5. Inside the sphere, at what distance from the sphere's center are there points where the gravitational acceleration is a_g/3?
(A)R/5
(B)R/4
(C)R/3
(D)R/2
(E)None of the above

6. Outside the sphere, at what distance from the sphere's center are there points where the gravitational acceleration is ag/3? (A uniform solid sphere of radius R produces a gravitational acceleration of a_g on its surface.) (A) R (B) R (C)2R (D)3R (E)None of the above

Problem of7and8 :In Fig. 2, the block 1 has mass m₁ = 460 g and block 2 has mass m₂ = 500 g, and the pulley, which is mounted on a horizontal axle with negligible friction, has radius R = 5 cm. When released from rest, block 2 falls 75 cm in 5 s without the cord slipping on the pulley.7. What is the magnitude of the acceleration of the blocks? (A)0.02 m/s² (B)0.2 m/s² (C)2 m/s² (D)20 m/s² (E)None of the above

8. What is the magnitude of the Tension T₁?(A)454 N (B)45.4 N (C)4.54 N (D)0.454 N (E)None of the above

9. A resistor R lies along each edge of a triangular pyramid (6 resistors in total), with connections at the corners. Find the equivalent resistance between point A and B. (A)R/3 (B)R/2 (C)R/6 (D)R (E)None of the above

10. In a double slit experiment, the spacing between the two slits is d, and the slit width is a. On a screen far away, the central diffraction maximum contains exactly seven interference fringes. (The interference maximum m = ±4 fall exactly on the position of the first diffraction minimum. What is the ratio of d/a? (A)4 (B)7 (C)8 (D)9 (E)None of the above

11. The earth can be treated as a conductor with electric charge on its surface. The resulting electric field near the surface is measured to be 150 N/C directed toward the center. The earth's radius is 6.38×10⁶m. What is the surface charge density of the earth? (A)-1.67 nC/m² (B)-1.67 C/m² (C)-1.33 nC/m² (D)-1.33 pC/m² (E)None of the above

12. An Alpha particle (charge = +2e) with kinetic energy 11 MeV makes a head on collision with a lead nucleus at rest (charge of lead nucleus = +82e). What is the distance of closest approach of the two particles? (Assume the lead nucleus remains stationary after the collision and is treated as a point particle.) (A)3.28×10⁻¹⁵ m (B)5.75×10⁻¹⁴ m (C)2.15×10⁻¹⁴ m (D)6.24×10⁻¹⁴ m (E)None of the above

13. John uses a multi-meter to measure the voltage across the battery when the switch S is open, and finds it is 1.5 Volt. When the switch is closed, and the battery is connected to a 10 Ω resistor, he finds the voltage across the battery is 1.25 Volt. What's the internal resistance of the battery? (A)8.33 Ω (B)2.0 Ω (C)1.67 Ω (D)2.5 Ω (E)None of the above

14. A pair of long rigid metal rods, each of length L, lie parallel to each other on a smooth table. Their ends are connected by two identical conducting springs with spring constant k and negligible unstretched length. If a current I runs through this circuit, by how much will each spring stretch? (A)(B)(C)(D) (E)None of the above

15. A metal bar with length L, mass m and resistance R is placed on frictionless metal rails inclined at an angle φ. A uniform magnetic field B is directed downward. The bar is released from rest and slides down the rails. What is the terminal velocity of the bar?(A) (B)(C)(D)(E)None of the above

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