Tiêu đề 08. Gravitation HARD.pdf ✅

1. 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 (a) 2 2 24 a m G (b) 2 2 6 a m G (c) 2 2 4 2 a Gm (d) Zero 2. Acceleration due to gravity on moon is 1/6 of the acceleration due to gravity on earth. If the ratio of densities of earth ( m ) and moon ( ) e is 3 5 =         m e   then radius of moon Rm in terms of Re will be (a) Re 18 5 (b) Re 6 1 (c) Re 18 3 (d) Re 2 3 1 3. A spherical planet far out in space has a mass M0 and diameter . D0 A particle of mass m falling freely near the surface of this planet will experience an acceleration due to gravity which is equal to (a) 2 0 0 GM / D (b) 2 0 0 4mGM / D (c) 2 0 0 4GM / D (d) 2 0 0 GmM / D 4. The moon's radius is 1/4 that of the earth and its mass is 1/80 times that of the earth. If g represents the acceleration due to gravity on the surface of the earth, that on the surface of the moon is (a) 4 g (b) 5 g (c) 6 g (d) 8 g 5. If the radius of the earth were to shrink by 1% its mass remaining the same, the acceleration due to gravity on the earth's surface would (a) Decrease by 2% (b) Remain unchanged (c) Increase by 2% (d) Increase by 1% 6. Mass of moon is 7.34 10 . 22  kg If the acceleration due to gravity on the moon is 1.4m/s 2 , the radius of the moon is ( 6.667 10 / ) 11 2 2 G Nm kg − =  (a) m 4 0.56 10 (b) m 6 1.87 10 (c) m 6 1.92 10 (d) m 8 1.01 10 7. Where will it be profitable to purchase 1 kg sugar (by spring balance) (a) At poles (b) At equator (c) At 450 latitude (d) At 400 latitude 8. The acceleration of a body due to the attraction of the earth (radius R) at a distance 2R from the surface of the earth is (g = acceleration due to gravity at the surface of the earth) (a) 9 g (b) 3 g (c) 4 g (d) g 9. The height of the point vertically above the earth's surface, at which acceleration due to gravity becomes 1% of its value at the surface is (Radius of the earth = R) (a) 8R (b) 9R (c) 10 R (d) 20R 10. At surface of earth weight of a person is 72 N then his weight at height R/2 from surface of earth is (R = radius of earth) (a) 28N (b) 16N (c) 32N (d) 72N 11. 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, change in its weight is (a) 2% decrease (b) 0.5% decrease (c) 1% increase (d) 0.5% increase 12. The depth at which the effective value of acceleration due to gravity is 4 g is (R = radius of the earth) (a)R (b) 4 3R (c) 2 R (d) 4 R 13. Assuming earth to be a sphere of a uniform density, what is the value of gravitational acceleration in a mine 100 km below the earth's surface (Given R = 6400km) (a) 2 9.66m / s (b) 2 7.64m / s (c) 2 5.06m / s (d) 2 3.10m / s 14. The depth d at which the value of acceleration due to gravity becomes n 1 times the value at the surface, is [R = radius of the earth] (a) n R (b)       − n n R 1 (c) 2 n R (d)       n + 1 n R 15. The angular velocity of the earth with which it has to rotate so that acceleration due to gravity on 60° latitude becomes zero is (Radius of earth = 6400 km. At the poles g = 10 ms–2 ) (a) 2.5×10–3 rad/sec (b) 5.0×10–1 rad/sec (c) 10 10 rad / sec 1  (d) 7.8 10 rad / sec −2  16. If earth stands still what will be its effect on man's weight (a) Increases (b) Decreases (c) Remains same (d) None of these 17. If the angular speed of earth is increased so much that the objects start flying from the equator, then the length of the day will be nearly (a) 1.5 hours (b) 8 hours
(c) 18 hours (d) 24 hours 18. The gravitational potential in a region is given by V = (3x + 4y + 12z) J/kg. The modulus of the gravitational field at (x = 1, y = 0,z = 3) is (a) 1 20 − N kg (b) 1 13 − N kg (c) 1 12 − N kg (d) 1 5 − N kg 19. Infinite bodies, each of mass 3kg are situated at distances 1m, 2m, 4m,8m....... respectively on x-axis. The resultant intensity of gravitational field at the origin will be (a)G (b) 2G (c) 3G (d) 4G 20. Two concentric shells of mass M1 and M2 are having radii 1 r and . 