16. Follow Problem 15. Consider four various bodies: solid cylinder (n=1/2), solid sphere (n-215), hollow cylinder (n=1), hollow sphere (n=2/3). Assume that these bodies have the same mass M and radius R. Which body rolls down the incline fastest?
(A) solid cylinder
(B) solid sphere
(C) hollow cylinder
(D) hollow sphere.

複選題1. Newton's law of gravitation states that there exists an attractive force between the planet and the sun of masses m and M, respectively. The magnitude of the force is written as F = GmM /r2, where r is the distance of the planet from the sun, which is called the central force. The orbital motion of a particle under a central force is always (A)unbounded (B) bounded (C) confined to a plane (D) None of these.

2. Hook's law of spring states that if you stretch a spring from its equilibrium length by a displacement x, then the force F that the spring exerts on you is F = -c . Now a particle of mass m is executing oscillation obeying Hook's law. If the amplitude of oscillation is A, then its period is (A)proportional to (B) independent of A (C) proportional to 1/ (D) proportional to A2.

3. Experiments show that any liquid is incompressible. This implies that the density of a liquid (A) is a constant (B) varies at different parts of liquid (C) behaves like a gas (D) None of these.

4. When a charged particle (charge q and mass m) moves with velocity u through a region of space where both electric field E and magnetic induction field B are present. The charged particle would experience a force F. In vector form, the force is (A) F=qE+uxB (B) F=qExB (C) F=qu(E.B) (D) F=q(E+uxB) .

5. Two conducting plates have an area A and are separated by a distance d. The capacitance C of the parallel-plate capacitor is (A)(B)(C) (D) , where ε0, is the electric constant and μ0is the magnetic constant in a vacuum.

6.A very long ideal solenoid with a cross-section area A has N turns and a length l . Assume that each turn is circular. The self-inductance Ls of this ideal solenoid is NA (A) (B)(C) (D) , where ε0 is the electric constant and μ0 is the magnetic constant in a vacuum.

7.The classic method used to demonstrate the essential features of interference of light was devised by Thomas Young, namely, Young's two-slit experiment. The distance between any two consecutive bright fringes (or dark fringes) is called fringe width. Now if the whole Young's two-slit apparatus is immersed in water, the fringe width will (A) increase (B) decrease (C) unchanged (D) disappear. N-uA

8. The unit of magnetic induction field B is denoted as [B]=[N]/[A.m] and the electric field is [E]=[V] /[m], where [N] is Newton, [A] Ampere [V] Volt, and [m] meter. The clectric field due to an infinite non-conducting plane with uniform surface charge densityσ is given by E=σ /2ε0, where ε0 is the electric constant. On the other hand, the magnetic induction inside an ideal solenoid with steady current I is given by B= μ0nl , where  μ0 is the magnetic constant and n is the number of turns per unit length. By using these hints, the quantity has the dimension of (A)pressure (B) charge current (C) angular momentum (D) resistance.

9. The total energy E= K +V of a particle traveling under the conservative force field is a constant of motion, where K is the kinetic energy and V is the potential energy. In a one-dimensional case, say the x-axis, the conservative force is related to potential energy by which equation? (A) (B) (C) (D)

10. A planet of mass m orbits the sun of mass M in an elliptical path (see Figure 1), with the sun at a focal point. In accord with Kepler's laws, a line drawn from the sun to a planet sweeps out equal areas in cqual times, i.e., dAidt is a constant. Assume that the angular momentum of the planet relative to the sun is L, then dA/ dt is given by  (A) (B) (C) (D)

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