Physics · JEE Main, NEET

Gravitation

223 practice questions with a worked solution for each. Tap an option to see instantly if you are right.

206MCQ17Numerical21With diagram
Start with question 1 See it move: Gravitation and orbits
  1. 1At what height hh above the Earth's surface does the acceleration due to gravity become g9\frac{g}{9}, where RR is the radius of Earth?JEE Main/MCQ/Medium
  2. 2The acceleration due to gravity at the center of the Earth is:NEET/MCQ/Medium
  3. 3Three identical spheres of mass m , are placed at the vertices of an equilateral triangle of length a. When released, they interact only through gravitational force and collide after a time T=4\mathrm{T}=4 seconds. If the sides of the triangle are increased to length 2 a and also the masses of the spheres are made 2 m , then they will collide after _____ seconds.JEE Main/Numerical/Medium/Newton's Law of Gravitation
  4. 4A small point of mass mm is placed at a distance 2R2 R from the centre ' O′O^{\prime} of a big uniform solid sphere of mass M and radius R . The gravitational force on ' m ' due to M is F1\mathrm{F}_1. A spherical part of radius R/3\mathrm{R} / 3 is removed from the big sphere as shown in the figure and the gravitational force on m due to remaining part of M is found to be F2\mathrm{F}_2. The value of ratio F1:F2\mathrm{F}_1: \mathrm{F}_2 is

    JEE Main/MCQ/Medium/Newton's Law of Gravitation/With diagram
  5. 5In hydrogen like system the ratio of coul0mbian force and gravitational force between an electron and a proton is in the order of :JEE Main/MCQ/Medium/Newton's Law of Gravitation
  6. 6A 90 kg90 \mathrm{~kg} body placed at 2R2 \mathrm{R} distance from surface of earth experiences gravitational pull of :  ( R= Radius of earth, g=10 m s−2 ) \text { ( } \mathrm{R}=\text { Radius of earth, } \mathrm{g}=10 \mathrm{~m} \mathrm{~s}^{-2} \text { ) }JEE Main/MCQ/Medium/Newton's Law of Gravitation
  7. 7Two identical particles each of mass mm go round a circle of radius aa under the action of their mutual gravitational attraction. The angular speed of each particle will be :JEE Main/MCQ/Medium/Newton's Law of Gravitation
  8. 8A planet has double the mass of the earth. Its average density is equal to that of the earth. An object weighing WW on earth will weigh on that planet:JEE Main/MCQ/Medium/Newton's Law of Gravitation
  9. 9Two particles of equal mass mm move in a circle of radius rr under the action of their mutual gravitational attraction. The speed of each particle will be :JEE Main/MCQ/Medium/Newton's Law of Gravitation
  10. 10Assume that the earth is a solid sphere of uniform density and a tunnel is dug along its diameter throughout the earth. It is found that when a particle is released in this tunnel, it executes a simple harmonic motion. The mass of the particle is 100g100g. The time period of the motion of the particle will be (approximately)
    (take     g=10ms−2g=10{ms}^{-2}, radius of earth =6400km=6400km)    JEE Main/MCQ/Medium/Newton's Law of Gravitation
  11. 11Three identical particle A,BA,B and CC of mass 100kg100kg each are placed in a straight line with AB=BC=13mAB=BC=13m. The gravitational force on a fourth particle PP of the same mass is FF, when placed at a distance 13m13m from the particle BB on the perpendicular bisector of the line ACAC. The value of FF will be approximatelyJEE Main/MCQ/Medium/Newton's Law of Gravitation
  12. 12Two objects of equal masses placed at certain distance from each other attracts each other with a force of FF. If one-third mass of one object is transferred to the other object, then the new force will beJEE Main/MCQ/Medium/Newton's Law of Gravitation
  13. 13Statement I : The law of gravitation holds good for any pair of bodies in the universe.
    Statement II : The weight of any person becomes zero when the person is at the centre of the earth.
