STD 11 - Gravitation PYQs: JEE Mains Physics – Page 2

Showing 51–100 of 179 questions

51. 51. At a certain depth "\(d\)" below surface of earth. value of acceleration due to gravity becomes four times that of its value at a height \(3\,R\) above earth surface. Where \(R\) is Radius of earth (Take \(R =6400\,km\) ). The depth \(d\) is equal to \(............\,km\) 2023 Medium
52. 52. Choose the incorrect statement from the following 2023 Medium
53. 53. Every planet revolves around the sun in an elliptical orbit : \(A.\) The force acting on a planet is inversely proportional to square of distance from sun. \(B.\) Force acting on planet is inversely proportional to product of the masses of the planet and the sun \(C.\) The centripetal force acting on the planet is directed away from the sun. \(D.\) The square of time period of revolution of planet around sun is directly proportional to cube of semi-major axis of elliptical orbit. Choose the correct answer from the options given below : 2023 Medium
54. 54. Given below are two statements: one is labelled as Assertion \(A\) and the other is labelled as Reason \(R\). Assertion \(A:\) A pendulum clock when taken to Mount Everest becomes fast. Reason \(R:\) The value of \(g\) (acceleration due to gravity) is less at Mount Everest than its value on the surface of earth. In the light of the above statements, choose the most appropriate answer from the options given below 2023 Medium
55. 55. Given below are two statements: one is labelled as Assertion \(A\) and the other is labelled as Reason \(R\). Assertion \(A :\) Earth has atmosphere whereas moon doesn't have any atmosphere. Reason \(R\) : The escape velocity on moon is very small as compared to that on earth. In the light of the above statement, choose the correct answer from the options given below : 2023 Medium
56. 56. Given below are two statements : Statement\(-I:\) Acceleration due to gravity is different at different places on the surface of earth. Statement\(-II:\) Acceleration due to gravity increases as we go down below the earth's surface. In the light of the above statements, choose the correct answer from the options given below 2023 Medium
57. 57. Given below are two statements: Statement \(I:\) Acceleration due to earth's gravity decreases as you go 'up' or 'down' from earth's surface. Statement \(II:\) Acceleration due to earth's gravity is same at a height ' \(h\) ' and depth ' \(d\) ' from earth's surface, if \(h = d\). In the light of above statements, choose the most appropriate answer form the options given below 2023 Medium
58. 58. Given below are two statements: Statement \(I:\) For a planet, if the ratio of mass of the planet to its radius increases, the escape velocity from the planet also increases. Statement \(II:\) Escape velocity is independent of the radius of the planet. In the light of above statements, choose the most appropriate answer from the options given below on : 2023 Medium
59. 59. Given below are two statements: Statement \(I:\) If \(E\) be the total energy of a satellite moving around the earth, then its potential energy will be \(\frac{E}{2}\). Statement \(II:\) The kinetic energy of a satellite revolving in an orbit is equal to the half the magnitude of total energy \(E\). In the light of the above statements, choose the most appropriate answer from the options given below 2023 Medium
60. 60. Given below are two statements: Statement \(I:\) Rotation of the earth shows effect on the value of acceleration due to gravity \((g)\). Statement \(II:\) The effect of rotation of the earth on the value of \(g\) at the equator is minimum and that at the pole is maximum. In the light of the above statements, choose the correct answer from the options given below. 2023 Medium
61. 61. If earth has a mass nine times and radius twice to the of a planet \(P\). Then \(\frac{v_e}{3} \sqrt{x}\; ms ^{-1}\) will be the minimum velocity required by a rocket to pull out of gravitational force of \(P\), where \(v_e\) is escape velocity on earth. The value of \(x\) is 2023 Medium
62. 62. If the distance of the earth from Sun is \(1.5 \times 10^6\,km\). Then the distance of an imaginary planet from Sun, if its period of revolution is \(2.83\) years is \(.............\times 10^6\,km\) 2023 Medium
63. 63. If the earth suddenly shrinks to \(\frac{1}{64}\) th of its original volume with its mass remaining the same, the period of rotation of earth becomes \(\frac{24}{ x } h\). The value of \(x\) is \(.......\) 2023 Hard
