Title 8. Gravitation.pdf ✅

66 NEET-AIPMT Chapterwise Topicwise Solutions Physics 8.2 Kepler's Laws 1. The kinetic energies of a planet in an elliptical orbit about the Sun, at positions A, B and C are KA, KB and KC, respectively. AC is the major axis and SB is perpendicular to AC at the position of the Sun S as shown in the figure. Then (a) KA < KB < KC (b) KA > KB > KC (c) KB < KA < KC (d) KB > KA > KC (NEET 2018) 2. A planet moving along an elliptical orbit is closest to the sun at a distance r1 and farthest away at a distance of r2. If v1 and v2 are the linear velocities at these points respectively, then the ratio v v 1 2 is (a) (r1/r2) 2 (b) r2/r1 (c) (r2/r1) 2 (d) r1/r2 (2011) 3. The figure shows elliptical orbit of a planet m about the sun S. The shaded area SCD is twice the shaded area SAB. If t 1 is the time for the planet to move from C to D and t 2 is the time to move from A to B then (a) t 1 = 4t 2 (b) t 1 = 2t 2 (c) t 1 = t 2 (d) t 1 > t2 (2009) 4. The period of revolution of planet A around the sun is 8 times that of B. The distance of A from the sun is how many times greater than that of B from the sun? (a) 4 (b) 5 (c) 2 (d) 3 (1997) 5. The distance of two planets from the sun are 1013 m and 1012 m respectively. The ratio of time periods of the planets is (a) 10 (b) 10 10 (c) 10 (d) 1 1 / 0 (1994, 1988) 6. A planet is moving in an elliptical orbit around the sun. If T, V, E and L stand respectively for its kinetic energy, gravitational potential energy, total energy and magnitude of angular momentum about the centre of force, which of the following is correct ? (a) T is conserved. (b) V is always positive. (c) E is always negative. (d) L is conserved but direction of vector L changes continuously. (1990) 7. The largest and the shortest distance of the earth from the sun are r1 and r2. Its distance from the sun when it is at perpendicular to the major-axis of the orbit drawn from the sun is (a) r r 1 2 4 + (b) r r r r 1 2 1 2 + − (c) 2 1 2 1 2 r r r r + (d) r r 1 2 3 + (1988) 8.3 Universal Law of Gravitation 8. Two astronauts are floating in gravitational free space after having lost contact with their spaceship. The two will (a) move towards each other (b) move away from each other (c) will become stationary (d) keep floating at the same distance between them. (NEET 2017) 9. Kepler’s third law states that square of period of revolution (T) of a planet around the sun, is proportional to third power of average distance r between sun and planet i.e. T2 = Kr3 here K is constant. If the masses of sun and planet are M and m respectively then as per Newton’s law of gravitation force of attraction between them is F GMm r = 2 , here G is gravitational constant. The relation between G and K is described as (a) K = G (b) K G= 1 (c) GK = 4p2 (d) GMK = 4p2 (2015 Cancelled) Gravitation 8 CHAPTER EduHulk.COM
Gravitation 67 10. Dependence of intensity of gravitational field (E) of earth with distance (r) from centre of earth is correctly represented by (a) (b) (c) (d) (2014) 11. Which one of the following plots represents the variation of gravitational field on a particle with distance r due to a thin spherical shell of radius R? (r is measured from the centre of the spherical shell) (a) (b) (c) (d) (Mains 2012) 12. Two spheres of masses m and M are situated in air and the gravitational force between them is F. The space around the masses is now filled with a liquid of specific gravity 3. The gravitational force will now be (a) 3 F (b) F (c) F/3 (d) F/9 (2003) 13. Gravitational force is required for (a) stirring of liquid (b) convection (c) conduction (d) radiation (2000) 14. A body of weight 72 N moves from the surface of earth at a height half of the radius of earth, then gravitational force exerted on it will be (a) 36 N (b) 32 N (c) 144 N (d) 50 N (2000) 15. Two particles of equal mass m go around a circle of radius R under the action of their mutual gravitational attraction. The speed v of each particle is (a) 1 2 Gm R (b) 4Gm R (c) 1 2 1 R Gm (d) Gm R (1995) 16. The earth (mass = 6 × 1024 kg) revolves around the sun with an angular velocity of 2 × 10–7 rad/s in a circular orbit of radius 1.5 × 108 km. The force exerted by the