1 03 2 04 3 0375 4 05 5 025 4 let m denote the mass

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of static friction between feet and ground? (1) 0.3 (2) 0.4 (3) 0.375 (4) 0.5 (5) 0.25 4. Let M denote the mass of Earth and let R denote its radius. What is the ratio g/G at Earth’s surface, where G is Newton’s constant and g is the acceleration due to gravity at the surface of the earth? (1) M/R 2 (2) R 2 /M (3) MR 2 (4) M/R (5) 1 . 0 5. Three point masses M are located on the y -axis, one at the origin ( y = 0) and the other two at y = ± d as shown in the figure. A fourth point mass m is on the x -axis a distance x = d from the origin. What is the magnitude of the net gravitational force on the mass m due to the other three masses? (1) 1 . 71 GMm/d 2 (2) 2 . 00 GMm/d 2 (3) 2 . 41 GMm/d 2 (4) 1 . 41 GMm/d 2 (5) 3 . 00 GMm/d 2 6. Assume the Earth is s sphere with a uniform mass density and radius R . If a man weighs 200 N on the surface of the Earth, how much does he weigh when he is in a deep mine shaft inside the Earth a distance of R/ 4 from the surface of the Earth? (1) 150 N (2) 50 N (3) 200 N (4) 100N (5) 75 N 7. Near the surface of the Earth (acceleration due to gravity = g ) it takes time t for an object of mass m to reach the surface of the Earth when dropped from rest a height h above the surface. If an object with mass 4 m is dropped from rest a height h from the surface of a planet with an acceleration due to gravity equal to g/ 4, how long will it take to hit the surface of the planet? (1) 2 t (2) 4 t (3) t/ 2 (4) t/ 4 (5) t
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77777 77777 8. Two satellites are in circular orbit around the Earth. The first satellite has mass M 1 and is travelling in a circular orbit of radius R 1 . The second satellite has mass M 2 = 2 M 1 is travelling in a circular orbit of radius R 2 = 4 R 1 . If the first satellite completes one revolution of the Earth in time T , how long does it take the second satellite to make one revolution of the Earth? (1) 8 T (2) 4 T (3) 2 T (4) T (5) T/ 2 9. A man enters a tall tower near the surface of the Earth. He notes that a long pendulum extends from the ceiling and nearly touches the floor and that the period of the pendulum is 18.85 s. Assuming that the pendulum is a simple pendulum, how tall is the tower?
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