44. Two stars are separated by an angle of 3 × 10⁻⁵ radians. What is the diameter of the smallest telescope that can resolve the two stars using visible light (nm)? (Ignore any effects due to Earth’s atmosphere.)
(A) 1 mm
(B) 2.5 cm
(C) 10 cm
(D) 2.5 m
(E) 10 m

40. A car approaches a stationary police car at 36 m/s. The frequency of the siren (relative to the police car) is 500 Hz. What is the frequency (in Hz) heard by an observer in the moving car as he approaches the police car? (Assume the velocity of sound in air is 343 m/s.) (A) 220 (B) 383 (C) 448 (D) 526 (E) 552

41. A pipe open at both ends has a fundamental frequency of f. A second pipe closed at one end and open at the other end has the same fundamental frequency. What is the ratio of the length of the pipe open at both ends to the length of the pipe closed at one end? (A) 1 (B) 2 (C) (D) 4 (E)

42. A converging glass lens with a refractive index of 1.5 is placed in water with a refractive index of 1.25. How many times of focal length of the lens will be changed in water? (A) 0.3 (B) 0.8 (C) 1.5 (D) 2 (E) 2.5

43. An object is located at 40 cm from the first of two thin converging lenses of focal lengths 20 cm and 10 cm, respectively, as shown in the figure above. The lenses are separated by 30 cm. The final image formed by the two-lens system is located ______. (A) 5.0 cm to the right of the second lens (B) 13.3 cm to the right of the second lens (C) infinitely far to the right of the second lens (D) 13.3 cm to the left of the second lens (E) 100 cm to the left of the second lens

45. Unpolarized light of intensityI0is incident on a series of three polarizing filters. The axis of the second filter is oriented at 45o to that of the first filter, while the axis of the third filter is oriented at 90o to that of the first filter. What is the intensity of the light transmitted through the third filter? (A) 0 (B) (C) (D) (E)

46. If a gas undergoes a series of pressure (P) and volume (V) changes, as shown below, how much work is done by the gas along the path a→b→c→d→e→f→a? (A) 20 J (B) 30 J (C) 40 J (D) 50 J (E) 60 J

47. There is a laminar flow in a tube. When both the radius and length of the tube are doubled, how many times of flow resistance is changed? (A) (B) (C) (D) (E)

48. A steam of water of densityρ, cross-sectional area A, and speed υ strikes a wall that is perpendicular to the direction of the stream, as shown in the figure below. The water then flows sideways across the wall. The force exerted by the stream on the wall is ______. (A) (B) (C) (D) (E)

49. Water is flowing at 4.0 m/s in a circular pipe. If the diameter of the pipe decreases to 1/2 its former value, what is the velocity of the water downstream? (A) 16 m/s (B) 4.0 m/s (C) 1.0 m/s (D) 8.0 m/s (E) 2.0 m/s

50. A 5.0 nC point charge is embedded at the center of a nonconducting sphere (radius = 2.0 cm) which has a charge of -8.0 nC distributed uniformly throughout its volume. What is the magnitude of the electric field at a point that is 1.0 cm from the center of the sphere? (where electric constant k=9.0×109 N·m 2 /C2 ) (A) 9.0 × 104 N/C (B) 1.8 × 105 N/C (C) 2.7 × 105 N/C (D) 3.6 × 105 N/C (E) 7.2× 105 N/C