sun on the earth, in newton, is (a) 36 × 1021 (b) 27 × 1039 (c) zero (d) 18 × 1025 (1995) 17. If the gravitational force between two objects were proportional to 1/R (and not as 1/R2 ), where R is the distance between them, then a particle in a circular path (under such a force) would have its orbital speed v, proportional to (a) R (b) R0 (independent of R) (c) 1/R2 (d) 1/R (1994, 1989) 8.5 Acceleration due to Gravity of the Earth 18. If the mass of the Sun were ten times smaller and the universal gravitational constant were ten times larger in magnitude, which of the following is not correct? (a) Raindrops will fall faster. (b) Walking on the ground would become more difficult. (c) Time period of a simple pendulum on the Earth would decrease. (d) g on the Earth will not change. (NEET 2018) 19. A spherical planet has a mass Mp and diameter Dp. A particle of mass m falling freely near the surface of this planet will experience an acceleration due to gravity, equal to (a) 4 2 GM D p p (b) GM m D p p 2 (c) GM D p p 2 (d) 4 2 GM m D p p (2012) 20. Imagine a new planet having the same density as that of earth but it is 3 times bigger than the earth in size. If the acceleration due to gravity on the surface of earth is g and that on the surface of the new planet is g′, then (a) g′ = g/9 (b) g′ = 27g (c) g′ = 9g (d) g′ = 3g (2005) 21. The density of a newly discovered planet is twice that of earth. The acceleration due to gravity at the surface of the planet is equal to that at the surface of the earth. If the radius of the earth is R, the radius of the planet would be (a) 2R (b) 4R (c) 1 4 R (d) 1 2 R (2004) 22. The acceleration due to gravity on the planet A is 9 times the acceleration due to gravity on planet B. A man jumps to a height of 2 m on the surface of A. What is the height of jump by the same person on the planet B ? (a) (2/9) m (b) 18 m (c) 6 m (d) (2/3) m (2003) EduHulk.COM
68 23. What will be the formula of mass of the earth in terms of g, R and G ? (a) G R g (b) g R G 2 (c) g R G 2 (d) G g R . (1996) 24. The acceleration due to gravity g and mean density of the earth r are related by which of the following relations? (where G is the gravitational constant and R is the radius of the earth.) (a) ρ π = 3 4 g GR (b) ρ π = 3 4 3 g GR (c) ρ π = 4 3 2 gR G (d) ρ π = 4 3 3 gR G (1995) 25. The radius of earth is about 6400 km and that of mars is 3200 km. The mass of the earth is about 10 times mass of mars. An object weighs 200 N on the surface of earth. Its weight on the surface of mars will be (a) 20 N (b) 8 N (c) 80 N (d) 40 N (1994) 8.6 Acceleration due to Gravity Below and Above the Surface of Earth 26. A body weighs 72 N on the surface of the earth. What is the gravitational force on it, at a height equal to half the radius of the earth? (a) 48 N (b) 32 N (c) 30 N (d) 24 N (NEET 2020) 27. A body weighs 200 N on the surface of the earth. How much will it weigh half way down to the centre of the earth ? (a) 100 N (b) 150 N (c) 200 N (d) 250 N (NEET 2019) 28. The acceleration due to gravity at a height 1 km above the earth is the same as at a depth d below the surface of earth. Then (a) d = 1 km (b) d = 3 2 km (c) d = 2 km (d) d = 1 2 km (NEET 2017) 29. Starting from the centre of the earth having radius R, the variation of g (acceleration due to gravity) is shown by (a) g O R r (b) g O R r (c) g r O R (d) g r R O (NEET-II 2016) 30. The height at which the weight of a body becomes 1 16       th, its weight on the surface of earth (radius R), is (a) 5R (b) 15R (c) 3R (d) 4R (2012) 31. The dependence of acceleration due to gravity g on the distance r from the centre of the earth, assumed to be a sphere of radius R and of uniform density is as shown in figures. (1) (2) (3) (4) The correct figure is (a) (4) (b) (1) (c) (2) (d) (3) (Mains 2010) 8.7 Gravitational Potential Energy 32. The work done to raise a mass m from the surface of the earth to a height h, which is equal to the radius of the earth, is (a) 3 2 mgR (b) mgR (c) 2mgR (d) 1 2 mgR (NEET 2019) 33. At what height from the surface of earth the gravitation potential and the value of g are –5.4 × 107 J kg–1 and 6.0 m s–2 respectively? Take the radius of earth as 6400 km. (a) 1400 