Title GRAVITATION.pdf ✅

Gravitation  Digital www.allendigital.in [ 199 ] NEWTON'S LAW OF GRAVITATION & GRAVITATIONAL FIELD 1. Newton's law of gravitation : (1) is not applicable outside the solar system (2) is used to govern the motion of satellites only (3) control the rotational motion of satellites and planets (4) control the rotational motion of electrons in atoms 2. Mass particles of 1 kg each are placed along x-axis at x = 1, 2, 4, 8,..... Then gravitational force on a mass of 3kg placed at origin is (G = universal gravitational constant) :- (1) 4G (2) 4G 3 (3) 2G (4)  3. Gravitational force between two masses at a distance 'd' apart is 6N. If these masses are taken to moon and kept at same separation, then the force between them will become : (1) 1 N (2) 1 N 6 (3) 36 N (4) 6 N 4. The value of universal gravitational constant G depends upon : (1) Nature of material of two bodies (2) Heat constant of two bodies (3) Acceleration of two bodies (4) None of these 5. Three identical bodies (each mass M) are placed at vertices of an equilateral triangle of arm L, keeping the triangle as such by which angular speed the bodies should be rotated in their gravitational fields so that the triangle moves along circumference of circular orbit : (1) 3 3GM L (2) 3 GM L (3) 3 GM 3L (4) 3 GM 3 L 6. Four particles of masses m, 2m, 3m and 4m are kept in sequence at the corners of a square of side a. The magnitude of gravitational force acting on a particle of mass m placed at the centre of the square will be : (1) 2 2 24m G a (2) 2 2 6m G a (3) 2 2 4 2Gm a (4) Zero 7. The tidal waves in the seas are primarily due to : (1) The gravitational effect of the sun on the earth (2) The gravitational effect of the moon on the earth (3) The rotation of the earth (4) The atmospheric effect of the earth itself 8. During the journey of space ship from earth to moon and back, the maximum fuel is consumed :- (1) Against the gravitation of earth in return journey (2) Against the gravitation of earth in onward journey (3) Against the gravitation of moon while reaching the moon (4) None of the above 9. If the distance between the centres of earth and moon is D and mass of earth is 81 times that of moon. At what distance from the centre of earth gravitational field will be zero : (1) D 2 (2) 2D 3 (3) 4D 5 (4) 9D 10 10. An earth's satellite is moving in a circular orbit with a uniform speed v. If the gravitational force of the earth suddenly disappears, the satellite will:- (1) vanish into outer space (2) continue to move with velocity v in original orbit (3) fall down with increasing velocity (4) fly off tangentially from the orbit with velocity v Exercise - I
NEET : Physics [ 200 ] www.allen digital.in  Digital 11. Following curve shows the variation of intensity of gravitational field (I) with distance from the centre of solid sphere(r) : (1) R r O I (2) O R r I (3) R r O I (4) R r O I 12. Suppose the acceleration due to gravity at the earth's surface is 10m/s2 and at the surface of mars it is 4.0 m/s2. A 60kg passenger goes from the earth to the mars in a spaceship moving with a constant velocity. Neglect all other objects in the sky. Which part of figure best represent the weight (Net gravitational force) of the passenger as a function of time : 600 200 D C B A Time 400 Weight (N) 240 (1) A (2) B (3) C (4) D 13. Assume that a tunnel is dug through earth from North pole to south pole and that the earth is a non-rotating, uniform sphere of density . The gravitational force on a particle of mass m dropped into the tunnel when it reaches a distance r from the centre of earth is (1) 3 mG r 4         (2) 4 mG r 3         (3) 4 2 mG r 3         (4) 4 2 m G r 3         14. Mars has a diameter of approximately 0.5 of that of earth, and mass of 0.1 of that of earth. The surface gravitational field strength on mars as compared to that on earth is a factor of – (1) 0.1 (2) 0.2 (3) 2.0 (4) 0.4 15. Three equal masses of 1 kg each are placed at the vertices of an equilateral triangle PQR and a mass of 2 kg is placed at the centroid O of the triangle which is at a distance of 2 m from each of the vertices of the triangle. The force, in newton, acting on the mass of 2 kg is :- (1) 2 (2) 2 (3) 1 (4) zero 16. One can easily “weigh the earth” by calculating the mass of earth using the formula (in usual notation) (1) 2 E G R g (2) 2 E g R G (3) E g R G (4) 3 E G R g ACCELERATION DUE TO GRAVITY 17. Acceleration due to gravity at the centre of the earth is :- (1) g (2) g 2 (3) zero (4) infinite 18. The value of 'g' on earth surface depends :- (1) only an earth's structure (2) only an earth's rotational motion (3) on above both (4) on none these and is same 19. The value of 'g' reduces to half of its value at surface of earth at a height 'h', then :- (1) h = R (2) h = 2R (3) h ( 2 1)R = + (4) h ( 2 1)R = −
