3. The volume charge density inside a solid sphere of radius a is ρ = ρ₀r²/a, where ρ₀ is a constant. The electric field strength within the sphere, as a function of distance r from the center is
(A) ρ₀r³/5ε₀a
(B) ρ₀r²/4ε₀a
(C) ρ₀r/3ε₀a
(D) ρ₀/2ε₀a
(E) ρ₀/ε₀a

1. A 1.5-m-long pipe has one end open and the other end closed. Among its possible standing-wave frequencies is 225 Hz; the next higher frequency is 375 Hz. The sound speed in the pipe is(A) 600 m/s(B) 450 m/s(C) 350 m/s(D) 300 m/s(E) 150 m/s

2. Consider a simple model for earth's atmosphere by neglecting winds, convection and variation in gravity etc. The distribution of molecules is varying with height. Assume that the atmosphere is isothermal (at 273 K) and the average molecular weight of the atmosphere is 30 g/mol, the height below which half the molecules ie approximately is(A) 3.5 km(B) 4.2 km(C) 5.4 km(D) 6.7 km(E) 8.1 km

4. Eight identical spherical raindrops are each at a potential V. They coalesce to make one spherical raindrop whose potential is:(A) V/8(B) V/2(C) 2V(D) 4V(E) 8V

5. A parallel plate capacitor, with air dielectric, is charged by a battery after which the battery is disconnected. A slab of glass dielectric is then slowly inserted between the plates. As it is being inserted,(A) a force repels the glass out of the capacitor.(B) the glass makes the plates repel each other.(C) no force acts on the glass.(D) a net charge appears on the glass.(E) a force attracts the glass into the capacitor.

6. An uncharged 2.0-μF capacitor is connected in series with a 50-kΩ resistor, an ideal 10.0-V battery, and an open switch. What is the voltage across the capacitor 100ms after closing the switch?(A) 2.0V(B) 3.7V(C) 5.0V(D) 6.3V(E) 10.0V

7. A 1500-m-wide dam holds back a lake 95 m deep. The torque that the water exerts about the bottom edge of the dam is(A) 2.1×10¹² N·m(B) 1.3×10¹¹ N·m(C) 2.1×10¹⁰ N·m(D) 1.3×10¹⁰ N·m(E) 2.1×10⁹ N·m

8. A solid cylinder of mass M and radius R is mounted on a axle through its center. The axle is attached to a horizontal spring of constant k, and the cylinder rolls back and forth without slipping. The angular frequency of the motion is (A) (B)(C)(D)(E)

9. The mass of a deuteron is about 2 u, compared with a neutron's 1u. The fraction of a neutron's kinetic energy that's transferred to an initially stationary deuteron in a head-on collision is(A) 11%(B) 25%(C) 50%(D) 75%(E) 89%

10. A gas mixture contains monatomic argon and diatomic oxygen. Suppose the temperature range is such that the numbers of degrees of freedom are 3 for the monatomic argon and 5 for the diatomic oxygen. An adiabatic expansion that doubles its volume results in the pressure dropping to one-third of its original value. What fraction of the molecules are argon?(A) 45%(B) 62%(C) 79%(D) 85%(E) 93%

11. A satellite is in circular orbit at an altitude of 1500 km above the surface of a non-rotating planet with an orbital speed of 9.2 km/s. The minimum speed needed to escape from the surface of the planet is 14.9 km/s. The orbital period of the satellite is closest to(A) 72 min.(B) 65 min.(C) 58 min.(D) 51 min.(E) 44 min.

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