1. If the magnitude of the sum of two vectors is less than the magnitude of either vector, then:
(A)the scalar product of the vectors must be negative
(B)the scalar product of the vectors must be positive
(C)the vectors must be parallel and in opposite directions
(D)the vectors must be parallel and in the same direction
(E)none of the above

2. A particle starts from rest at time t = 0 and moves along the x axis. If the net force on it is proportional to t, its kinetic energy is proportional to: (A)\( t \) (B)\( t^2 \) (C)\( t^4 \) (D)\( 1/t^2 \) (E)\( 1/t \)

3. A ball of mass m, at one end of a string of length L, rotates in a vertical circle just fast enough to prevent the string from going slack at the top of the circle. Assuming mechanical energy is conserved, the speed of the ball at the bottom of the circle is (A)\( \sqrt{2gL} \) (B)\( \sqrt{3gL} \) (C)\( \sqrt{4gL} \) (D)\( \sqrt{5gL} \) (E)\( \sqrt{7gL} \)

4. At one instant of time a rocket is traveling in outer space at 2500 m/s and is exhausting fuel at a rate of 100 kg/s. If the speed of the fuel as it leaves the rocket is 1500 m/s, relative to the rocket, the thrust is: (A)0 N (B)\( 1.0 \times 10^5 \) N (C)\( 1.5 \times 10^5 \) N (D)\( 2.9 \times 10^5 \) N (E)\( 2.5 \times 10^5 \) N

5. A cylinder is 0.10 m in radius and 0.20 m in length. Its rotational inertia, about the cylinder axis on which it is mounted, is 0.020 kg·m². A string is wound around the cylinder and pulled with a force of 1.0 N. The angular acceleration of the cylinder is: (A)2.5 rad/s² (B)5.0 rad/s² (C)10 rad/s² (D)15 rad/s² (E)20 rad/s²

6. A uniform disk, a thin hoop, and a uniform sphere, all with the same mass and same outer radius, are each free to rotate about a fixed axis through its center. Assume the hoop is connected to the rotation axis by light spokes. With the objects starting from rest, identical forces are simultaneously applied to the rims, as shown. Rank the objects according to their angular momenta after a given time t, least to greatest. (A)all tie (B)disk, hoop, sphere (C)sphere, disk, hoop (D)hoop, sphere, disk (E)hoop, disk, sphere

7. An 80-N uniform plank leans against a frictionless wall as shown. The torque (about point P) applied to the plank by the wall is, in the unit of N·m, (A)40 (B)60 (C)120 (D)160 (E)240

8. If Earth were to rotate only 100 times per year about its axis, then which of the following is correct: (A)airplanes flying west to east would make better time (B)we would fly off Earth's surface (C)our apparent weight would slightly increase (D)Earth's atmosphere would float into outer space (E)our apparent weight would slightly decrease

9. Standing waves are produced by the interference of two traveling sinusoidal waves, each of frequency 100 Hz. The distance from the 2nd node to the 5th node is 60 cm. The wavelength of each of the two original waves is, in cm,: (A)50 (B)40 (C)30 (D)20 (E)15

10. A heat engine operates between a high temperature reservoir at \( T_H \) and a low temperature reservoir at \( T_L \). Its efficiency is given by \( 1 - T_L/T_H \): (A)only if the working substance is an ideal gas. (B)only if the engine is reversible. (C)only if the engine is quasi-static (D)only if the engine operates on a Stirling cycle (E)no matter what characteristics the engine has

11. A particle with charge Q is on the y axis a distance a from the origin and a particle with charge q is on the x axis a distance d from the origin. The value of d for which the x component of the force on the second particle is the greatest is: (A)0 (B)a (C)\( \sqrt{2}a \) (D)a/2 (E)\( a/\sqrt{2} \)

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