59. A sample of radioactive nuclei of a certain element can decay only by γ -emission and β -emission. If the half-life for γ -emission is 24 minutes and that for β -emission is 36 minutes, the half-life for the sample is
(A) 30 minutes
(B) 24 minutes
(C) 20.8 minutes
(D) 14.4 minutes
(E) 6 minutes

34. A box of mass 1 kg was placed on the edge of a rotating table with radius 10 cm, as shown below. At what rotating speed, the box begins to slide away? (The coefficient of static friction between the box and table is 0.8) (A) 32 cm/s (B) 53 cm/s (C) 68 cm/s (D) 89 cm/s (E) 98 cm/s

35. A 10 N tangential force is applied at the edge of a 20 kg disk with a radius of 2.0 m. Then, the disk rotates from rest. What is the kinetic energy of the disk 3.0 s after the force is applied? (A) 180 J (B) 360 J (C) 45 J (D) 90 J (E) 23 J

36. A uniform beam of weight 300 N and length 3.0 m is suspended horizontally. On the left it is hinged to a wall; on the right it is supported by a cable bolted to the wall at distance D above the beam. The tension on the cable is 250 N. What value of D corresponds to that tension? (A) 1.25 m (B) 1.50 m (C) 1.75 m (D) 2.00 m (E) 2.25 m

37. A forceis applied on a particle. What is the work done by the force as the particle moves in an x-y plane from (1.0 m, 0.0 m) to (-2.0 m, 3.0 m)? (A) 15 J (B) 1.0 J (C) 3.0 J (D) 17 J (E) 11 J 

38. A single conservative forceacts on a particle that moves along an x axis. The particle has mass of 2.0 kg. The potential energy associated withis described by =, where x is in meters. What is the value of x whereis equal to zero? (A) -1.0 m (B) 1.0 m (C) 0.5 m (D) -0.5 m (E) 0 m 

39. In the figure, a block of mass m = 20.0 kg slides through a horizontal frictionless ground at a speed of v = 0.50 m/s. It then compresses the spring with spring constant k = 5.0 N/m. When the block decelerates to a stop, by what distance d is the spring compressed? (A) 0.5 m (B) 1.0 m (C) 1.5 m (D) 2.0 m (E) 2.5 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 oneend?(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

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