14. A cube of side 2a and mass M is sliding on a frictionless surface with uniform velocity v₀, as shown in Fig. a. It hits a small obstacle at the end of the table, which causes the cube to tilt as in Fig. b. Find the minimum value of v₀ such that the cube will fall off the table (g is the gravitational acceleration constant on earth).

(A)
(B)
(C)
(D)
(E)

1. An object of mass m is observed to move in a straight line with velocity given by v = bt² − ct, where b and c are positive constants. The expression for the force on the object as a function of time is (A) mbt² − mct (B) 2mbt² − 2mct (C) 2mbt − mc (D) mbt − mc (E) mbt² − 0.5mct

2. A stone of mass 0.2 kg is tied to a string of length 0.8 m. If you hold the end of this string in your hand and whirl the stone around a circle at the rate of 2 revolutions per second, what is the tension in the string? Ignore gravity in this problem. (A) 20 N (B) 25 N (C) 30 N (D) 40 N (E) 45 N

3. A meteoroid (a chunk of rock) is initially at rest in interplanetary space at a large distance from the Sun. Under the influence of gravity, the meteoroid begins to fall toward the Sun along a straight radial line. With what speed does it strike the Sun? (A) 88 km/s (B) 320 km/s (C) 483 km/s (D) 618 km/s (E) 721 km/s

4. A quantity of an ideal gas is compressed to half its initial volume. The process may be adiabatic, isothermal or isobaric. The greatest amount of work is required if the process is: (A) adiabatic (B) isothermal (C) isobaric (D) adiabatic or isothermal (both require the same work; isobaric requires less) (E) isothermal or isobaric (both require the same work; adiabatic requires less).

5. The "Principle of Equipartition of Energy" states that the energy of a gas is shared equally: (A) among the molecules (B) between kinetic and potential energy (C) between translational and vibrational kinetic energy (D) among the relevant degrees of freedom (E) between heat and work.

6. Choose the INCORRECT statement: (A) Gauss's law holds in a vacuum (B) Gauss's law states that the net number of lines crossing any closed surface in an outward direction is proportional to the net charge enclosed within the surface (C) Coulomb's law can be derived from Gauss's law and symmetry (D) Gauss's law applies to a closed surface of any shape (E) according to Gauss's law, if a closed surface encloses no charge, then the electric field must vanish everywhere on the Gaussian surface.

7. A magnetic field CANNOT: (A) exert a force on a charge (B) accelerate a charge (C) change the momentum of a charge (D) change the kinetic energy of a charge (E) change the velocity of a charge.

8. The electric flux through the surface of a sphere is NOT Q/ε₀ if Q is (A) outside the sphere near the surface (B) inside the sphere (C) at the middle of the sphere (D) spread out occupying the whole inside volume of the sphere (E) none of above.

9. In the diagram, assume that all the lines of B generated by coil #1 pass through coil #2. Coil #1 has 100 turns and coil #2 has 400 turns. Then: (A) the current in coil #1 will be 1/4 that in coil #2 (B) the voltage in coil #2 will be 1/4 that in coil #1 (C) the current will be the same in the two coils (D) the voltage will be the same in the two coils (E) the power supplied to coil #1 is equal to the power delivered by coil #2.

10. Incompressible liquid flows along the pipe as shown in the following. The ratio of the speeds v₂/v₁ is: (A) A₁/A₂ (B) A₂/A₁ (C) (A₁/A₂)^(1/2) (D) (A₂/A₁)^(1/2) (E) (A₂/A₁)²

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