40. A parallel-plate capacitor without dielectrics is charged with +Q₀ and -Q₀ on their two metal
plates, and the charging battery is disconnected. When a dielectric layer with a dielectric constant k (k ≥ 1) is inserted to fill the gap between the two metal plates, what is the bound charge on the surface of the dielectric layer in contact with the metal plate?
(A) Q₀(k − 1)/k
(B) (k − 1)Q₀
(C) (2 − k)Q₀
(D) kQ₀/(k − 1)
(E) Q₀/(k + 1)

36. A uniform and thin stick of mass (m) and length (l) is held vertically by two strings of negligible mass. fmmediately after one string is cut, what is the magnitude of linear acceleration of the middle of the stick? (The moment of inertia of the thin stick is ml2/3 for an axis through one end.)(A) g/4 (B) g/2 (C) 3g/4 (D) g (E) 3g/2

37. A uniformly charged ring with a radius of α is placed on the xy planewith its central axis aligned with the z-axis. ff the total charge on the ring isQ, what is the electric field at z = z0? (k = 1/4πε0, = )(A) (B) (C)(D) (E)

38. A technician wearing a brass bracelet enclosing area 0.005 m2 places her hand in a solenoid whose magnetic B-field is 7.0 T directed perpendicular to the plane of the bracelet. The resistance R around the bracelet’s circumference is 0.02 Ω. An unexpected power failure causes the field to drop to 1.5 T in a time interval of 20 ms. Estimate the power delivered to the bracelet.(A) 23.6 W (B) 31.5 W (C) 47.3 W (D) 63.1 W (E) 94.6 W

39. The howler monkey is the loudest land animal and, under some circumstances, can be heard up to a distance of 8.9 km. Assume the acoustic output of a howler to be uniform in all directions and that the threshold of hearing is W/m2. A juvenile howler monkey has an acoustic output of 63 μW. What is the ratio of the acoustic intensity produced by the juvenile howler to the reference intensity I0, at a distance of 200 m?(A) 63 (B) 125 (C) 175 (D) 250 (E) 375

41. The human ear canal is, on average, 2.5 cm long. ft is open to the outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range)of the standing waves in the ear canal. Recall that, at 20C, the speed of sound in air is about 343 m/s.(A) 1715 Hz (B) 3430 Hz (C) 6860 Hz (D) 13720 Hz (E) 20580 Hz

42. The charge Q is -3.0 nC. How much charge q1 is needed to bringcharge q2 into static equilibrium?(A) -6 nC (B) 6 nC (C) 3 nC (D) 12 nC (E) -12 nC

43. A rectangular coil of N turns, each of width α and length b is in amagnetic field B directed into the page, with only half of the coil in theregion of the magnetic field. The resistance of the coil is R. The coil canbe moved to the right, up or down. What is the magnitude of the inducedcurrent if the coil is moved with a speed v down?(A) 4NBav/R (B) NBav/R (C) 2NBav/R (D) 2NBav (E)NBav/R

44. The surface water temperature in tropical oceans is above 25℃, and the deep-water temperature is about 4°C. If the Carnot engine is operated at these two temperatures, what is the maximum efficiency of this engine?(A) 7 % (B) 9 % (C) 16 % (D) 84 % (E) 93 %

45. A cube of metal has an edge length of 10 cm. It has a density 3.0 g/cm3 and a specific heat 0.2cal/g°C. When the internal energy of the cube increases by 9000 cal, its temperature increases by _____.(A) 9°C (B) 10°C (C) 12°C (D) 15°C (E) 20°C

46. Sound pressure level is defined as SPL(dB) = (P⁄P0), where P is sound wave pressureand P0 = 20 μPa. SPL decreases 6 dB as a listener's distance doubles from the sound source. Thesound level is 110 dB at one meter away from the explosion of firecrackers. How far away wouldit be needed to reduce the sound level to an acceptable level of 80 decibels?(A) 5 m (B) 16 m (C) 32 m (D) 60 m (E) 100 m