    In the light of the above statements, choose the correct answer from the options given below.    JEE Main/MCQ/Medium/Newton's Law of Gravitation
  14. 14Four particles each of mass M,M, move along a circle of radius RR under the action of their mutual gravitational attraction as shown in figure. The speed of each particle is :
    JEE Main/MCQ/Medium/Newton's Law of Gravitation/With diagram
  15. 15The masses and radii of the earth and moon are (M1,R1)\left({M}_{1},{R}_{1}\right) and (M2,R2)\left({M}_{2},{R}_{2}\right) respectively. Their centres are at a distance rr apart. Find the minimum escape velocity for a particle of mass mm to be projected from the middle of these two masses :JEE Main/MCQ/Medium/Newton's Law of Gravitation
  16. 16The planet Mars has two moons, if one of them has a period 77 hours, 3030 minutes and an orbital radius of 9.0×103km.9.0\times {10}^{3}km. Find the mass of Mars.
    {\left\{\right. Given 4π2G=6×1011N−1m−2kg2}\left.\dfrac{4{\pi }^{2}}{G}=6\times {10}^{11}{N}^{-1}{m}^{-2}{kg}^{2}\right\}    JEE Main/MCQ/Medium/Newton's Law of Gravitation
  17. 17Consider a binary star system of star AA and star BB with masses mA{m}_{A} and mB{m}_{B} revolving in a circular orbit of radii rA{r}_{A} and rB,{r}_{B}, respectively. If TA{T}_{A} and TB{T}_{B} are the time period of star AA and star B,B, respectively, then:JEE Main/MCQ/Medium/Newton's Law of Gravitation
  18. 18A person whose mass is 100kg100kg travels from Earth to Mars in a spaceship. Neglect all other objects in sky and take acceleration due to gravity on the
    surface of the Earth and Mars as     10ms−210m{s}^{-2} and 4ms−24m{s}^{-2}, respectively. Identify from the below figures, the curve that fits best for the weight of the passenger as a function of time.
    JEE Main/MCQ/Medium/Newton's Law of Gravitation/With diagram
  19. 19A solid sphere of radius RR gravitationally attracts a particle placed at 3R3R from its centre with a force F1.{F}_{1}. Now a spherical cavity of radius (R2)\left(\dfrac{R}{2}\right) is made in the sphere (as shown in figure) and the force becomes F2{F}_{2}. The value of F1:F2{F}_{1}:{F}_{2} is:
    JEE Main/MCQ/Medium/Newton's Law of Gravitation/With diagram
  20. 20Two stars of masses mm and 2m2m at a distance dd rotate about their common centre of mass in free space. The period of revolution isJEE Main/MCQ/Medium/Newton's Law of Gravitation
  21. 21Four identical particles of equal masses 1kg1kg made to move along the circumference of a circle of radius 1m1m under the action of their own mutual gravitational attraction. The speed of each particle will be:JEE Main/MCQ/Medium/Newton's Law of Gravitation
  22. 22The mass density of a spherical galaxy varies as Kr\dfrac{K}{r} over a large distance rr from its center. In that region, a small star is in a circular orbit of radius RR. Then the period of revolution,TT depends on RR as:JEE Main/MCQ/Medium/Newton's Law of Gravitation
  23. 23A satellite of massMM is launched vertically upwards with an initial speed uu from the surface of the earth. After it reaches height RR ( R=R= radius of the earth), it ejects a rocket of mass M10\dfrac{M}{10} so that subsequently the satellite moves in a circular orbit. The kinetic energy of the rocket is ( GG is the gravitational constant; Me{M}_{e} is the mass of the earth):JEE Main/MCQ/Medium/Newton's Law of Gravitation
  24. 24The ratio of the weights of a body on Earth’s surface to that on the surface of a planet is 9:49:4 The mass of the planet is 19th\dfrac{1}{9}th of that of the Earth. If RR is the radius of the Earth, what is the radius of the planet? (Take the planets to have the same mass density)JEE Main/MCQ/Medium/Newton's Law of Gravitation
  25. 25Four identical particles of mass MM are located at the corners of a square of side ‘a’‘a’ . What should be their speed if each of them revolves under the influence of other’s gravitational field in a circular orbit circumscribing the square?