64. 64. If the gravitational field in the space is given as \(\left(-\frac{ K }{ r ^2}\right)\). Taking the reference point to be at \(r =2\,cm\) with gravitational potential \(V =10\,J / kg\). Find the gravitational potential at \(r =3\,cm\) in \(SI\) unit (Given, that \(K =6\,J cm / kg\) ) 2023 Hard
65. 65. If \(V\) is the gravitational potential due to sphere of uniform density on it's surface, then it's value at the center of sphere will be:- 2023 Hard
66. 66. \(T\) is the time period of simple pendulum on the earth's surface. Its time period becomes \(x T\) when taken to a height \(R\) (equal to earth's radius) above the earth's surface. Then, the value of \(x\) will be: 2023 Medium
67. 67. The acceleration due to gravity at height \(h\) above the earth if \(h \ll R\) (radius of earth) is given by 2023 Medium
68. 68. The escape velocities of two planets \(A\) and \(B\) are in the ratio \(1: 2\). If the ratio of their radii respectively is \(1: 3\), then the ratio of acceleration due to gravity of planet \(A\) to the acceleration of gravity of planet \(B\) will be: 2023 Medium
69. 69. The orbital angular momentum of a satellite is \(L\), when it is revolving in a circular orbit at height \(h\) from earth surface. If the distance of satellite from the earth centre is increased by eight times to its initial value, then the new angular momentum will be \(............\,L\) 2023 Medium
70. 70. The radii of two planets \(A\) and \(B\) are \(R\) and \(4 R\) and their densities are \(\rho\) and \(\rho / 3\) respectively. The ratio of acceleration due to gravity at their surfaces \(\left(g_A: g_B\right)\) will be 2023 Medium
71. 71. The ratio of escape velocity of a planet to the escape velocity of earth will be:Given : Mass of the planet is \(16\) times mass of earth and radius of the planet is \(4\) times the radius of earth. 2023 Medium
72. 72. The time period of a satellite of earth is \(24\) hours. If the separation between the earth and the satellite is decreased to one fourth of the previous value, then its new time period will become \(.......\,hours\) 2023 Easy
73. 73. The time period of a satellite, revolving above earth's surface at a height equal to \(R\) will be (Given \(g =\pi^2 m / s ^2, R =\) radius of earth) 2023 Medium
74. 74. The weight of a body at the surface of earth is \(18\,N\). The weight of the body at an altitude of \(3200\,km\) above the earth's surface is \(........\,N\) (given, radius of earth \(R _{ e }=6400\,km\) ) 2023 Easy
75. 75. The weight of a body on the surface of the earth is \(100\,N\). The gravitational force on it when taken at a height, from the surface of earth, equal to onefourth the radius of the earth is \(..........\,N\) 2023 Medium
76. 76. Two identical particles each of mass \(m\) go round a circle of radius \(a\) under the action of their mutual gravitational attraction. The angular speed of each particle will be 2023 Medium
77. 77. Two planets \(A\) and \(B\) of radii \(R\) and \(1.5 R\) have densities \(\rho\) and \(\rho / 2\) respectively. The ratio of acceleration due to gravity at the surface of \(B\) to \(A\) is : 2023 Easy
78. 78. Two satellites \(A\) and \(B\) move round the earth in the same orbit. The mass of \(A\) is twice the mass of \(B\). The quantity which is same for the two satellites will be : 2023 Medium
79. 79. Two satellites of masses \(m\) and \(3\,m\) revolve around the earth in circular orbits of radii \(r\) and \(3 r\) respectively. The ratio of orbital speeds of the satellites respectively is : 2023 Medium
80. 80. A body is projected vertically upwards from the surface of earth with a velocity equal to one third of escape velocity. The maximum height attained by the body will be \(......km\) (Take radius of earth \(=6400\,km\) and \(g =10\,ms^{-2}\) ) 2022 Hard
81. 81. A body of mass \(m\) is projected with velocity \(\lambda v_{e}\) in vertically upward direction from the surface of the earth into space. It is given that \(v _{ e }\) is escape velocity and \(\lambda<1\). If air resistance is considered to the negligible, then the maximum height from the centre of earth, to which the body can go, will be. ( \(R\) : radius of earth) 2022 Hard
82. 82. An object is taken to a height above the surface of earth at a distance \(\frac{5}{4} R\) from the centre of the earth. Where radius of earth, \(R=6400\,km\). The percentage decrease in the weight of the object will be \(....\%\) 2022 Medium
83. 83. An object of mass \(1 kg\) is taken to a height from the surface of earth which is equal to three times the radius of earth. The gain in potential energy of the object will be \(....MJ\)[If, \(g =10\,ms ^{-2}\) and radius of earth \(=6400\,km\) ] 2022 Medium
