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Class Test : Gravitation, 1. If the distance between two masses is doubled, the gravitational attraction between them, (a) Is doubled, (b) Becomes four times, (c) Is reduced to half (d) Is reduced to a quarter, 2. The gravitational force between two point masses m1 and m 2 at separation r is given by, Fk, , m 1m 2, r2, , . The constant k, , (a)Depends on system of units only, (b)Depends on medium between masses only, (c)Depends on both (a) and (b), (d)Is independent of both (a) and (b), 3. If the change in the value of ‘g’ at a height h above the surface of the earth is the same, as at a depth x below it, then (both x and h being much smaller than the radius of the earth), (a) x h, , (b), , x 2h, , (c) x , , h, 2, , (d) x h 2, , 4. Which of the following statements is true, (a) g is less at the earth's surface than at a height above it or a depth below it, (b) g is same at all places on the surface of the earth, (c) g has its maximum value at the equator, (d) g is greater at the poles than at the equator, 5. If mass of a body is M on the earth surface, then the mass of the same body on the moon, surface is?, (a M/6, (b) Zero, (c), M, (d), None of these, 22, 6. Mass of moon is 7.34 10 kg. If the acceleration due to gravity on the moon is 1 .4 m / s 2 ,, the radius of the moon is (G 6.667 10 11 Nm 2 / kg 2 ), (a) 0 .56 10 4 m, , (b), , 1 . 87 10 6 m, , (c) 1 .92 10 6 m, , (d), , 1 . 01 10 8 m, , 7. An object weights 72 N on earth. Its weight at a height of R/2 from earth is, (a), 32 N, (b), 56 N (c), 72 N (d), Zero, 8. the angular speed of earth, so that the object on equator may appear weightless, is, (g 10 m /s 2 , radius of earth 6400 km), (a), , 1 .25 10 3 rad/sec, , (b), , 1 . 56 10 3 rad/sec (c) 1 . 25 10 1 rad/sec, , (d), , 1.56 rad/sec, , 9. If mass of earth is M, radius is R and gravitational constant is G, then work done to take 1, kg mass from earth surface to infinity will be, (a), , GM, 2R, , (b), , GM, R, , (c), , 2GM, R, , (d), , GM, 2R, , 10. The kinetic energy needed to project a body of mass m from the earth surface (radius R) to, infinity is, (a) mgR/2, (b) 2 mgR (c), mgR, (d), mgR/4, 11. v e and v p denotes the escape velocity from the earth and another planet having twice the, radius and the same mean density as the earth. Then
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(a), , ve v p, , (b), , ve v p / 2, , (c), , ve 2v p, , (d), , ve v p / 4, , 12. The escape velocity of a projectile from the earth is approximately, (a) 11.2 m/sec, (b) 112 km/sec, (c), 11.2 km/sec (d), 11200 km/sec, 13. The escape velocity of a planet having mass 6 times and radius 2 times as that of earth is, (a), (b) 3 Ve, (c), 2 Ve, 3 Ve, 2 Ve (d), 14. A geostationary satellite, (a) Revolves about the polar axis, (b) Has a time period less than that of the near earth satellite, (c) Moves faster than a near earth satellite, (d) Is stationary in the space, 15. If V, R and g denote respectively the escape velocity from the surface of the earth radius of, the earth, and acceleration due to gravity, then the correct equation is, (a), , V gR, , (b), , V, , 4, gR 3, 3, , (c), , VR g, , (d), , V 2 gR, , SUBJECTIVE QUESTION:, 1. Find the gravitational force between two stones of mass 1 kg and 5kg separated by a, distance of 3metre in vacuum is., 2. If the mass and diameter of a planet have twice the value of the corresponding parameters, of earth. Find Acceleration due to gravity on the surface of the planet., 3. The radius of the earth is 6400 km and g 10m / sec 2 . In order that a body of 5 kg weighs, zero at the equator, find the angular speed of the earth., 4. The value of g on the earth's surface is 980 cm / sec 2 . Find its value at a height of 64 km, from the earth's surface., 5. Mass of moon is 7.34 10 22 kg. If the acceleration due to gravity on the moon is 1 .4 m / s 2 ,, then find radius of the moon. take (G 6.667 10 11 Nm 2 / kg 2 ), 6. If the density of the earth is doubled keeping its radius constant then acceleration due to, gravity will be (g 9 .8 m /s 2 ), 7. If the density of a small planet is the same as that of earth, while the radius of the planet, is 0.2 times that of the earth, then find the gravitational acceleration on the surface of, that planet., 8. A simple pendulum has a time period T1 when on the earth’s surface and T2 when taken, to a height R above the earth’s surface, where R is the radius of the earth. Then find value, of T2 / T1 ., 9. The orbital angular momentum of a satellite revolving at a distance r from the centre is L., If the distance is increased to 16r, then find the new angular momentum., 10. What will be the distance between two equal mass object of 104 kg each so that they can, attract each other by a force of 66.7N.
