Problem of 1and 2:Three identical stars, each star's mass is M, form an equilateral triangle that rotates around the triangle's center as the stars move in a common circle about that center. The triangle has edge length L. (The gravitational constant is G)
1. What is the net force on each star?
(A)2(GM²/L²)
(B)
(C)(GM²/L²)/2
(D)
(E)None of the above

2. What is the speed of the stars?  (A)(B) (C) (D) (E)None of the above

3. What is the angular speed of the system just after the putty wad hits?(A)1.148 rad/s (B)11.48 rad/s (C)0.0148 rad/s (D)0.1480 rad/s (E)None of the above

4. What is the ratio of the kinetic energy of the system after the collision to that of the putty wad just before?(A)0.0123 (B)0.123 (C)1.23 (D)12.3 (E)None of the above

5. Inside the sphere, at what distance from the sphere's center are there points where the gravitational acceleration is ag/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

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