3. A rocket of mass M (including fuel) in space is accelerating from rest by ejecting the fuel at a velocity -u relative to the rocket. What is the speed of the rocket when its mass becomes M/2?
(A) u/2
(B) u ln 2
(C) 3u/2
(D) u ln

19. A rocket ship of rest length 100 m is moving at speed 0.8 C past a timing device which records the time interval between the passage of the front and back ends of the ship. This time interval is: (A)0.20 με (B) 0.33 με (C) 0.25 με (D) 0.52 με(Ε) 0.69 μs.

20. Three different monochromatic light sources are used to liberate free electrons from the surface of an unknown material. Source 1 has wavelength 500 nm, and a stopping potential of 1.08 volts is observed. Source 2 has wavelength 650 nm and a stopping potential of 0.510 volts. If source 3 has wavelength 590 nm, what is the maximum energy of electrons that can be liberated from the surface by source 3? Answer in electron volts. (A) 0.50 (B) 0.70 (C) 0.20 (D) 0.90 (E) 0.10

1. Which of the following statements regarding the reaction force is false?(A) The reaction force of the centripetal force is the centrifugal force.(B) As to the force that the earth attracts the moon, the reaction force is the one that the moon attracts the earth.(C) The Lorentz force violates Newton's third law without considering the contribution of the field.(D) Newton's third law is compatible with conservation of linear momentum.

2. Consider a yoyo of mass m and moment of inertia βmR² rolling without slipping on a surface in the figure. The radius of the large disk is 2R. A string wrapping the axis of radius R is pulled by a force to the right. Setting the direction of F to be positive. The linear acceleration of the center of mass of the yoyo is then given by(A)(B)(C) (D)

4. A billiard ball hits another ball at rest of identical mass on a surface, making the latter to leave at an angle of 37° relative to the incident direction of the first ball. Suppose the incident speed is u. What is the speed of the first ball after collision?(A) 0.36u(B) 0.6u(C) 0.64u(D) 0.8u.

5. A bomb explodes and breaks into two pieces of mass ratio 2:1. Neglect the mass of the explosive chemicals. What is the ratio of the kinetic energy obtained by the two pieces?(A) 1:2(B) 2:1(C) 4:1(D) 1:3.

6. Consider a solar system with a sun of mass two times of our sun. A planet orbiting this sun has a period of one earth year. What is the distance from the sun to the planet? (Hint: au is the average distance from the earth to our sun.)(A) 2⁻¹/² au(B) 2⁻¹/³ au(C) 2¹/² au(D) 2¹/³ au.

7. A sphere of mass m and another sphere of mass 2m are connected by a string of length R. Suppose they are now rotating about their center of mass at an angular velocity ω. Suddenly the string breaks. What is the velocity of the massive one (2m) after the string breaks?(A) Rω(B) Rω/2(C) Rω/3(D) 2Rω/3.

8. Suppose the velocity of a falling sphere of mass m due to the gravity and the air resistance is given by v(t) = v₁(1-e⁻ᵞᵗ) with the condition that the air resistance vanishes when v = 0. The formula of the air drag force is then given by(A) -2mγv(B) -mγv(C) -mγv²(D) -mγv²/2.

9. Which of the following statements is not compatible with other 3 statements? (A) It is impossible for a heat engine that operates in a cycle to convert its heat input completely into work. (B) It is impossible for a cyclical device to transfer heat continuously from a cold body to a hot one without the input of work or other effect on the environment. (C) The change in the internal energy of the system comes from the heat input minus the work done on its surroundings. (D) The entropy change of an isolated system always stays constant or increases.