    JEE Main/MCQ/Medium/Newton's Law of Gravitation/With diagram
  26. 26A straight rod of length LL extends from x=ax=a to x=L+a.x=L+a. The gravitational force it exerts on a point mass 'm' at x=0,x=0, if the mass per unit length of the rod is A+Bx2,A+B{x}^{2}, is given by:JEE Main/MCQ/Medium/Newton's Law of Gravitation
  27. 27Take the mean distance of the moon and the sun from the earth to be 0.4×106 km0.4 \times 10^6 \mathrm{~km} and 150×106 km150 \times 10^6 \mathrm{~km} respectively. Their masses are 8×1022 kg8 \times 10^{22} \mathrm{~kg} and 2×2 \times 1030 kg10^{30} \mathrm{~kg} respectively. The radius of the earth is 6400 km6400 \mathrm{~km}. Let ΔF1\Delta F_1 be the difference in the forces exerted by the moon at the nearest and farthest points on the earth and ΔF2\Delta \mathrm{F}_2 be the difference in the force exerted by the sun at the nearest and farthest points on the earth. Then, the number closest to ΔF1ΔF2\frac{\Delta F_1}{\Delta F_2} is:JEE Main/MCQ/Medium/Newton's Law of Gravitation
  28. 28A particle is moving with a uniform speed in a circular orbit of radius R in a central force inversely proportional to the nth{n}^{th} power of R. If the period of rotation of the particle is T, then:JEE Main/MCQ/Medium/Newton's Law of Gravitation
  29. 29Match List‐I‐I (Event) with List‐II‐II (Order of the time interval for the happening of the event) and select the correct option from the options given below the lists. List-I List-II (a)(a) The rotation period of earth (i)(i) 105s{10}^{5}s (b)(b) Revolution period of earth (ii)(ii) 107s{10}^{7}s (c)(c) Period of a light wave (iii)(iii) 10−15s{10}^{-15}s (d)(d) Period of a sound wave (iv)(iv) 10−3s{10}^{-3}sJEE Main/MCQ/Medium/Newton's Law of Gravitation
  30. 30Acceleration due to gravity on the surface of earth is ' gg '. If the diameter of earth is reduced to one third of its original value and mass remains unchanged, then the acceleration due to gravity on the surface of the earth is ……\ldots\ldots g.JEE Main/Numerical/Medium/Gravitational field
  31. 31A metal wire of uniform mass density having length LL and mass MM is bent to form a semicircular arc and a particle of mass m\mathrm{m} is placed at the centre of the arc. The gravitational force on the particle by the wire is :JEE Main/MCQ/Medium/Gravitational field
  32. 32Four identical particles of mass mm are kept at the four corners of a square. If the gravitational force exerted on one of the masses by the other masses is (22+132)Gm2L2\left(\dfrac{2\sqrt{2}+1}{32}\right)\dfrac{G{m}^{2}}{{L}^{2}}, the length of the sides of the square isJEE Main/MCQ/Medium/Gravitational field
  33. 33If the radius of earth shrinks by 22% while its mass remains same. The acceleration due to gravity on the earth's surface will approximatelyJEE Main/MCQ/Medium/Gravitational field
  34. 34The elongation of a wire on the surface of the earth is 10−4m{10}^{-4}m. The same wire of same dimensions is elongated by 6×10−5m6\times {10}^{-5}m on another planet. The acceleration due to gravity on the planet will be _____ ms−2m{s}^{-2}. (Take acceleration due to gravity on the surface of earth =10ms−2=10{ms}^{-2})JEE Main/Numerical/Medium/Gravitational field
  35. 35Inside a uniform spherical shell :
    (a) The gravitational field is zero.
    (b) The gravitational potential is zero.
    (c) The gravitational field is the same everywhere.
    (d) The gravitation potential is the same everywhere.
    (e) All the above.
