of the major axis of the ellipse is 5 (in arbitrary units), and the length of the minor axis is 4. The star is located at one focus of the ellipse. What is the ratio of the planet's maximum speed to its minimum speed?
(A) 1:1
(B) 2:1
(C) 3:1
(D) 4:1
(E) 5:1

48. A bullet of mass m moving horizontally with initial speed vo strikes a stationary block of mass M that is suspended from the ceiling by a light string, forming a pendulum. The bullet becomes embedded in the block immediately upon impact, and the combined object swings upward to a maximum vertical rise of h as shown on the right. Air resistance is negligible. Which of the following statements is correct? (A) The collision between the bullet and the block is elastic. ///// Vo h m M (B) The mechanical energy of the entire process is conserved. (C) The linear momentum of the block is conserved during the entire process. (D) The maximum height is (E) The mechanical energy lost during the collision is

49. Estimate the typical (order-of-magnitude) speed of air molecules (eg. N2 or O2) under ambient conditions (approximately 20 °C and 1 atm).(A) Nearly at rest (B) A few micrometers per second (C) Several meters per second (D) A few hundred meters per second (E) Several kilometers per second

50.A Carnot cycle is an ideal thermodynamic cycle that consists of two isothermal processes exchanging heat with reservoirs and two adiabatic processes. For the Carnot cycle, which of the following statements is true? (A) The entropy of the reservoir does not change during the cycle. (B) Work is performed only during the adiabatic processes. (C) All of the heat absorbed from the hot reservoir is converted into work. (D) The entropy of the universe increases during one complete cycle. (E) The thermal efficiency does not depend on the volume of the Carnot engine.

51. Two people, A and B, each ofmass 70 kg, are inside an elevator. Person A stands on the floor, while person B hangs from a light rope attached to the ceiling. Let be the force exerted on A by the floor, and be the force exerted on B by the rope. Which of the following statements is correct? (A) (B) (C)(D)(E)

52. A particle of extremely small mass m is confined in a one-dimensional infinite potential well (box) of width L. Its quantum mechanical nature must be taken into account. Which of the following statements is correct? (A) The ground state energy of the particle is zero. (B) The allowed wavenumbers depend on the particle's mass. (C) The allowed energy states of the particle are multiples of the ground state energy. (D) The allowed wavelengths of the particle are multiples ofthe wavelength of the ground state. (E) The allowed wavenumbers of the particle are multiples of the wavenumber ofthe3. A cylindrical tube of length 17.0 cm is closed at one end and open at the other.

53.Assuming the speed of sound in air is v = 340 m/s, what are the lowest two resonance frequencies of the tube? (A) 250 Hz and 500 Hz (B) 250 Hz and 750 Hz (C) 500 Hz and 1000 Hz (D) 500 Hz and 1500 Hz (E) 1000 Hz and 2000 Hz

54. A uniform rod of mass M and length L is pivoted at one end and allowed to swing freely under gravity. For small-angle oscillations, what is the period T of the motion? (Assume gravitational acceleration is g and neglect air resistance.)2L (A)(B)  (C) (D) (E)

55. Two copper wires are connected in parallel. Both wires have the same resistivity, p≈2.0 x 10-8 Ω•m. Wire A has length 200 m and cross-sectional area 1.0 mm². Wire B has length 300 m and cross-sectional area 0.5 mm². What is the equivalent resistance of the two-wire combination? (A) 2.0 Ω(B) 3.0Ω (C) 4.0Ω(D) 8.0 Ω (E) 12.0Ω

56. A soap film (refractive index of n≈ 1.35) is surrounded by air and illuminated by normally incident monochromatic light of wavelength 540 nm (in air). What is the minimum film thickness required to produce constructive interference in the reflected light? (A) 50 nm (B) 75 nm (C) 100 nm (D) 200 nm (E) 300 nm

57. An electric kettle with resistance 12 Ωis connected to a 110 V (rms), 60 Hz AC power supply. The kettle is used to heat 1.0 L of water. Assuming all electrical energy is converted into heat, approximately how long will it take to raise the water temperature by 1 °C? The specific heat of water is about 4.2(A) about 2 s (B) about 4 s (C) about 6s (D) about 8 s (E) about 10 s

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