5. A thin ring of mass M and radius R rotates about an axis through its edge. The ring starts at its highest point and is given a very small push to start its rotation. Its angular velocity at the lowest point is

(A)

(B)

(C)

(D)

(E)

6. A speedboat moving at 20.6 m/s sounds a signal on its horn, producing a tone of 320 Hz. There is no wind, and the speed of sound in air is 329 m/s. The apparent frequency of the sound heard by an observer in another boat moving in the opposite direction and approaching the first at a speed of 15.4 m/s is(A)282 Hz(B)287 Hz(C)316 Hz(D)357 Hz(E)369 Hz

7. The relation PV = nRT holds for all ideal gases. The additional relation \( PV^\gamma \) holds for an adiabatic process. The figure below shows two curves: one is an adiabat and one is an isotherm. Each starts at the same pressure and volume. Which statement is correct? (Note: "∝" means "is proportional to".)(A)Isotherm: \( P \propto \frac{1}{V} \); Adiabat: \( P \propto \frac{1}{V^\gamma} \): A is both an isotherm and an adiabat.(B)Isotherm: \( P \propto \frac{1}{V^\gamma} \); Adiabat: \( P \propto \frac{1}{V} \): B is an isotherm, A is an adiabat.(C)Isotherm: \( P \propto \frac{1}{V} \); Adiabat: \( P \propto \frac{1}{V^\gamma} \): A is an isotherm, B is an adiabat.(D)Isotherm: \( P \propto \frac{1}{V^\gamma} \); Adiabat: \( P \propto \frac{1}{V} \): B is both an isotherm and an adiabat.(E)I cannot answer this without additional information about the starting temperature.

8. 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)

9. 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

10. A satellite revolves around a planet in an elliptical orbit and experiences only the gravitational force. If the satellite's speed at point a is 8000 m/s, the satellite's speed at point c is(A)8000 m/s(B)6000 m/s(C)4000 m/s(D)2000 m/s(E)1000 m/s

11. The mass density of a certain planet has spherical symmetry but varies in such a way that the mass inside every spherical surface with center at the center of the planet is proportional to the radius of the surface. If r is the distance from the center of the planet to a point mass inside the planet, the gravitational force on the mass is(A)not dependent on r(B)proportional to \( r^2 \)(C)proportional to r(D)proportional to \( \frac{1}{r} \)(E)proportional to \( \frac{1}{r^2} \)

12. 10C (Coulomb) of charge are placed on a spherical conducting shell. A particle with a charge of -3C is placed at the center of the cavity. The net charge on the outer surface of the shell is:(A)-7C(B)-3C(C)0C(D)+3C(E)+7C

13. In the circuit shown, both resistors have the same value R. Suppose switch S is initially closed. When it is then opened, the circuit has a time constant \( \tau_a \). Conversely, suppose S is initially open. When it is then closed, the circuit has a time constant \( \tau_b \). The ratio \( \tau_a / \tau_b \) is(A)1(B)2(C)0.5(D)0.667(E)1.5

14. The field just outside the surface of a long conducting cylinder which has a 2.0-cm radius points radially outward and has a magnitude of 200 N/C. What is the charge density on the surface of the cylinder?(A)2.7 nC/m²(B)1.8 nC/m²(C)3.5 nC/m²(D)4.4 nC/m²(E)0.90 nC/m²

15. Positive charge Q is placed on a conducting spherical shell with inner radius \( R_1 \) and outer radius \( R_2 \). A point charge q is placed at the center of the cavity. The magnitude of the electric field at a point outside the shell, a distance r from the center, is(A)\( Q / 4\pi\varepsilon_0 R_2^2 \)(B)\( Q / 4\pi\varepsilon_0 (R_2^2 - r^2) \)(C)\( q / 4\pi\varepsilon_0 r^2 \)(D)\( (q+Q) / 4\pi\varepsilon_0 r^2 \)(E)\( (q+Q) / 4\pi\varepsilon_0 (R_2^2 - r^2) \)

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