    Choose the most appropriate answer from the options given below:    JEE Main/MCQ/Medium/Gravitational field
  36. 36Find the gravitational force of attraction between the ring and sphere as shown in the diagram, where the plane of the ring is perpendicular to the line joining the centres. If 8R\sqrt{8}R is the distance between the centres of a ring (of mass mm) and a sphere (mass MM) where both have equal radius RR
    JEE Main/MCQ/Medium/Gravitational field/With diagram
  37. 37Consider two solid spheres of radii R1=1m{R}_{1}=1m,R2=2m{R}_{2}=2m and masses M1{M}_{1} and M2,{M}_{2}, respectively. The gravitational field due to sphere (1)\left(1\right) and (2)\left(2\right) are shown. The value of M1M2\dfrac{{M}_{1}}{{M}_{2}} is:
    JEE Main/MCQ/Medium/Gravitational field/With diagram
  38. 38A test particle is moving in a circular orbit in the gravitational field produced by a mass density ρ(r)=Kr2.\rho \left(r\right)=\dfrac{K}{{r}^{2}}. Identify the current relation between the radius RR of the particle’s orbit and its period T:T:JEE Main/MCQ/Medium/Gravitational field
  39. 39A solid sphere of mass MM and radius aa is surrounded by a uniform concentric spherical shell of thickness 2a2a and mass 2M.2M. The gravitational field at distance 3a3a from the centre will be:JEE Main/MCQ/Medium/Gravitational field
  40. 40The mass density of a spherical body is given by ρ(r)=kr\rho \left(r\right)=\dfrac{k}{r} for r≤Rr\leq R and ρ(r)=0\rho \left(r\right)=0 for r>R,r\gt R, where rr is the distance from the center. The correct graph that describes qualitatively the acceleration, aa of a test particle as a function of rr is:JEE Main/MCQ/Medium/Gravitational field
  41. 41An astronaut of mass mm is working on a satellite orbiting the earth at a distance hh from the earth's surface. The radius of the earth is RR, while its mass is MM. The gravitational pull FG{F}_{G} on the astronaut isJEE Main/MCQ/Medium/Gravitational field
  42. 42Four particles, each of mass MM and equidistant from each other, move along a circle of radius RR under the action of their mutual gravitational attraction. The speed of each particle isJEE Main/MCQ/Medium/Gravitational field
  43. 43The change in the value of acceleration of earth towards sun, when the moon comes from the position of solar eclipse to the position on the other side of earth in line with sun is:
    (mass of the moon     =7.36×1022 kg=7.36 \times 10^{22} \mathrm{~kg}, radius of the moon's orbit =3.8×108 m=3.8 \times 10^8 \mathrm{~m} ).    JEE Main/MCQ/Medium/Gravitational field
  44. 44The gravitational field, due to the 'left over part' of a uniform sphere (from which a part as shown, has been 'removed out'), at a very far off point, P\mathrm{P}, located as shown, would be (nearly) :
    JEE Main/MCQ/Medium/Gravitational field/With diagram
  45. 45This question contains Statement −1-1 and Statement-2. Of the four choices given after the statements, choose the one that best describes the two statements.
    Statement - I:
    For a mass     MM kept at the centre of a cube of side ' aa ', the flux of gravitational field passing through its sides is 4π4 \pi GM.
    and
    Statement - II
    If the direction of a field due to a point source is radial and its dependence on the distance '     rr ' for the source is given as 1/r21 / r^2, its flux through a closed surface depends only on the strength of the source enclosed by the surface and not on the size or shape of the surface    JEE Main/MCQ/Medium/Gravitational field
  46. 46Suppose the gravitational force varies inversely as the nth power of distance. Then the time period planet in circular orbit of radius R\mathrm{R} around the sun will be proportional toJEE Main/MCQ/Medium/Gravitational field
  47. 47Two spherical bodies of mass MM and 5M&5 M \& radii R&2RR \& 2 R respectively are released in free space with initial separation between their centres equal to 12R12 \mathrm{R}. If they attract each other due to gravitational force only, then the distance covered by the smaller body just before collision isJEE Main/MCQ/Medium/Gravitational field
  48. 48If suddenly the gravitational force of attraction between Earth and a satellite revolving around it
    becomes zero, then the satellite will    JEE Main/MCQ/Medium/Gravitational field
  49. 49When one moves from a point 1616 km below the earth's surface to a point 1616 km above the earth's surface. The change in gg is approximately α\alpha %. The value of α\alpha is _____.
