37.A parallel-plate capacitor is connected to an ideal battery that maintains a constant voltage V. A dielectric slab initially completely fills the space between the plates. An engineer slowly pulls the slab out at constant speed while the battery remains connected. Which of the following correctly describes the work done by the engineer (W_ext) and the change in the electrostatic energy stored in the capacitor (△U)?
(A) W_ext is positive and AU is positive.
(B) W_ext is positive and △U is negative.
(C) Wext is negative and △U is positive.
(D) W_ext =0 and △U is negative.
(E) W_ext =0 and△U is positive.

38.X-ray imaging relies on the fact that different biological tissues have distinct attenuation coefficients (µ). An X-ray beam with an initial intensity I0 passes through a bone of thickness x and attenuation coefficient u, emerging with intensity 1= Ioe -μX. If the same X-ray beam instead passes through another tissue of the same thickness but with half the attenuation coefficient (μ'= µ/2), what is the resulting intensity I? (A) I' = 1/2 (B) I'=I (C) I' = I2/I0 (D)(E)

39.To visualize a virus with a diameter of approximately 20 nm, a researcher uses a transmission electron microscope. Electrons are accelerated from rest through a potential difference V, acquiring a non-relativistic kinetic energy K= eV. According to the de Broglie relation, how do the electron wavelength and the microscope's resolution change if the accelerating voltage is increased to four times its original valuе? (A) The wavelength doubles; resolution becomes worse. (B) The wavelength is halved; resolution becomes better. (C) The wavelength decreases by a factor of 4; resolution becomes better. (D) The wavelength increases by a factor of ; resolution becomes worse. (E) The wavelength decreases by a factor of 2; the resolution decreases by a factor of 2.

40.A rigid container holds a mixture of two non-reacting ideal gases: 1.0 mole of He and 2.0 moles of N2. The temperature of the mixture is maintained at 27 °C. Let R denote the universal gas constant. What is the constant-volume molar specific heat Cv of the gas mixture? (Assume all degrees of freedom appropriate at room temperature are active.) (A) 3R/2 (B) 13R/6 (C) 5R/2 (D) 3R (E) 7R/2

41. A nonrelativistic charged particle (speed ＜＜c) with mass m and charge +q moves with velocity in a uniform magnetic field .Which of the following statement is correct? (A) Regardless of the direction of , the magnetic field does no work on the charged particle. (B) Regardless of the direction of , the magnetic force on the particle has magnitude qvB. (C) If is parallel to, the particle experiences an acceleration due to the magnetic field. (D) If is perpendicular to, the particle undergoes circular motion with аш radius r= (E) If is perpendicular to , the magnitude of changes due to the magnetic force.

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

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