Tiêu đề 08. Gravitation Medium.pdf ✅

1. Kepler’s second law is a consequence of (a) Conservation of energy (b) Conservation of linear momentum (c) Conservation of angular momentum (d) Conservation of mass 2. Which of the following Kepler’s laws is also known as harmonic law ? (a) First law (b) Second law (c)Third law (d) None of these 3. Which of the following orbits is a possible orbit for a planet ? (a) (b) (c) (d) 4. The time period of an artificial satellite in a circular or bit of radius R is 2 days and its orbital velocity is o v If time period of another satellite in a circular orbit is 16 days then (a) Its radius of orbit is 4R and orbital velocity is o v (b) Its radius of orbit is 4R and orbital velocity 2 vo is (c) Its radius of orbit is 2R and orbital velocity is o v (d) Its radius of orbit is 2R and orbital velocity is 2 vo 5. In our solar system, the inter-planetary region has chunks of matter (much smaller in size compared to planets) called asteriods. They (a) Will not move around the sun since they have very small masses compared to sun. (b) Will move in an irregular way because of their small masses and will drift away into outer space. (c) Will move around the sun in closed orbits but not obey Kepler’s laws. (d) Will move in orbits like planets and obey kepler’s laws. 6. Figure shows elliptical orbit of a planet P about the sun S. The shaded area SCD is twice the shaded area SAB. If is the timer for the planet to move from C to D and is the time to move from A to B, then (a) 1 2 t = t (b) 1 2 t = 2t (c) 1 2 t = 4t (d) 1 2 t  t 7. A satellite is in an elliptic orbit around the earth with aphelion of RE 6 and perihelion of RE 2 where RE is the radius of the earth. The eccenttricity of the orbit is (a) 2 1 (b) 3 1 (c) 4 1 (d) 6 1 8. In the question number 11, lthe ratio of the velocity of the satellite at apogee and perigee is. (a) 2 1 (b) 3 1 (c) 4 1 (d) 6 1 9. A satrun year is 29.5 times the earth year. How far is the Saturn from the sun if the earth is 8 1.510 away from the sun? (a) 1.4 10 km6  (b) 1.4 10 km7  (c) 1.4 10 km8  (d) 1.4 10 km9  10. A planet revolves around the sun in an elliptical orbit of eccentricity e. if T is the time period of the planet, then the time spent by the planet between the ends of the minor axis and major axis close to the sum is. (a) 2e T (b)       −  1 2e T (c) 2 Te (d)        − 2 e 4 1 T 11. A planet revolves around the sun in an elliptical orbit. If are the velocities of the planet at the perigee and apogee respectively, then the eccentricity of elliptical orbit is given by (a) a P v v (b) a p a p v v v v + − (c) p a p a v v v v − + (d) p a p a v v v v + − 12. A planet revolves around the sun in an elliptical orbit. The linear speed of the planet will be maximum at (a) A (b) B (c) C (d) D 13. Work done in taking a mass from one point to another in a gravitational field depends on. (a) The end points only. (b) The path followed. (c) The velocity of the mass (d) Both length of the path and the end points 14. If a graph is plotted between 2 T and 3 r for a planet, then its slope will be (where, MS is the mass of the sun) (a) S 2 GM 4 (b) 4 GMS (c) 4GMS (d) GMS 15. The period of moon’s rotation around the earth is nearly 29 days. If moon’s mass were 2 fold its present value, and all other things remain unchanged, the period of Moon’s rotation would be nearly (a) 29 2 days (b) 2 29 days
(c) 29 ×2 days (d) 29 days 16. Three masses each of mass m are placed at the vertices of an equilateral triangle ABC of side as shown in figure. The force acting on a mass 2m placed at the centroid O of the triangle is (a) Zero (b) 2 2 l 2Gm (c) 2 2 l 4Gm (d) 2 2 l 6Gm 17. Which of the following statements is correct regarding the gravitational force ? (a) The gravitational force is dependent on the intervening medium. (b) The gravitational force is a non-conservative force. (c) The gravitational force action-reaction pair. (d) The gravitational force is a non-central force. 