46. A solid conducting sphere (radius = 5.0 cm) has a charge of 0.25 nC distributed uniformly on its surface. If point A is located at the center of the sphere and point B is 15 cm from the center, what is the magnitude of the electric potential difference between these two points? (k_e = 9 x 109 N•m² /C2 )
(A) 15 V
(B) 23 V
(C) 30 V
(D) 45 V
(E) 60 V

42. An ambulance moves at a speed of 50 km/hr, and its siren emitting sound at a frequency of 5.0x102 Hz. What frequency of sound is heard by a runner who is running at 4 m/s approaching each other in the opposite direction (the speed of sound in air is 345 m/s)? (A) 47 Hz (B) 475 Hz (C) 506 Hz (D) 527 Hz (E) 555 Hz

43. One rope is wiggled with frequency f = 2.0 Hz, amplitude A = 1.0 m, and wave speed v = 4.0 m/s. What is the mathematical description of this wave? (A) y(x,t) = cosπ (2x − t) (B) y(x,t) = cosπ (2x + t) (C) y(x,t) = cosπ (x − 2t) (D) y(x,t) = cosπ (x + 2t) (E) y(x,t) = cosπ (x − 4t)

44. There is a 1 kg gallium block and its melting point is around 30°C. What is the change of entropy when it was melted from solid to liquid at 30°C? (The fusion heat of gallium is Lf = 80.18 kJ/kg) (A) 0 (B) 0.265 kJ/K (C) 0.374 kJ/K (D) 2.673 kJ/K (E) 3.779 kJ/K

45. Two charges of 15 pC and −40 pC are inside a cube with sides that are of 0.40 m length. Determine the net electric flux through the surface of the cube. (εo= 8.85 x 10-12 C2 / N•m2 ) (A) 2.8 N•m2 /C (B) −2.8 N•m2 /C (C) 1.1 N•m2 /C (D) −1.1 N•m2 /C (E) −0.47 N•m2 /C

47. A segment of wire of total length 2.0 m is formed into a circular loop having 5.0 turns. If the wire carries a 1.2-A current, determine the magnitude of the magnetic field at the center of the loop. (μ0 = 4π• 10-7 T∙m/A) (A) 59 μT (B) 69 μT (C) 79 μT (D) 89 μT (E) 94 μT

48. A circuit consists of a capacitor and an inductor that are sequentially connected. If the capacitance is 0.5 mF and the inductance is1 H, what is the resonance frequency of this circuit? (A) 23.4 rad/s (B) 44.7 rad/s (C) 50.5 rad/s (D) 76.8 rad/s (E) 87.6 rad/s

49. Three thin lenses with focal lengths 0.1 m, 0.2 m, and 0.3 m are placed next to each other. What is the equivalent focal length of a single lens? (A) 0.05 m (B) 0.15 m (C) 0.25 m (D) 0.33 m (E) 0.45 m

50. A cloud layer is 1000 m above the planet, with the area of 1x106 m2 , considered as the plates of a parallel-plate capacitor. If an electric field strength is greater than 3.0x106 N/C, it causes lightning, what is the maximum charge the cloud can hold? (εo= 8.85 x 10-12 C2 /N•m2 ) (A) 28.55 C (B) 26.55 C (C) 24.55 C (D) 22.55 C (E) 20.55 C

51. Two isotopes leave the slit at point S and into a magnetic field of magnitude 0.100 T pointing into the page, each has speed of 1.00 x 106 m/s. The first one contain one proton and has a mass of 1.67 x 10-27 kg and the other contains a proton and a neutron and has a mass of 3.34 x 10-27 kg. What is the distance that they could be separated when they strike a photographic plate? (e = 1.6 x 10-19C) (A) 0.520 m (B) 0.313 m (C) 0.210 m (D) 0.105 m (E) 0.104 m

52. If a farsighted patient’s near point of eyes is 40 cm, what kinds of lens and focal length of a corrective lens have to enable the eye to see clearly an object 20 cm away? (A) converging lens, f = 13.3 cm (B) diverging lens, f = 13.3 cm (C) converging lens, f = 40 cm (D) diverging lens, f = 40 cm (E) converging lens, f = 20 cm