2 r Which of the following is the correct expression for the gravitational field on a mass m. (a) 2 1 2 ( ) r G M M I + = for 1 r  r (b) 2 1 2 ( ) r G M M I + = for 2 r  r (c) 2 2 r M I = G for 1 2 r  r  r (d) 2 1 r GM I = for 1 2 r  r  r 21. A uniform ring of mass m is lying at a distance 1.73 a from the centre of a sphere of mass M just over the sphere where a is the small radius of the ring as well as that of the sphere. Then gravitational force exerted is (a) 2 8a GMm (b) 2 (1.73 a) GMm (c) 2 3 a GMm (d) 2 8 1.73 a GMm 22. In some region, the gravitational field is zero. The gravitational potential in this region (a) Must be variable (b) Must be constant (c) Cannot be zero (d) Must be zero 23. The gravitational field due to a mass distribution is 3 E = K / x in the x - direction (K is a constant). Taking the gravitational potential to be zero at infinity, its value at a distance x is (a) K / x (b) K / 2x (c) 2 K / x (d) 2 K / 2x 24. The intensity of gravitational field at a point situated at a distance of 8000 km from the centre of the earth is 6N / kg . The gravitational potential at that point is – (in Joule / kg) (a) 6 8 10 (b) 3 2.4 10 (c) 7 4.8 10 (d) 14 6.4 10 25. The gravitational potential due to the earth at infinite distance from it is zero. Let the gravitational potential at a point P be −5J / kg . Suppose, we arbitrarily assume the gravitational potential at infinity to be + 10 J / kg , then the gravitational potential at P will be (a) −5 J / kg (b) +5 J / kg (c) −15 J / kg (d) +15 J / kg 26. An infinite number of point masses each equal to m are placed at x =1. x = 2, x = 4, x = 8 ......... What is the total gravitational potential at x = 0 (a) −Gm (b) −2Gm (c) − 4Gm (d) − 8Gm 27. For a satellite escape velocity is 11 km / s . If the satellite is launched at an angle of o 60 with the vertical, then escape velocity will be (a) 11 km / s (b) 11 3 km / s (c) km / s 3 11 (b) 33 km / s 28. The escape velocity from the earth is about 11 km / s . The escape velocity from a planet having twice the radius and the same mean density as the earth, is (a) 22 km/s (b) 11 km/s (c) 5.5 km/s (d) 15.5 km/s 29. If the radius of earth reduces by 4% and density remains same then escape velocity will (a) Reduce by 2% (b) Increase by 2% (c) Reduce by 4% (d) Increase by 4% 30. A rocket of mass M is launched vertically from the surface of the earth with an initial speed V. Assuming the radius of the earth to be R and negligible air resistance, the maximum height attained by the rocket above the surface of the earth is (a)       − 1 2 2 V gR R (b)       − 1 2 2 V gR R a m a M 1.73 a M1 M2 r2 r1 m r
(c)       − 1 2 2 V gR R (d)       − 1 2 2 V gR R 31. A body of mass m is situated at a distance Re 4 above the earth’s surface, where Re is the radius of earth. How much minimum energy be given to the body so that it may escape (a) mgR e (b) mgR e 2 (c) 5 mgR e (d) 16 mgR e 32. The distance of a planet from the sun is 5 times the distance between the earth and the sun. The Time period of the planet is (a) years 3 / 2 5 (b) years 2 / 3 5 (c) years 1 / 3 5 (d) years 1 / 2 5 33. A satellite is moving around the earth with speed v in a circular orbit of radius r. If the orbit radius is decreased by 1%, its speed will (a) Increase by 1% (b) Increase by 0.5% (c) Decrease by 1% (d) Decrease by 0.5% 34. If the gravitational force between two objects were proportional to 1/R; where R is separation between them, then a particle in circular orbit under such a force would have its orbital speed v proportional to (a) 2 1 / R (b) 0 R (c) 1 R (b) 1 / R 35. The distance between centre of the earth and moon is 384000 km. If the mass of the earth is 24 6 10 kg and 6.67 10 / . 11 2 2 G Nm kg − =  The speed of the moon is nearly (a) 1 km / sec (b) 4 km / sec (c) 8 km / sec (d) 11.2 km / sec 36. A satellite is launched into a circular orbit of radius ‘R’ around earth while a second satellite is launched into an orbit of radius 1.02 R. The percentage difference in the time periods of the two satellites is (a) 0.7 (b) 1.0 (c) 1.5 (d) 3 37. Periodic time of a satellite revolving above Earth’s surface at a height equal to R, where R the radius of Earth, is [gis acceleration due to gravity at Earth’s surface] (a) g 2R 2 (b) g R 4 2 (c) g R 2 (d) g R 8 38. An earth satellite S has an orbit radius which is 4 times that of a communication satellite C. The period of revolution of S is (a) 4 days (b) 8 days (c) 16 days (d) 32 days 39. One project after deviation from its path, starts moving round the earth in a circular path at radius equal to nine times the radius at earth R, its time period will be (a) g R 2 (b) g R 27  2 (c) g R  (d) g R 8  2 40. Two particles of equal mass go round