18. The mass of moon is 1% of mass of earth. The ratio of gravitational pull of earth on moon and that of moon on earth will be (a) 1 : 1 (b) 1 : 10 (c) 1 : 100 (d) 2 : 1 19. Six point masses each of mass are placed at the vertices of a regular hexagon of side l.The force acting on any of the masses is (a)       + 3 1 4 5 l Gm 2 2 (b)       + 3 1 4 3 l Gm 2 2 (c)       − 3 1 4 5 l Gm 2 2 (d)       − 3 1 4 3 l Gm 2 2 20. A mass m is placed at point P lies on the axis of a ring of mass M and radius R at a distance R from its centre. The gravitational force on mass m is. (a) 2 2R GMm (b) 2 2R GMm (c) 2 2 2R GMm (d) 2 4R GMm 21. Two spheres of masses and 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) 3F (b) F (c) 3 F (d) 9 F 22. A point mass m is placed inside a spherical shell of radius R and mass M at a distance 2 R from the centre of the shell. The gravitational force exerted by the shell on the point mass is. (a) 2 R GMm (b) 2 R 2GMm (c) Zero (d) 2 R 4GMm 23. Two stars of masses are parts of a binary star system. The radii of their orbits are 1 r and 2 r respectively, measured from the centre of mass of the system. The magnitude of gravitational force m1 exerts on m2 is (a) ( ) 1 2 1 2 r r m m G + (b) ( ) 2 1 2 1 r r m G + (c) ( ) 2 1 2 2 r r m G + (d) (r r ) G(m m ) 1 2 1 2 + + 24. Which of the following statements is correct regarding the universal gravitational constant G ? (a) G has same value in all systems of units. (b) The value of G is same everywhere in the universe. (c) The value of G was first experimentally determined by Johannes Kepler. (d) G is a vector quantity. 25. Mass of the earth has been determined through (a) Use of Kepler’s 3 2 R T constancy law (b) Sampling the density of earth’s crust and using earth’s radius (c) Cavendish’s determination of G and using earth’s radius and at its surface (d) Use of periods of satellites at different heights above earth’s surface 26. The acceleration due to gravity and density of the earth are related by which of the following relations ? (where G is the gravitational constant and RE is the radius of the earth) (a) 3g 4GRE  = (b) 4 GRE 3g   = (c) E 4 gR 3G   = (d) 3G 4gRE  = 27. The tidal wave in the sea are primarily due to gravitational effect of (a) Earth on the sun (b) Sun on the earth (c) Earth on the moon (d) Moon on the earth 28. If ME is the mass of the earth and RE its radius, the ratio of the acceleration due to gravity and the gravitational constant is (a) E 2 E M R (b) 2 E E R M (c) 2 MERE (d) E E R M 29. Which of the following statements is correct? (a) Acceleration due to gravity increases with increasing altitude. (b) Acceleration due to gravity increases with increasing depth (c) Acceleration due to gravity increases with increasing latitude. (d) Acceleration due to gravity is independent of the mass of the earth.
30. Value of g is (a) Maximum at poles (b) Maximum at equator (c) Same everywhere (d) Minimum at poles 31. The dependence of acceleration due to gravity on the distance r from the centre of the earth assumed to be a sphere of radius R of uniform density is as shown figure below. (i) (ii) (iii) (iv) The correct figure is. (a) (i) (b) (ii) (c) (iii) (d) (iv) 32. The change in potential energy when a body of mass m is raised to a height nRE from earth’s surface is ( RE = radius of the earth) (a) (n 1) n mgRE − (b) mgRE (c) (n 1) n mgRE + (d) n mgRE 33. A particle of mass m is placed at the centre of a uniform spherical shell of mass and radius R. The gravitational potential on the surface of the shell is (a) R Gm − (b) R 3Gm − (c) R 4Gm − (d) R 2Gm − 34. Two spheres each of mass M and radius R are separated by a distance of r.The gravitational potential at the midpoint of the line joining the centre of the spheres is (a) r GM − (b) r 2GM − (c) 2r GM − (d) r 4GM − 35. The escape velocity of a body from the earth depends on (i) The mass of the body. (ii) The location from where it is projected. (iii) The direction of projection. (iv) The height of the location from where the body is launched. (a) (i) and (ii) (b) (ii) and (iv) (c) (i) and (iii) (d) (iii) and (iv) 36. There is no atmosphere on moon as (a) It is closer to earth. (b) It revolves around the earth. (c) It gets light from the sun. (d) The rms speed of gas molecules is greater than the escape speed. 37. The escape velocity from the surface of the earth is (where RE is the radius of the earth) (a) E 2gR (b) E gR (c) E 2 gR (d) E 3gR 38. Match the column I with column II. (where ME is the mass of the earth, m is mass of the satellite and r is the radius of the orbit) Column I Column II (A) Kinetic energy (p) 2r GMEm − (B) Potential energy (q) r GME (C) Total energy (r) r GMEm − (D) Orbital velocity (s) 2r GMEm (a) A –r, B – s, C – q, D –P (b) A – q, B – p, C- r, D – s (c) A – p, B – q, C – s, D – r (d) A – S, B – r, C – p, D – q 39. A satellite of mass m is in a circular orbit of radius 2RE about the earth. The energy required to transfer it to a circular orbit of radius 4RE is (where ME and RE is the mass and radius of the earth respectively) (a) E E 2R GM m (b) E R 4R GM m (c) E E 8R GM m (d) E E 16R GM m 40. In the question number 67, the change in potential energy is (a) F E 2R GM m (b) E E 4R GM m (c) E E 8R GM m (d) E e R GM m 41. A satellite is orbiting the earth in a circular orbit of radius r. its. (a) Kinetic energy varies as r (b) Angular momentum varies as r 1 (c) Linear momentum varies as r 1 (d) Frequency of revolution varies as 3/ 2 r 1 42. If a small part separates from an orbiting satellite, the part will (a) Fall to the earth directly (b) Move in a spiral and reach earth after a few rotations. (c) Continue to move in the same orbit as the Satellite (d) Move farther away from the earth gradually. 