Gravitation  Digital www.allendigital.in [ 201 ] 20. At some planet 'g' is 1.96 m/sec2. If it is safe to jump from a height of 2m on earth, then what should be corresponding safe height for jumping on that planet:- (1) 5m (2) 2m (3) 10m (4) 20m 21. If the earth stops rotating suddenly, the value of g at a place other than poles would :- (1) Decrease (2) Remain constant (3) Increase (4) Increase or decrease depending on the position of earth in the orbit round the sun 22. Diameter and mass of a planet is double that earth. Then time period of a pendulum at surface of planet is how much times of time period at earth surface :- (1) 1 2 times (2) 2 times (3) Equal (4) None of these 23. Gravitation on moon is 1/6th of that on earth. When a balloon filled with hydrogen is released on moon then, this :- (1) Will rise with an acceleration less then g 6       (2) Will rise with acceleration g 6       (3) Will fall down with an acceleration less than 5g 6       (4) Will fall down with acceleration g 6       24. The acceleration due to gravity g and mean density of earth  are related by which of the following relations ? [G = gravitational constant and R = radius of earth] : (1) 2 4 gR 3G  = (2) 3 4 gR 3G  = (3) 3g 4 gR =  (4) 3 3g 4 gR  =  25. More amount of sugar is obtained in 1kg weight: (1) At North pole (2) At equator (3) Between pole and equator (4) At South pole 26. When you move from equator to pole, the value of acceleration due to gravity (g) :- (1) increases (2) decreases (3) remains the same (4) first increases then decreases 27. When the radius of earth is reduced by 1% without changing the mass, then the acceleration due to gravity will (1) increase by 2% (2) decrease by 1.5% (3) increase by 1% (4) decrease by 1% 28. Weight of a body of mass m decreases by 1% when it is raised to height h above the earth's surface. If the body is taken to a depth h in a mine, then in its weight will (1) decrease by 0.5% (2) decrease by 2% (3) increase by 0.5% (4) increase by 1% 29. Acceleration due to gravity at earth's surface is 'g' m/s2. Find the effective value of acceleration due to gravity at a height of 32 km from sea level : (Re = 6400 Km) (1) 0.5g m/s2 (2) 0.99g m/s2 (3) 1.01g m/s2 (4) 0.90g m/s2 30. The mass of the moon is 1% of mass of the earth. The ratio of gravitational pull of earth on moon to that of moon on earth will be : (1) 1 : 1 (2) 1 : 10 (3) 1 : 100 (4) 2 : 1 31. Imagine a new planet having the same density as that of earth but its radius 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 : (1) g' = 3g (2) g' = g/9 (3) g' = 9g (4) g'=27 g 32. The change in the value of 'g' at a height 'h' above the surface of the earth is same as at a depth 'd'. If 'd' and 'h' are much smaller than the radius of earth, then which one of the following is correct? (1) d = h (2) d = 2h (3) d = 3h 2 (4) d = h/2 33. If the rotational speed of earth is increased then weight of a body at the equator (1) increases (2) decreases (3) becomes double (4) does not changes
NEET : Physics [ 202 ] www.allen digital.in  Digital 34. A body weighs W newton at the surface of the earth. Its weight at a height equal to half the radius of the earth will be : (1) W 2 (2) 2W 3 (3) 4W 9 (4) W 4 35. The imaginary angular velocity of the earth for which the effective acceleration due to gravity at the equator shall be zero is equal to (1) 1.25 × 10–3 rad/s (2) 2.50 × 10–3 rad/s (3) 3.75 × 10–3 rad/s (4) 5.0 × 10–3 rad/s [Take g = 10m/s2 for the acceleration due to gravity if the earth were at rest and radius of earth equal to 6400 km.] GRAVITATIONAL POTENTIAL ENERGY & POTENTIAL 36. Two different masses are dropped from same heights. When these just strike the ground, the following is same : (1) kinetic energy (2) potential energy (3) linear momentum (4) acceleration 37. Which of the following curve expresses the variation of gravitational potential with distance for a hollow sphere of radius R : (1) r V R (2) R V r (3) r V R (4) r V R 38. Gravitational potential difference between surface of a planet and a point situated at a height of 20m above its surface is 2 J/kg. If gravitational field is uniform, then the work done in taking a 5kg body upto height 4 meter above surface will be : (1) 2 J (2) 20 J (3) 40 J (4) 10 J 39. If Me is the mass of earth and Mm is the mass of moon (Me = 81 Mm). The potential energy of an object of mass m situated at a distance R from the centre of earth and r from the centre of moon, will be :- (1) m R GmM r 81   − +     (2) e 81 1 GmM r R   − +     (3) m 81 1 GmM r R   − +     (4) m 81 1 GmM r R   −     40. The gravitational potential energy is maximum at: (1) infinity (2) the earth's surface (3) The centre of the earth (4) Twice the radius of the earth 41. A missile is launched with a velocity less than the escape velocity. Sum of its kinetic energy and potential energy is :- (1) Positive (2) Negative (3) May be negative or positive depending upon its initial velocity (4) Zero 42. A body attains a height equal to the radius of the earth when projected from earth' surface. The velocity of the body with which it was projected is : (1) GM R (2) 2GM R (3) 5 GM 4 R (4) 3GM R 43. The gravitational potential energy of a body at a distance r from the center of the earth is U. The force at that point is : (1) 2 U r (2) U r (3) Ur (4) Ur2 44. A particle falls from infinity to the earth. Its velocity on reaching the earth surface is : (1) 2Rg (2) Rg (3) Rg (4) 2Rg 45. A projectile of mass m is thrown vertically up with an initial velocity  from the surface of earth (mass of earth = M). If it comes to rest at a height h, the change in its potential energy is (1) GMmh/R(R + h) (2) GMmh2/R(R + h)2 (3) GMmhR/R(R + h) (4) GMm/hR(R+h)