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.

8. A meter stick 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 = 0.5 m (B) a = 0.3 m (C) a = 0.2 m (D) a = 0.1 m (E) a = 0 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

15. In the Drude model of electrical conduction, the current density is directly proportional to (A) the average time interval between successive collisions, (B) the number of charge carriers per unit volume, (C) the square of the electron charge, (D) the electric field present in the wire, (E) the product of all four quantities listed above.

16. The magnitude of the magnetic field at point P, at the center of the semicircle shown below is given by: (A) μ0i/R2, (B) (μ0i/2)R, (C) μ0i/2R, (D) (μ0i/4)R, (E) μ0i/4R.

17. The magnetic flux through a loop perpendicular to a uniform magnetic field will change (A) if the loop is replaced by two loops, each of which has half of the area of the original loop, (B) if the loop moves at constant velocity in a direction parallel to the axis of the loop while remaining in the uniform magnetic field, (C) if the loop moves at constant velocity while remaining perpendicular to and within the unifom magnetic field, (D) if the loop is rotated through 180 degrees about an axis through its center and in the plane of the loop, (E) in none of the above cases.

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