Title 7-gravitation-.pdf ✅

Gravitation 1. The energy required to move a satellite of mass m from an orbit of radius 2R to 3R is (where M is the mass of the earth and R is the radius of the earth) (A) GMm 12R (B) GMm 8R (C) GMm 3R (D) GMm 6R 2. If suddenly the gravitational force of attraction between the earth and a satellite revolving around it becomes zero, then the satellite will : (A) continue to move in its orbit with the same velocity (B) move tangentially to the original orbit with the same velocity (C) become stationary in its orbit (D) move towards the earth 3. The escape velocity of a body depends upon mass as : (A) m0 (B) m1 (C) m2 (D) m3 4. The kinetic energy needed to project a body of mass m from the earth's surface (radius R ) to infinity is : (A) mgR 2 (B) 2mgR (C) mgR (D) mgR 4 5. The time period of a satellite of the earth is 5h. If the separation between the earth and the satellite is increased to four times the pervious value, the new time period will become. (A) 10h (B) 80h (C) 40 h (D) 20h 6. Two spherical bodies of masses m and 5M and radii R and 2R, respectively, are released in free space with initial separation between their centres equal to 12R. If they attract each other by gravitational force only, then the distance covered by the smaller body just before collision is : (A) 2.5R (B) 4.5R (C) 7.5R (D) 1.5R 7. The escape velocity for a body projected vertically upward from the surface of the earth is 11 km/s. If the body is projected at an angle of 45∘ with vertical, the escape velocity will be : (A) 11√2 km/s (B) 22 km/s (C) 11 km/s (D) 11 √2 km/s 8. A satellite of mass m revolves around the earth of radius R at a height x from its surface. If g is the acceleration due to gravity on the surface of the earth, the orbital speed of the satellite is : (A) gx (B) ( gR 2 R+x ) 1/2 (C) gR 2 R+x (D) gR R−x 9. The time period of an earth satellite in circular orbit is independent of (A) the mass of the satellite (B) radius of its orbit (C) both the mass and radius of the orbit (D) neither the mass of the satellite nor the radius of its orbit 10. If g is the acceleration due to gravity on the earth's surface the gain in the potential energy of an object of mass m raised from the earth's surface to a height equal to the radius R of the earth is : (A) 2mgR (B) 1 2 mgR (C) 1 4 mgR (D) mgR 11. Suppose the gravitational force varies inversely as the nth power of distance. Then the time period of a planet in a circular orbit of radius R around the sun will be proportional to : (A) R (n+1)/2 (B) R (n−1)/2 (C) R n (D) R (n−2)/2
12. The average density of the earth (A) does not depend on g. (B) is a complex function of g. (C) is directly proportional to g (D) is inversely proportional to g. 13. The change in the value of g at a height h above the surface of the earth is the same as at a depth d below the earth. When both d and h are much smaller than the radius of the earth, which one of the following is correct? (A) d = h 2 (B) d = 3h 2 (C) d = 2h (D) d = h 14. A particle of mass 10 g is kept on the surface of a uniform sphere of mass 100 kg and radius 10 cm. Find the work done against the gravitational force between them to take the particle far away from the sphere. (A) 13.34 × 10−10 J (B) 3.33 × 10−10J (C) 6.67 × 10−9 J (D) 6.67 × 10−10 J 15. If gE and gM are the acceleration due to gravity on the moon, respectively, and if Millikan oil drop experiment could be performed on the two surfaces, one will find the ratio electronic charge on moon electronic chargeon earth to be : (A) 0 (B) gE gM (C) gM gE (D) 1 16. A planet in a distant solar system is 10 times more massive then the earth and its radius is 10 times smaller. Given that the velocity from the earth is 11 km/s the escape velocity from the surface of the planet would be : (A) 1.1 km/s (B) 11 km/s (C) 110 km/s (D) 0.11 km/s 17. The height at which the acceleration due to gravity become g/9 (where g is the acceleration due to gravity on the surface of the earth) in terms of R, the radius of the earthy is: (A) 2R (B) R √2 (C) R 2 (D) √2R 18. Statement : I For A mass M kept at a centre of a cube of side a, the flux of gravitational field passing through its side is 4πGM. Statement : II If the direction of a field due to a point source is radial and its dependence on the distance r from the source is given is 1/r 2 , its flux through a closed surface depends only on the strength of the source enclosed by the surface and not on the size or shape of the surface. (A) Statement-I is True, Statement-II is True and Statement-II is a correct explanation for Statement-I (B) Statement-I is True, Statement-II is True and Statement-II is NOT a correct explanation for Statement-I (C) Statement-I is True, Statement-II is False (D) Statement-I is False, Statement-II is True 19. Two bodies of masses m and 4m are placed at a distance r. The gravitational potential at a point on the line joining them where the gravitational field is zero is : (A) zero (B) 4Gm r (C) 6Gm r (D) 9Gm r 20. The mass of a spaceship is 1000 kg. It is to be launched from the earth's surface out into free space. The value of ' g ' and ' R ' (radius of earth) are 10 m/s 2 and 6400 km, respectively. The required energy for this work will be : (A) 6.4 × 1011J (B) 6.4 × 108 J (C) 6.4 × 109 J (D) 6.4 × 1010J 21. What is the minimum energy required to launch a satellite of mass m from the surface of a planet of mass M and radius R in a circular orbit at an altitude of 2R ? (A) 2GmM 3R (B) GmM 2R (C) GmM 3R (D) 5GmM 6R 22. Four particles, each of mass M and equidistant from each other, move along a circle of radius R under the action of their mutual gravitational attraction. The speed of each particle is :