    (Take radius of the earth     =6400= 6400 km.)    JEE Main/MCQ/Medium/Acceleration Due to Gravity
  50. 50The height in terms of radius of the earth (R)(R), at which the acceleration due to gravity becomes g9\dfrac{g}{9}, where gg is acceleration due to gravity on earth's surface, is ______.JEE Main/MCQ/Medium/Acceleration Due to Gravity
  51. 51Assuming the earth to be a sphere of uniform mass density, a body weighed 300 N300 \mathrm{~N} on the surface of earth. How much it would weigh at R/4 depth under surface of earth ?JEE Main/MCQ/Medium/Acceleration Due to Gravity
  52. 52A simple pendulum doing small oscillations at a place R\mathrm{R} height above earth surface has time period of T1=4 sT_1=4 \mathrm{~s}. T2T_2 would be it's time period if it is brought to a point which is at a height 2R2 \mathrm{R} from earth surface. Choose the correct relation [R=[R= radius of earth ]] :JEE Main/MCQ/Medium/Acceleration Due to Gravity
  53. 53If RR is the radius of the earth and the acceleration due to gravity on the surface of earth is g=π2ms−2g={\pi }^{2}m{s}^{-2}, then the length of the second's pendulum at a height h=2Rh=2R from the surface of earth will be:JEE Main/MCQ/Medium/Acceleration Due to Gravity
  54. 54At what distance above and below the surface of the earth a body will have same weight? (Take radius of earth as RR)JEE Main/MCQ/Medium/Acceleration Due to Gravity
  55. 55The acceleration due to gravity on the surface of earth is gg. If the diameter of earth reduces to half of its original value and mass remains constant, then acceleration due to gravity on the surface of earth would be :JEE Main/MCQ/Medium/Acceleration Due to Gravity
  56. 56Two planets A and B of radii RR and 1.5R1.5R have densities ρ\rho and ρ2\dfrac{\rho }{2} respectively. The ratio of acceleration due to gravity at the surface of B to A is:JEE Main/MCQ/Medium/Acceleration Due to Gravity
  57. 57The radii of two planets AA and BB are RR and 4R4R and their densities are ρ\rho and ρ3\dfrac{\rho }{3} respectively. The ratio of acceleration due to gravity at their surfaces (gA:gB)\left({g}_{A}:{g}_{B}\right) will beJEE Main/MCQ/Medium/Acceleration Due to Gravity
  58. 58Given below are two statements:
    Statement I : Rotation of the earth shows effect on the value of acceleration due to gravity     (g)(g).
    Statement II : The effect of rotation of the earth on the value of     gg 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    JEE Main/MCQ/Medium/Acceleration Due to Gravity
  59. 59Assuming the earth to be a sphere of uniform mass density, the weight of a body at a depth d=R2d=\dfrac{R}{2} from the surface of earth, if its weight on the surface of earth is 200N200N, will be : (Given R=R= radius of earth)JEE Main/MCQ/Medium/Acceleration Due to Gravity
  60. 60The acceleration due to gravity at height hh above the earth if h≪Rh≪R (Radius of earth) is given byJEE Main/MCQ/Medium/Acceleration Due to Gravity
  61. 61The weight of a body on the earth is 400N.400N. Then weight of the body when taken to a depth half of the radius of the earth will be:JEE Main/MCQ/Medium/Acceleration Due to Gravity
  62. 62The weight of a body on the surface of the earth is 100N100N. The gravitational force on it when taken at a height, from the surface of earth, equal to one-fourth the radius of the earth is:JEE Main/MCQ/Medium/Acceleration Due to Gravity
  63. 63Given 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    JEE Main/MCQ/Medium/Acceleration Due to Gravity
  64. 64A body weight WW, is projected vertically upwards from earth's surface to reach a height above the earth which is equal to nine times the radius of earth. The weight of the body at that height will be:JEE Main/MCQ/Medium/Acceleration Due to Gravity
  65. 65Spherical insulating ball and a spherical metallic ball of same size and mass are dropped from the same height. Choose the correct statement out of the following {Assume negligible air friction}JEE Main/MCQ/Medium/Acceleration Due to Gravity
  66. 66At a certain depth dd below surface of earth, value of acceleration due to gravity becomes four times that of its value at a height 3R3R above earth surface. Where RR is Radius of earth (Take R=6400kmR=6400km). The depth dd is equal toJEE Main/MCQ/Medium/Acceleration Due to Gravity
  67. 67TT is the time period of simple pendulum on the earth's surface. Its time period becomes xTxT when taken to a height RR (equal to earth's radius) above the earth's surface. Then, the value of xx will be:JEE Main/MCQ/Medium/Acceleration Due to Gravity
  68. 68Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R
    Assertion     AA: A pendulum clock when taken to Mount Everest becomes fast.