84. 84. Assume there are two identical simple pendulum Clocks\(-1\) is placed on the earth and Clock\(-2\) is placed on a space station located at a height \(h\) above the earth surface. Clock\(-1\) and Clock\(-2\) operate at time periods \(4\,s\) and \(6\,s\) respectively. Then the value of \(h\) is \(....km\) (consider radius of earth \(R _{ E }=6400\,km\) and \(g\) on earth \(10\,m / s ^{2}\) ) 2022 Hard
85. 85. Four spheres each of mass \(m\) form a square of side \(d\) (as shown in figure). A fifth sphere of mass \(M\) is situated at the centre of square. The total gravitational potential energy of the system is
    2022 Medium
86. 86. Given below are two statements: One is labelled as Assertion \(A\) and the other is labelled as Reason \(R\). Assertion \(A\): If we move from poles to equator, the direction of acceleration due to gravity of earth always points towards the center of earth without any variation in its magnitude. Reason \(R \): At equator, the direction of acceleration due to the gravity is towards the center of earth. In the light of above statements, choose the correct answer from the options given below 2022 Medium
87. 87. If the acceleration due to gravity experienced by a point mass at a height \(h\) above the surface of earth is same as that of the acceleration due to gravity at a depth a depth \(\alpha\) h \(\left(h \ll R_{e}\right)\) from the earth surface. The value of \(\alpha\) will be\(....\)(use \(R _{ e }=6400\,km\) ) 2022 Medium
88. 88. If the radius of earth shrinks by \(2 \%\) while its mass remains same. The acceleration due to gravity on the earth's surface will approximately. 2022 Medium
89. 89. The approximate height from the surface of earth at which the weight of the body becomes \(\frac{1}{3}\) of its weight on the surface of earth is \(..........km\) : [Radius of earth \(R =6400 \,km\) and \(\sqrt{3}=1.732]\) 2022 Medium
90. 90. The distance between Sun and Earth is \(R.\) The duration of year if the distance between Sun and Earth becomes \(3R\) will be  2022 Medium
91. 91. The escape velocity of a body on a planet  \('A'\)  is \(12 \,kms ^{-1}\). The escape velocity of the body on another planet  \('B'\) , whose density is four times and radius is half of the planet  \('A'\), is ................... \(kms ^{-1}\) 2022 Medium
92. 92. The height of any point \(P\) above the surface of earth is equal to diameter of earth. The value of acceleration due to gravity at point \(P\) will be : (Given \(g=\) acceleration due to gravity at the surface of earth) 2022 Medium
93. 93. The percentage decrease in the weight of a rocket, when taken to a height of \(32 km\) above the surface of earth will, be\(.....\%\) (Radius of earth \(=6400\,km\) ) 2022 Medium
94. 94. The time period of a satellite revolving around earth in a given orbit is \(7 \,hours\). If the radius of orbit is increased to three times its previous value, then approximate new time period of the satellite will be ...... \(hours\) 2022 Medium
95. 95. Three identical particle \(A , B\) and \(C\) of mass \(100\, kg\) each are placed in a straight line with \(AB = BC =13 \,m\). The gravitational force on a fourth particle \(P\) of the same mass is \(F\), when placed at a distance \(13 \,m\) from the particle \(B\) on the perpendicular bisector of the line \(AC\). The value of \(F\) will be approximately\(....G\) 2022 Hard
96. 96. Two objects of equal masses placed at certain distance from each other attracts each other with a force of \(F\). If one-third mass of one object is transferred to the other object, then the new force will be 2022 Easy
97. 97. Two planets \(A\) and \(B\) of equal mass are having their period of revolutions \(T_{A}\) and \(T_{B}\) such that \(T_{A}=2 T_{B}\). These planets are revolving in the circular orbits of radii \(I_{A}\) and \(I_{B}\) respectively. Which out of the following would be the correct relationship of their orbits? 2022 Medium
98. 98. Two satellites \(A\) and \(B\) having masses in the ratio \(4: 3\) are revolving in circular orbits of radii \(3\,r\) and \(4\,r\) respectively around the earth. The ratio of total mechanical energy of \(A\) to \(B\) is. 2022 Medium
99. 99. Two satellites \(S _{1}\) and \(S _{2}\) are revolving in circular orbits around a planet with radius \(R _{1}=3200 \,km\) and \(R _{2}=800\, km\) respectively. The ratio of speed of satellite \(S_{1}\) to the speed of satellite \(S_{2}\) in their respective orbits would be \(\frac{1}{ x }\) where \(x =\) 2022 Medium
100. 100. A body is projected vertically upwards from the surface of earth with a velocity sufficient enough to carry it to infinity. The time taken by it to reach height \(h\) is \(....\,S.\) 2021 Hard

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