km (b) 2000 km (c) 2600 km (d) 1600 km (NEET-I 2016) 34. Infinite number of bodies, each of mass 2 kg are situated on x-axis at distances 1 m, 2 m, 4 m, 8 m, ..., respectively, from the origin. The resulting gravitational potential due to this system at the origin will be (a) − 4 3 G (b) –4G (c) – G (d) − 8 3 G (NEET 2013) 35. A body of mass ‘m’ is taken from the earth’s surface to the height equal to twice the radius (R) of the earth. The change in potential energy of body will be (a) 3mgR (b) 1 3 mgR (c) mg 2R (d) 2 3 mgR (NEET 2013) 36. A particle of mass M is situated at the centre of a spherical shell of same mass and radius a. The EduHulk.COM
Gravitation 69 magnitude of the gravitational potential at a point situated at a/2 distance from the centre, will be (a) GM a (b) 2GM a (c) 3GM a (d) 4GM a (Mains 2011, 2010) 37. A body of mass m is placed on earth’s surface which is taken from earth surface to a height of h = 3R, then change in gravitational potential energy is (a) mgR 4 (b) 2 3 mgR (c) 3 4 mgR (d) mgR 2 (2003) 8.8 Escape Speed 38. The ratio of escape velocity at earth (ve ) to the escape velocity at a planet (vp) whose radius and mean density are twice as that of earth is (a) 1 : 4 (b) 1 2 : (c) 1 : 2 (d)1 2: 2 (NEET-I 2016) 39. A black hole is an object whose gravitational field is so strong that even light cannot escape from it. To what approximate radius would earth (mass = 5.98 × 1024 kg) have to be compressed to be a black hole? (a) 10–9 m (b) 10–6 m (c) 10–2 m (d) 100 m (2014) 40. The radius of a planet is twice the radius of earth. Both have almost equal average mass-densities. VP and VE are escape velocities of the planet and the earth, respectively, then (a) VP = 1.5 VE (b) VP = 2 VE (c) VE = 3 VP (d) VE = 1.5 VP (Karnataka NEET 2013) 41. A particle of mass ‘m’ is kept at rest at a height ‘3R’ from the surface of earth, where ‘R’ is radius of earth and ‘M’ is mass of earth. The minimum speed with which it should be projected, so that it does not return back, is (g is acceleration due to gravity on the surface of earth) (a) GM 2R 1 2       / (b) gR 4 1 2       / (c) 2g R       1 2/ (d) GM R       1 2/ (Karnataka NEET 2013) 42. A particle of mass m is thrown upwards from the surface of the earth, with a velocity u. The mass and the radius of the earth are, respectively, M and R. G is gravitational constant and g is acceleration due to gravity on the surface of the earth. The minimum value of u so that the particle does not return back to earth, is (a) 2 2 GM R (b) 2GM R (c) 2 2 gM R (d) 2 2 gR (Mains 2011) 43. The earth is assumed to be a sphere of radius R. A platform is arranged at a height R from the surface of the earth. The escape velocity of a body from this platform is fv, where v is its escape velocity from the surface of the Earth. The value of f is (a) 1/2 (b) 2 (c) 1 2 / (d) 1/3 (2006) 44. With what velocity should a particle be projected so that its height becomes equal to radius of earth? (a) GM R       1 2/ (b) 8 1 2 GM R       / (c) 2 1 2 GM R       / (d) 4 1 2 GM R       / (2001) 45. For a planet having mass equal to mass of the earth but radius is one fourth of radius of the earth. The escape velocity for this planet will be (a) 11.2 km/s (b) 22.4 km/s (c) 5.6 km/s (d) 44.8 km/s (2000) 46. The escape velocity of a sphere of mass m is given by (G = Universal gravitational constant; Me = Mass of the earth and Re = Radius of the earth) (a) 2GM m R e e (b) 2GM R e e (c) GM R e e (d) 2GM R R e e e + (1999) 47. The escape velocity of a body on the surface of the earth is 11.2 km/s. If the earth’s mass increases to twice its present value and radius of the earth becomes half, the escape velocity becomes (a) 22.4 km/s (b) 44.8 km/s (c) 5.6 km/s (d) 11.2 km/s (1997) 48. The escape velocity from earth is 11.2 km/s. If a body is to be projected in a direction making an angle 45° to the vertical, then the escape velocity is (a) 11.2 × 2 km/s (b) 11.2 km/s (c) 11. / 2 2 km/s (d) 11.2 2 km/s (1993) 49. For a satellite escape velocity is 11 km/s. If the satellite is launched at an angle of 60° with the vertical, then escape velocity will be (a) 11 km/s (b) 11 3 km/s (c) 11 3 km/s (d) 33 km/s (1989) EduHulk.COM