30. Which one is Bragg equation?
(A) F = ma
(B) Hɸ = Eɸ
(C) nλ = 2dsinθ
(D) Δx ∙ Δp = h
(E) E = mc²

31. A uniform solid ball with mass M is supported by a massless rod. Derive the period of the pendulum with a small displacement. (A) T = 2π(1.1L/g)1/2 (B) T = 2π(1.8L/g)1/2 (C) T = 2π(1.5L/g)1/2 (D) T = 2π(0.9L/g)1/2 (E) T = 2π(0.7L/g)1/2

32. A rocket moving in space, far from all other objects, has a speed of vi relative to the Earth. Its engines are turned on, and fuel is ejected in a direction opposite to the rocket’s motion at a speed of vrel relative to the rocket. What is the speed of the rocket, vf relative to the earth once the rocket’s mass is reduced to half its mass before ignition? (A) vi+ vrel ln2 (B) vi+ vrel ln(1/2) (C) vi+ 2vrel (D) (vi+ vrel) / 2 (E) vi+ vrel / 2

33. A satellite is in a circular orbit and has a total mechanical energy of U. If the satellite lost half of its weight and doubled its radius of the circular orbit, what will be its total mechanical energy? (A) 1/4 U (B) 1/2 U (C) U (D) 2 U (E) 4 U

34. A particle of mass m = 0.10 kg and speed v0 = 5.0 m/s collides and sticks to the end of a uniform solid cylinder of mass M = 1.0 kg and radius R = 20 cm. If the cylinder is initially at rest and is pivoted about a frictionless axle through its center, what is the final angular velocity (in rad/s) of the system after the collision? (A) 2.0 (B) 4.2 (C) 6.1 (D) 8.1 (E) 10

35. A set of pulleys is used for supporting the calf (100 N). Please determine the weight of the subject in the right hand side. (A) 50 N (B) 73 N (C) 100 N (D) 141 N (E) 173 N

36. Nadal received a shot with the tennis ball (60 g) travelling horizontally at 50 m/s, and returned the shot at 60 m/s horizontally in the opposite direction in 0.02 sec, what is the average force that Nadal suffered during this stroke? (A) 22 N (B) 30N (C) 180 N (D) 330 N (E) 550 N

37. The aluminum cylinder is 0.10 m2 (cross-sectional area) and 0.35 m long. What is the force exerted on its ends if the elongation is0.20 mm? (Young’s modulus of aluminum is 7.0 × 1010 Pa) (A) 2.00 × 106 N (B) 4.00 × 106 N (C) 8.00 × 106 N (D) 4.00 × 103 N (E) 2.00 × 103 N

38. The wing of an airplane has an area of 1 m2 , and its wing thickness is 0.5 m. Air flows over the top at 20 m/s and under the wing at 10 m/s. The density of air is 1.2 kg/m3 . What is the net force on the wing due to Bernoulli effect? (Gravitational acceleration g = 10 m/s2 ) (A) 12 N (B) 15 N (C) 18 N (D) 183 N (E) 186 N

39. A large tank of water has a hose connected to it. The tank is sealed at the top and has compressed air between the water surface and the top. When the water height h is 3.5 m the pressure of the compressed air is 4.0 x 105 Pa. Take the atmospheric pressure to be 1.0 x105 Pa. What is the speed of the water when it flows out of the hose if h is 3.5 m? (A) 30.8 m/s (B) 28.4 m/s (C) 26.8 m/s (D) 25.5 m/s (E) 23.4 m/s

40. A stainless steel container has a surface area of 0.5 m2 and thickness of 2 cm. If the container is fully filled with 57°C hot-water and the temperature in the room is 27°C, what is the rate of energy loss through the container? (The thermal conductivity of stainless steel is 80 W/m/K) (A) 30 kW (B) 60 kW (C) 120 kW (D) 180 kW (E) 210 kW

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