8. A stick of length 1.0 m is pivoted at a point a distance a from its center and swings as a physical pendulum. Of the following values for a, which results in the shortest period of oscillation?
(A) a = 0.1 m
(B) a = 0.2 m
(C) a = 0.3 m
(D) a = 0.4 m
(E) a = 0.5 m.

4. A particle moves along the x axis. The net force on the particle, which is conservative, is given by F = (8 N/m3)x3. If the potential energy is taken to be zero for x = 0 then the potential energy as a function ofx is given by: (A) (2 J/m4)x4 (B) (-2 J/m4)x4 (C) (24 J/m2)x4 (D) (-24 J/m2)x2(E) (8 J/m2)x2.

5. Bullets from two guns are fired with the same velocity. The bullet from gun #1 is twice as heavy as the bullet from gun #2, and gun #1 weighs three times as much as gun #2. The ratio of the momentum imparted to gun #1 to that imparted to gun #2 is: (A) 2:3 (B) 3:2 (C) 3:1 (D) 2:1 (E) 6:1.

6. A forward force acting on the axle accelerates a rolling wheel on a horizontal surface. If the wheel does not slide, the frictional force of the surface on the wheel is: (A) zero. (B) in the forward direction and does zero work on the wheel. (C) in the forward direction and does positive work on the wheel. (D) in the backward direction and does zero work on the wheel. (E) in the backward direction and does negative work on the wheel.

7. A 2.0-kg block starts from rest on the positive x axis 3.0 m from the origin and thereafter has an acceleration given by . The torque, relative to the origin, acting on it at the end of 2.0 s is: (A) (0 N●m) (B)(-18N●m) (C) (+24 N●m)  (D)(-I44N●m) (E) (+144 N● m) .

9. The displacement of a string wave is given by: y(x,t) = ymsin(kx + ωt). The traveling wave velocity is: (A) +2πkω(B)-2πkω(C) +kω (D) +ω/k (E) -ω/k .

10. A hot object and a cold object are placed in thermal contact and the combination is isolated. They transfer energy until they reach a common temperature. The change △Sh in the entropy of the hot object, the change △Scin the entropy of the cold object, and the change△Sioiai in the entropy of the combination are: (A) △Sh > 0,△Sc>0, △Stotai ＞ 0 (B) △Sh<0，△Sc> 0, △Sioiai= 0 (C) △Sh ＞ 0, △Sci<0 ,△Sioiai=0 (D)△Sh> 0, △Sc<  0, △Sioiai>0(E) A△Sh＜0, △Sc＞ 0, △Sioiai＞ 0.

11. The units ofk= 1/(4πε0)are: (A) N2/C2, (B) N●m/C, (C) N2●m2/C2, (D) N●m2/C2, (E) m2/C2.

12. Two infinite parallel surfaces carry uniform charge densities of 0.20 nC/m2 and -0.60 nC/m2. What is the magnitude of the electric field at a point between the two surfaces? (A) 30 N/C, (B) 5 N/C, (C) 45 N/C, (D) 10 N/C, (E) 90 N/C.

13. Which statement is always correct when applied to a charge distribution located in a finite region of space? (A) Electric potential is always zero at infinity, (B) Electric potential is always infinite at a boundary surface to a charge distribution, (C) Electric potential is always zero at a boundary surface to a charge distribution, (D) Electric potential is always zero at the origin, (E) The location where electric potential is zero may be chosen arbitrarily.

14. How much energy is stored in the 50-μF capacitor when Va-Vb = 22 V? (A) 0.85 mJ, (B) 0.28 mJ, (C) 0.70 mJ, (D) 0.48 mJ, (E) 0.10 mJ. Il 25gF50