    Reason     RR: 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    JEE Main/MCQ/Medium/Acceleration Due to Gravity
  69. 69Given 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 '    hh' and depth 'dd' from earth's surface, if h=dh=d.
    In the light of above statements, choose the most appropriate answer form the options given below    JEE Main/MCQ/Medium/Acceleration Due to Gravity
  70. 70The weight of a body at the surface of earth is 18N18N. The weight of the body at an altitude of 3200km3200km above the earth's surface is (given, radius of earth Re=6400km{R}_{e}=6400km)JEE Main/MCQ/Medium/Acceleration Due to Gravity
  71. 71If the acceleration due to gravity experienced by a point mass at a height hh above the surface of earth is same as that of the acceleration due to gravity at a depth αh(h≪Re)\alpha h\left(h≪{R}_{e}\right) ) from the earth surface. The value of α\alpha will be _____ .
    (use     Re=6400km{R}_{e}=6400km)    JEE Main/Numerical/Medium/Acceleration Due to Gravity
  72. 72Assume there are two identical simple pendulum Clocks-11 is placed on the earth and Clock-22 is placed on a space station located at a height h above the earth surface. Clock-11 and Clock-22 operate at time periods 4s4s and 6s6s respectively. Then the value of hh is -
    (consider radius of earth     RE=6400km{R}_{E}=6400km and gg on earth 10ms−210m{s}^{-2})    JEE Main/MCQ/Medium/Acceleration Due to Gravity
  73. 73The percentage decrease in the weight of a rocket, when taken to a height of 32km32km above the surface of earth will, be
    (Radius of earth     =6400km=6400km)    JEE Main/MCQ/Medium/Acceleration Due to Gravity
  74. 74An object is taken to a height above the surface of earth at a distance 54R\dfrac{5}{4}R from the centre of the earth. Where radius of earth, R=6400kmR=6400km. The percentage decrease in the weight of the object will beJEE Main/MCQ/Medium/Acceleration Due to Gravity
  75. 75The length of a seconds pendulum at a height h=2Rh=2R from earth surface will be:
    (Given:     R=R= Radius of earth and acceleration due to gravity at the surface of earth g=π2ms−2g={\pi }^{2}m{s}^{-2})    JEE Main/MCQ/Medium/Acceleration Due to Gravity
  76. 76Given 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    JEE Main/MCQ/Medium/Acceleration Due to Gravity
  77. 77The variation of acceleration due to gravity (g)\left(g\right) with distance (r)\left(r\right) from the center of the earth is correctly represented by
    (Given     R=R= radius of earth)    JEE Main/MCQ/Medium/Acceleration Due to Gravity
  78. 78The height of any point PP above the surface of earth is equal to diameter of earth. The value of acceleration due to gravity at point PP will be : (Given g=g=acceleration due to gravity at the surface of earth).JEE Main/MCQ/Medium/Acceleration Due to Gravity
  79. 79The approximate height from the surface of earth at which the weight of the body becomes 13\dfrac{1}{3} of its weight on the surface of earth is :
    [Radius of earth     R=6400kmR=6400km and 3=1.732\sqrt{3}=1.732]    JEE Main/MCQ/Medium/Acceleration Due to Gravity
  80. 80If RE{R}_{E} be the radius of Earth, then the ratio between the acceleration due to gravity at a depth rr below and a height rr above the earth surface is:
    (Given :     r<REr\lt {R}_{E})    JEE Main/MCQ/Medium/Acceleration Due to Gravity
  81. 81Consider a planet in some solar system that has a mass double the mass of earth and density equal to the average density of the earth. If the weight of an object on earth is WW, the weight of the same object on that planet will be:JEE Main/MCQ/Medium/Acceleration Due to Gravity
  82. 82In the reported figure of earth, the value of acceleration due to gravity is same at point AA and CC but it is smaller than that of its value at point BB (surface of the earth). The value of OA:ABOA:AB will be x:5x:5. The value of xx is
    JEE Main/Numerical/Medium/Acceleration Due to Gravity/With diagram
  83. 83A body weighs 49N49N on a spring balance at the north pole. What will be its weight recorded on the same weighing machine, if it is shifted to the equator?