a circle of radius R under the action of their mutual gravitational attraction. The speed of each particle is (a) R Gm v 1 2 1 = (b) R Gm v 2 = (c) R Gm v 2 1 = (d) R Gm v 4 = 41. Two types of balances, the beam balance and the spring balance are commonly used for measuring weight in shops. If we are on the moon, we can continue to use (a) Only the beam type balance without any change (b) Only the spring balance without any change (c) Both the balances without any change (d) Neither of the two balances without making any change 42. A body released from a height h takes time t to reach earth’s surface. The time taken by the same body released from the same height to reach the moon’s surface is (a)t (b) 6t (c) 6t (d) 6 t 43. A satellite is revolving round the earth with orbital speed 0 v . If it stops suddenly, the speed with which it will strike the surface of earth would be ( v e = escape velocity of a particle on earth’s surface) (a) 0 2 v ve (b) 0 v (c) 2 0 2 v v e − (d) 2 0 2 v 2v e − 44. The escape velocity for a planet is e v . A tunnel is dug along a diameter of the planet and a small body is dropped into it at the surface. When the body reaches the centre of the planet, its speed will be (a) e v (b) 2 e v (c) 2 e v (d) Zero
45. Earth is revolving around the sun if the distance of the earth from the sun is reduced to 1/4th of the present distance then the present length of the day is reduced by (a)1⁄4 (b)1⁄2 (c) 1/8 (d) 1/6 46. Find the weight of an object at Neptune which weighs 19.6 N on the earth. Mass of Neptune = 1026 kg, radius R = 2.5 × 104 km and rotates one around its axis in 16 h. (a) 19.6 N (b) 20.0 N (c) 20.4 N (d) 20.8 N 47. An earth’s satellite moves in a circular orbit with an orbital speed 6280 ms-1 . Find the time of revolution. (a) 130 min (b) 145 min (c) 155 min (d) 175 min 48. A mass m1 is placed at the centre of a shell of radius R, m2 is placed at a distance R from the surface and is immersed in an oil of dielectric constant 10. Find the force on m1. (a) Zero (b) ( ) 2 2 1 10R G M + m m (c) 2 1 2 4R Gm m (d) ( ) 2 1 2 4R Gm 4M + m 49. 5 kg and 10 kg spheres are 1 m apart. Where the gravitation field intensity be zero from 5 kg block. (a) 0.4 m (b) 0.3 m (c) 0.25 m (d) 0.35 m 50. A satellite is in sufficiently low obit so that it encounter air drag and if orbit changes from r to r - r. Find the change in orbital velocity and change in PE. (a) 3 2 r GMm r , r GM 2 r  (b) r GMm , r GM 2 r 2  (c) 3 2 2r GMm r , r GM 2 r  (d) None 51. A body is fired from the surface of the earth. It goes to a maximum height R(radius of the earth) from the surface of the earth. Find the initial velocity given. (a) 6.9 km s-1 (b) 7.4 km s-1 (c) 7.9 km s-1 (d) 8.4 km s-1 52. Find the height above the surface of the earth where weight becomes half. (a) 2 R (b) (2 - 1)R (c) ( 2 1) R + (d) 2 R 53. A pendulum clock which keeps correct time at the surface of the earth is taken into a min then (a) It keeps correct time (b) It gains time (c) It loses time (d) None of these 54. Find the velocity of the earth at which it should rotate so that weight of a body becomes zero at the equator. (a) 1.25 rad s-1 (b) 1.25 × 10-1 rad s-1 (c) 1.25 × 10-2 rad s-1 (d) 1.25 × 10-3 rad s-1 55. The radius of a planet is R1 and a satellite revolves around it in a radius R2s Time period of revolution is T. Find the acceleration due to gravity. (a) 2 2 1 3 2 2 R T 4 R (b) 2 1 2 2 2 R T 4 R (c) 2 1 3 2 2 R T 2 R (d) 2 2 2 T 4 R 56. A solid sphere of mass m and radius r is placed inside a hollow thin spherical shell of mass M and radius R as shown in Fig. A particle of mass m' is placed on the line joining the two centres at a distance x from the point of contact of the sphere and shell. Find the magnitude of force (gravitational) on this particle when 2r < x < 2R. (a) 2 x Gmm' (b) ( ) 2 x r Gmm' − (c) 2 2 x GmM x Gmm' + (d) ( ) ( ) 2 2 x R GmM x r Gmm' − + − 57. A satellite of moon revolves around it in a radius n times the radius of moon (R). Due to cosmic dust it experiences a resistance F = v 2 . Find how long it will stay in the orbit. (a) n GM/R m  (b) ( n 1) am m R −  (c) ( ) v m n −1  (d) 2 f i v m v  58. Find the minimum velocity to be imparted to a body so that it escape the solar system (a) SE S E E R 2GM R 2GM + (b) ( ) SE S 2 E E R GM 2 1 R 2GM + −