47. An ideal parallel-plate capacitor connected to a battery of voltage V₀, it has charge of magnitude Q0 on its plates. The plates are pulled apart to a separation from d to 2d while the capacitor remains connected to the battery. After the plates are 2d apart, what are the magnitude of the charge on the plates and the potential difference between them?
(A) 0.5Q₀, 0.5V₀
(B) 0.5Q₀, V₀
(C) Q₀, V₀
(D) 2Q₀, V₀
(E) 2Q₀, 2V₀

43. Ethanol of density ?? flows smoothly through a horizontal pipe that tapers in cross-sectional area from A1 to A2 (A1 = 2A2) as shown in the figure. The pressure difference between the wide and narrow sections of pipe is ∆P. What is the volume flow rate of the ethanol? (A) (B) (C) (D) (E)

44. An ideal monoatomic gas of one mole is at pressure P, volume V, and temperature T. The gas is heated at constant volume to 2T. Then the gas is allowed to expand at constant temperature to 2V. Finally, the gas cools at constant pressure to T. What is the net entropy change for this ideal gas? (The ideal gas constant is R) (A) R ln 2 (B) −R ln 2 (C) 0 (D) R ln 4 (E) not calculatable by the above information

45. The figure shows a closed cycle for a gas. From c to b, 60 J is transferred from the gas as heat. From b to a, 100 J is transferred from the gas as heat, and the magnitude of the work done by the gas is 80 J. From a to c, 400 J is transferred to the gas as heat. What is the work done by the gas from a to c?  (A) -240 J (B) 240 J (C) 320 J (D) -320J (E) -160 J

46. A quantity of an ideal gas is compressed to half its initial volume. The process may be adiabatic, isothermal or occurring at isobaric. Rank those three processes in order of the work required of an external agent, least to greatest. (A) adiabatic, isothermal, isobaric (B) adiabatic, isobaric, isothermal (C) isothermal, adiabatic, isobaric (D) isobaric, adiabatic, isothermal (E) isobaric, isothermal, adiabatic

48. A group of identical capacitors is connected first in series and then in parallel. The combined capacitance in parallel is 100 times larger than for the series connection. How many capacitors are in the group? (A) 5 (B) 10 (C) 50 (D) 100 (E) 200

49. A cylinder contains n mol of helium gas (ideal monatomic gas) at a temperature of 300 K. The universal gas constant is R (R=) , where is Avogadro’ number and is Boltzmann’s constant. If the gas is heated at constant pressure, how much energy must be transferred by heat to the gas after it is heated to 500 K? (A) 200n? (B) 300nR (C) 500nR (D) 800nR (E) 1000nR

50. The switch is connected to position a for a long time interval as shown in the figure. At t = 0, the switch is thrown to position b. After this time, what are the frequency of oscillation of the LC circuit? (A) 159 Hz (B) 359 Hz (C) 559 Hz (D) 759 Hz (E) 959 Hz

51. An infinite long wire is charged uniformly with line charge density λ. What is the electric field at a point with a distance y from the stick? (Electric constant is ε0) (A) (B)(C) (D) (E)

52. A charge +q is at the position a and a second charge –q is placed at –a as shown in the figure. What is the limiting form of the electric field for x ≫ a? (Coulomb’s constant is ) (A) (B) (C) (D) (E)

53. A 30-turn circular coil of radius 1 m and resistance 1 Ω is placed in a magnetic field directed perpendicular to the plane of the coil. The magnitude of the magnetic field varies in time according to the expression B = 0.1 t + 0.04 t2 , where B is in tesla and t is in second. Calculate the induced emf in the coil at t = 5 s. (A) 27 V (B) 37 V (C) 47 V (D) 57 V (E) 67 V