    [Use     g=GMR2=9.8ms−2g=\dfrac{GM}{{R}^{2}}=9.8m{s}^{-2} and radius of earth, R=6400km.R=6400km.]    JEE Main/MCQ/Medium/Acceleration Due to Gravity
  84. 84The acceleration due to gravity on the earth's surface at the poles is gg and angular velocity of the earth about the axis passing through the pole is ω\omega. An object is weighed at the equator and at a height hh above the poles by using a spring balance. If the weights are found to be same, then hh is: (h≪Rh≪R, where RR is the radius of the earth)JEE Main/MCQ/Medium/Acceleration Due to Gravity
  85. 85The value of the acceleration due to gravity is g1{g}_{1} at a height h=R2h=\dfrac{R}{2} (R=R= radius of the earth) from the surface of the earth. It is again equal to g1{g}_{1} at a depth dd below the surface the earth. The ratio (dR)\left(\dfrac{d}{R}\right) equals:JEE Main/MCQ/Medium/Acceleration Due to Gravity
  86. 86The mass density of a planet of radius R varies with the distance r from its centre as ρ(r)=ρ0(1−r2R2)\rho (r)={\rho }_{0}\left(1-\dfrac{{r}^{2}}{{R}^{2}}\right) Then the gravitational field is maximum at:JEE Main/MCQ/Medium/Acceleration Due to Gravity
  87. 87The height ‘hh’ at which the weight of a body will be the same as that at the same depth ‘h’ from the surface of the earth is (Radius of the earth is RR and effect of the rotation of the earth is neglected)JEE Main/MCQ/Medium/Acceleration Due to Gravity
  88. 88A box weighs 196N196N on a spring balance at the north pole. Its weight recorded on the same balance if it is shifted to the equator is close to (Take g=10ms−2g=10{ms}^{-2} at the north pole and the radius of the earth =6400km=6400km ):JEE Main/MCQ/Medium/Acceleration Due to Gravity
  89. 89The value of acceleration due to gravity at Earth's surface is 9.8ms−29.8m{s}^{-2} . The altitude above its surface at which the acceleration due to gravity decreases to 4.9ms−24.9m{s}^{-2}, is close to: (Radius of earth =6.4×106m=6.4\times {10}^{6}m )JEE Main/MCQ/Medium/Acceleration Due to Gravity
  90. 90The mass and the diameter of a planet are three times the respective values for the Earth. The period of oscillation of a simple pendulum on the Earth is 2 s2 \mathrm{~s}. The period of oscillation of the same pendulum on the planet would be:JEE Main/MCQ/Medium/Acceleration Due to Gravity
  91. 91A heavy ball of mass MM is suspended from the ceiling of a car by a light string of mass m(m≪M).m\left(m≪M\right). When the car is at rest, the speed of transverse waves in the string is 60ms−1.60{ms}^{-1}. When the car has acceleration a,a, the wave-speed increases to 60.5ms−1.60.5{ms}^{-1}. The value of a,a, in terms of gravitational acceleration g,g, is closed toJEE Main/MCQ/Medium/Acceleration Due to Gravity
  92. 92Suppose that the angular velocity of rotation of the Earth is increased. Then, as a consequence,JEE Main/MCQ/Medium/Acceleration Due to Gravity