43. The time period T of the moon of planet mars (mass Mm ) is related to its orbital radius R as (G = Gravitational constant)
(a) m 2 3 2 GM 4 R T  = (b) m 2 3 2 M 4 GR T  = (c) m 3 2 M 2 R G T  = (d) 3 m 2 T = 4M GR 44. The additional kinetic energy to be provided to a satellite of mass m revolving around a planet of mass M, to transfer it from a circular orbit of radius R1 to another of radius R (R R ) 2 2  1 is (a)         − 2 2 2 1 R 1 R 1 GmM (b)         − 1 R2 1 R 1 GmM (c)         − 1 R2 1 R 1 2GmM (d)         − 1 R2 1 R 1 GmM 2 1 45. A rocket is fired vertically from the surface of the earth with a speed v How far from the earth does the rocket go before returning to the earth ? (where RE is the radius of the earth and g is acceleration due to gravity) (a) 2 E 2 E gR v R v − (b) 2 E 2 E gR v R v + (c) 2 E 2 E 2gR v R v − (d) 2 E 2 E 2gR v R v + 46. A satellite of mass orbits the earth at a height h above the surface of the earth. How much energy must be expended to rocket the satellite out of earth’s gravitational influence ? (where ME and RE be mass and radius of the earth respectively) (a) 4(R h) GM m E E + (b) 2(R h) GM m E E + (c) (R h) GM m E E + (d) (R h) 2GM m E E + 47. A comet orbits the sun in a highly elliptical orbit. Which of the following quantities remains constant through out its orbit ? (i)Linear speed (ii) Angular speed (iii)Angular momentum (iv) Kinetic energy (v)Potential energy (vi) Total energy (a) (i), (ii), (iii) (b) (iii), (iv), (v) (c) (iii) and (vi) (d) (ii), (iii) and (vi) 48. An artificial satellite moving in a circular orbit around the earth has a total energy E . 0 Its potential energy is. (a) −E0 (b) E0 (c) E0 2 (d) Eo − 2 49. In motion of an object under the gravitational influence of another object. Which of the following quantities is not conserved ? (a) Angular momentum (b) Mass of an object (c) Total mechanical energy (d) Linear momentum 50. As observed from earth, the sun appears to move in an approximate circular orbit. For the motion of another planet like mercuary as observed from earth, this would (a) Be similarly ture. (b) Not be true because the force between earth and mercury is not inverse square law. (c) Not be true because the major gravitational force on mercury is due to sun. (d) Not be true because mercury is influenced by force other than gravitational forces. 51. An asteroid of mass m is approaching earth, initially at a distance 10 RE with speed vi It hits earth with a speed vf ( RE and ME are radius and mass of earth). Then (a)       = + + 10 1 1 R 2Gm v v E 2 i 2 f (b)       = + + 10 1 1 R 2GM v v E 2 E i 2 f (c)       = + − 10 1 1 R 2GM v v E 2 E i 2 f (d)       = + − 10 1 1 R 2Gm v v E 2 i 2 f 52. 53. For a satellite moving in an orbit around the earth, the ratio of its potential energy to kinetic energy is (a) 1 (b) -1 (c) 2 (d) - 2 54. Which of the following statements is correct about satellites ? (a) A satellite cannot move in a stable orbit in a plane passing through the earth’s centre (b) Geostationary satellites are launched in the equatorial plane. (c) We can use just one geostationary satellite for global communication around the globe. (d) The speed of satellite increases with an increase in the radius of its orbit. 55. Two satellites of earth S1 are S2 moving in the same orbit. The mass of S1 is four times the mass of S2 . Which one of the following statements is true ? (a) The potential energies of earth and satellite in the two cases are equal. (b) S1 are S2 moving with the same speed. (c) The kinetic energies of the two satellites are equal. (d) The time period of S1 is four times that S2 56. Which of the following statements is correct regarding a geostationary satellite? (a) A geostationary satellite goes around the earth in east-west direction (b) A geostationary satellite goes around the earth in west-east direction