31. In a baseball game, the pitcher throw a ball (150 g) at a speed of 30.0 m/s. The batter hit it straight back with a speed of 40.0 m/s. What is the average force exerted by the bat if the bat-ball contact time is 0.005 sec?
(A) 300 N
(B) 14000 N
(C) 1200 N
(D) 2100 N
(E) 900 N

1. Consider the block and spring system shown in the drawing. On the earth’s surface the natural frequency is ω. The system is then transported into moon’s surface (Gravitational acceleration: gMoon = gEarth/6). How will the natural frequency of the system change? (A) 6ω (B) ω (C) ω/6 (D) ω/(E) The frequency doesn’t change.

2. What is this body’s moment of inertia I about axis through disk A? (A) 1.8 kg · m (B) 1.8 kg · m2 (C) 4.0 kg · m (D) 4.0 kg · m2 (E) 5.0 kg ·m2

3. The figure shows a plot of the time-dependent force acting on a particle in motion along the x-axis. What is the total impulse delivered to the particle? (A) 0 kg · m/s (B) 1 kg · m/s (C) 2 kg · m/s (D) 3 kg · m/s (E) 4 kg · m/s

4. A block of mass m sliding down an incline at constant speed is initially at a height h above the ground, as shown in the figure. The coefficient of kinetic friction between the mass and the incline is μ.If the mass continues to slide down the incline at a constant speed, how much energy is dissipated by friction by the time the mass reaches the bottom of the incline? (A) mgh/µ (B) mgh (C) µmgh/ sin θ (D) mgh sin θ (E) 0

5. A baseball is thrown vertically upward and feels no air resistance. As it is rising (A) both its momentum and its mechanical energy are conserved. (B) both its momentum and its kinetic energy are conserved. (C) its kinetic energy is conserved, but its momentum is not conserved. (D) its momentum is not conserved, but its mechanical energy is conserved. (E) its gravitational potential energy is not conserved, buts its momentum is conserved.

6. Which step is one of the Carnot cycle? (A) Isobaric compression (B) Isochoric compression (C) Isothermal compression (D) Isochoric expansion (E) Isobaric expansion

7. One surface is remained at temperature of 300 K and it’s heat current in radiation is H. When it was heated to 600 K, what is the heat current in radiation of this surface comparing to that at 300 K? (A) 32H (B) 16H (C) 8H (D) 4H (E) 2H

8. A conducting sphere is charged up such that the potential on its surface is 100 V (relative to infinity). If the sphere's radius were twice as large, but the charge on the sphere were the same, what would be the potential on the surface relative to infinity? (A) 25 V (B) 50 V (C) 100 V (D) 200 V (E) 400 V

9. There is a solid insulating sphere with radius R and total charge Q. Which diagram is correct for electric field E at any point inside or outside the sphere? (A) (B) (C) (D) (E)

10. An object is placed at a distance 5.0 cm to the left of a concave mirror with a curvature radius 5.0 cm. Determine the location and magnification of the image formed by this image system. (A) The image is formed 2.5 cm to the right of the mirror and it has a magnification of −1/2. (B) The image is formed 5.0 cm to the right of the mirror and it has a magnification of −1. (C) The image is formed 2.5 cm to the left of the mirror and it has a magnification of 1. (D) The image is formed 5.0 cm to the left of the mirror and it has a magnification of −1. (E) The image is formed 1.25 cm to the left of the mirror and it has a magnification of −1/4.

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