6. My weight is mg and the maximum speed my jump is v₀. If I jump off a cart of mass M that can move without friction, what is my maximum horizontal displacement via adjusting the angle of my jump? Note that v₀ is now measured relative to the car.

(A)
(B)
(C)
(D)
(E) none of the above.

7. An object of mass m that is initially at rest slides down from the top of a smooth sphere (of radius R). If the size of the object is negligible, at what angle θ will it detach from the sphere? (A) cosθ = 1/2 (B) sinθ = 1/2 (C) sinθ = 2/3 (D) cosθ = 2/3 (E) none of the above.

8. A uniform soda can of base area A = 12 cm², mass m = 10 g and height h = 20 cm is filled with soda of density ρ = 1 g/cm³. Use x to denote the height of the remaining soda; find the x that makes the center of mass of the whole system the lowest. It occurs when the soda is (A) half-filled (B) less than half, but more than a quarter filled (C) less than a quarter filled (D) completely empty (E) none of the above.

9. A 10 kg monkey climbs up a light rope that runs over a frictionless tree limb and back down to a 20 kg package on the ground. What is the least acceleration the monkey must have if it is to lift the package off the ground? (A) g/4 (B) g/2 (C) g (D) 2g (E) none of the above.

10. A block of mass m = 10 kg slides from vertical height h = 1 m down a slope of angle θ = π/3 and kinetic friction coefficient μk = 0.5. At the foot of the slope lies a spring of constant K = 200 nt/m. What is the maximum compression of the spring? (A) 1 (B) 1.5 (C) 2 (D) 2.5 (E) none of the above.

11. Three masses are connected by two massless pulleys as shown in the figure. Find the acceleration of the 10 kg mass?  (A) 6 (B) 4 (C) 2 (D) 1 (E) none of the above.

12. How much gravitational potential energy is stored in a uniform solid sphere of mass M and radius R? (Use G to denote the gravitational constant). (A) GM/R (B) GM²/R (C) 2GM²/R (D) 2GM²/5R (E) none of the above.

13. A bowler throws a bowling ball of radius R and mass M (and moment of inertia I = 2MR²/5) along a lane. The ball slides on the lane with initial speed v₀ and initial angular speed ω₀. The coefficient of kinetic friction between the ball and the lane is μk. How long does it take before the ball rolls without slipping? (A)(B)(C)(D)(E) none of the above.

14. A cubic block of size ℓ and density ρ floats in a container of base area A which is filled with fluid of density ρf. If I tap the block on the top surface, it will oscillate up and down. What will be the period of this simple harmonic motion? (A)(B)(C) (D) (E) none of the above.

15. Four capacitors are arranged as shown in the right figure. A potential difference ΔV is applied between the terminal C and D. A voltmeter M is connected between A and B. What is the capacitance of capacitor X such that the meter reads zero? (A) 5C/2 (B) 8C/5 (C) 20C/11 (D) 1C (E) 20C.

16. What is the potential of point a with respect to point b in the right figure when switch S is open? (A) -4V (B) 4V (C) 8V (D) 0V (E) 2V.

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