3. A boy is seated on the top of a hemispherical mound of ice (frictionless) of radius R as shown in the figure. He is given a very small push and starts sliding. What is the height of the point at which the boy leaves the ice?

(A) R/3
(B) R/2
(C) 2R/3
(D) 3R/4
(E) None of the above.

20. The fact that light can be polarized indicates which of the following? (A) Polarized light travels faster than non-polarized light. (B) Polarized light is monochromatic. (C) Light travels with a constant speed regardless of the reference frame. (D) Light is longitudinal wave. (E) Light is transverse wave.

1. An elevator is accelerating upward with a constant acceleration of g/5 (g is the gravitational acceleration). A simple pendulum of length l is suspended from the ceiling of the elevator. What is the period T of the pendulum for small oscillations? (A)(B) (C) (D) (E)

2. An elevator is accelerating upward with a constant acceleration of g/5 (g is the gravitational acceleration). An ideal spring with spring constant k is suspended vertically from the ceiling of the elevator and is attached by a block of mass m. What is the period T of this spring-block system for small vertical oscillations? (A) (B)(C)(D) (E)

4. A pendulum is formed by pivoting a long thin rod of length L and mass M about a point on the rod. Apparently, the period (T) of this pendulum (for small oscillations) depends on the position of the pivot. Suppose the pivot is at a distance d from the center of the rod. What d would give a minimum T? (The moment of inertia of a thin rod about its center is ML²/12) (A) L/√6 (B) L/6 (C) L/√12 (D) L/12 (E) None of the above.

5. A particle of mass m travels in a horizontal circle of radius R on a frictionless table. The centripetal force is provided by a string passing through a hole in the table attached to two blocks of equal mass M, as shown in the figure. If one hanging block is removed, what will the radius of the particle motion become? (A) ∛(2)R (B) ∛(2)R (C) √2 R (D) 2R (E) None of the above.

6. The two spheres (#2, #3) in the figure are slightly separated and initially at rest; the left sphere (#1) is incident with speed v₀. If M ＞ m, what is the final velocity of sphere #2? We assume head-on elastic collisions. (A) (B) (C) (D) (E) 0.

7. The transverse displacement of a standing wave on a string is given by y(x,t) = 4 sin(0.5x) cos(30t), where x and y are in centimeters (cm).  What is the wave speed of component waves? (A) 10 cm/s (B) 15 cm/s (C) 30 cm/s (D) 60 cm/s (E) 120 cm/s.

8. For an ideal gas undergoing an adiabatic process, both its volume (V) and temperature (T) change. Which one of the following would remain constant? (γ = Cp/Cv) (A) (B) TVγ-1 (C) TγV (D) TγV-1 (E) None of the above.

9. One mole of monatomic ideal gas is used as the working substance of an engine that operates the reversible cycle abcd shown in the figure. What is the efficiency of this engine? (A) 1/2 (B) 1/4 (C) 2/11 (D) 2/13 (E) None of the above.

10. Continued from problem 9. Suppose there is a Carnot engine operating between the highest and the lowest temperature in the cycle abcd. What is the efficiency of this Carnot engine? (A) 1/4 (B) 1/2 (C) 5/8 (D) 3/4 (E) 4/5.

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