1. Consider a rocket of mass M_R carries its fuel of mass M_F. The speed of the rocket varies as the burnt fuel is expelled. The velocity of the exhaust gas relative to the rocket is v_ex. If the initial velocity of the rocket is zero, what the velocity of the rocket is when the fuel is depleted?
(A)
(B)
(C)
(D)
(E)

2. A vertical chain has a length L and a mass M. It is released with the bottom just touching a table as shown in the right figure. The force on the table varies with time. What is the maximum force on the table? (A) Mg (B) 2Mg (C) 2.5Mg (D) 3Mg (E) 4Mg where g is the gravitational acceleration.

3. Water emerges from a small opening at a height h from the bottom of a large container, which is filled to a constant depth H. What is the distance R from the base at which water hits the ground? (A) (B)(C)(D) (E)

4. A block of mass m = 0.4 (kg) is placed on a block of mass M = 0.8 (kg) as shown in the left figure. The coefficient of kinetic friction for all surfaces is μk = 0.1. Ignore the pulley and the rope. For what value of the horizontal force F will the blocks move at constant speed?(A) 0.98 Nt (B) 1.18 Nt (C) 1.57 Nt (D) 1.96 Nt (E) 2.35 Nt

5. The Kepler's second law of planetary motion is that the line joining the sun to a planet sweeps out equal areas in equal times. Which one of the following principles is the fundamental of Kepler's second law? (A) second law of thermal dynamics (B) conservation of linear momentum (C) conservation of angular momentum (D) conservation of energy (E) Hooke's law

6. Consider an ideal gas system. Which one of the following physical quantities is not a "state variable"? (A) heat (B) volume (C) pressure (D) temperature (E) density

7. The Temperature(T)-Entropy(S) diagram of the Carnot cycle is shown in the right figure (solid line). What area in the T-S diagram represents the work done by the system in each cycle?(A) α (B) β (C) γ (D) α + β (E) β + γ

8. Which one of the following statements of the second law of thermodynamics is wrong? (A) It is impossible for a heat engine that operates in a cycle to convert its work input completely into heat. (B) It is impossible for a cyclical device to transfer heat continuously from a cold body to a hot body without the input of work or other effect on the environment. (C) No cyclical heat engine has a greater efficiency than a reversible engine operating between the same two temperatures. (D) In a reversible process the entropy of an isolated system stays constant; in an irreversible process the entropy increases. (E) None of the above is wrong.

9. Assume v is the speed of sound and f₀ is its frequency. If the sound source S moves toward an observer O at speed v_S and the observer O moves away from the sound source S at speed v_O. What is the frequency heard by O? (A) (B) (C) (D) (E)

10. A uniform disk of mass m and radius R is hanged as a physical pendulum as shown in the right figure. What is the oscillation period of that pendulum? (A) (B)(C) (D) (E)where g is the gravitational acceleration.

11. A charge q sits at the back corner of a cube, as shown. The length of its edges is L. What is the flux of electric field E through the shaded side of the figure? (A) (B) (C) (D) (E)

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