42. A circuit consists of a single inductor L and a single capacitor C, with natural angular frequency wo. A new circuit is constructed by connecting two identical inductors (each of inductance L) in parallel and two identical capacitors (each of capacitance  C) in parallel, as shown on the right. What is LCc the natural angular frequency of the new circuit? Wo
(A)
(B) ω₀
(C)
(D) 2ω₀
(E) 4ω₀

43. A string of length L=0.75 mL is fixed at both ends and vibrates in a standing-wave pattern at a frequency of 100 Hz. A mass of 1.02 kg is attached to one end, providing the tension in the string. The standing-wave pattern shows three loops as shown on the right. Use g =9.8 m/s². What is the linear mass density of the string? (A) 8.0 x 10-4 kg/m (B) 1.6 × 10-3 kg/m(C) 4.0 × 10-3 kg/m (D) 2.0 x 10-2 kg/m(E) 8.0 × 10-2 kg/m

44.In a single-slit diffraction experiment, monochromatic light of wavelength λ passes through a slit of width a, producing a diffraction pattern on a distant screen. Which of the following statements is correct? (A) If the width of the slit changes, the diffraction pattern does not change. (B) If the wavelength of the light changes, the diffraction pattern does not change. (C) The diffraction pattern is dark at the center of the screen. (D) If the slit width is doubled and the wavelength is also doubled, the positions of the dark fringes remain the same. (E) The width of the central maximum is proportional to the slit width a.

45. A particle moves along the x-axis under the influence of a potential energy function U(x) = x4 - 8x2. Which of the following values of x correspond to positions of stable equilibrium?(A) x = 0(B) x = +2(C) x = -2(D) x = +2 and x = -2(E) x = 0, x = +2, and x = -2

46. A deuteron has the same charge as a proton (qd = qp), but twice the mass (md =2mp). Both particles move in circular paths in a plane perpendicular to a uniform magnetic field. The radius of the deuteron's circular path is twice that of the proton (rd= 2rp). Which of the following statements is correct? (A) The relation between their angular momentum Ld/Lp is 2. (B) The relation between their acceleration is ad/ap is 2. (C) The relation between their angular speed is ωd/ωp =2. (D) The relation between their tangential speed is vd/vp is 2. (E) The relation between their period of the circular motion is Td/Tp is 2.

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.

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