  93. 93Take the mean distance of the moon and the sun from the earth to be 0.4×106km0.4\times {10}^{6}km and 150×106km150\times {10}^{6}km, respectively. Their masses are 8×10228\times {10}^{22} kgkg and 2×10302\times {10}^{30} kgkg, respectively. The radius of the earth is 6400km6400km. Let ΔF1\Delta {F}_{1} be the difference in the forces exerted by the moon at the nearest and farthest point on the earth, and ΔF2\Delta {F}_{2} be the difference in the forces exerted by the sun at the nearest and farthest points on the earth. Then, the number closest to ΔF1ΔF2\dfrac{\Delta {F}_{1}}{\Delta {F}_{2}} is,JEE Main/MCQ/Medium/Acceleration Due to Gravity
  94. 94If the Earth has no rotational motion, the weight of a person on the equator is WW. Determine the speed with which the earth would have to rotate about its axis so that the person at the equator will weigh 34W\dfrac{3}{4}W. The radius of the Earth is 6400km6400km and g=10ms−2g=10m{s}^{-2}JEE Main/MCQ/Medium/Acceleration Due to Gravity
  95. 95The variation of acceleration due to gravity gg with distance dd from the centre of the earth is best represented by (RR= Earth's radius):JEE Main/MCQ/Medium/Acceleration Due to Gravity
  96. 96Assuming the earth to be a sphere of uniform density, the acceleration due to gravity inside the earth at a distance of rr from the centre is proportional toJEE Main/MCQ/Medium/Acceleration Due to Gravity
  97. 97Which graph correctly presents the variation of acceleration due to gravity with the distance from the centre of the earth (radius of the earth =RE=R_E )?JEE Main/MCQ/Medium/Acceleration Due to Gravity
  98. 98The height at which the acceleration due to gravity becomes g9\frac{\mathrm{g}}{9} (where g=\mathrm{g}= the acceleration due to gravity on the surface of the earth) in terms of RR, the radius of the earth isJEE Main/MCQ/Medium/Acceleration Due to Gravity
  99. 99The change in the value of gg at a height ' hh ' above the surface of the earth is the same as at a depth 'd' below the surface of earth. When both ' dd ' and ' hh ' are much smaller than the radius of earth, then which one of the following is correct?JEE Main/MCQ/Medium/Acceleration Due to Gravity
  100. 100Average density of the earthJEE Main/MCQ/Medium/Acceleration Due to Gravity
  101. 101Net gravitational force at the center of a square is found to be F1F_{1} when four particles having mass M,2M,3MM, 2 M, 3 M and 4M4 M are placed at the four corners of the square as shown in figure and it is F2F_{2} when the positions of 3M3 M and 4M4 M are interchanged. The ratio F1F2\frac{F_{1}}{F_{2}} is α5\frac{\alpha}{\sqrt{5}}. The value of α\alpha is ____\_\_\_\_.
    JEE Main/MCQ/Medium/Work done/With diagram
  102. 102Net gravitational force at the center of a square is found to be F1F_{1} when four particles having mass M,2M,3MM, 2 M, 3 M and 4M4 M are placed at the four corners of the square as shown in figure and it is F2F_{2} when the positions of 3M3 M and 4M4 M are interchanged. The ratio F1F2\frac{F_{1}}{F_{2}} is α5\frac{\alpha}{\sqrt{5}}. The value of α\alpha is ____\_\_\_\_.
    JEE Main/MCQ/Medium/Newton’s Law of Gravitation/With diagram
  103. 103A body of mass mm is taken from the surface of earth to a height equal to twice the radius of earth (ReR_e). The increase in potential energy will be _______.
    (    gg is acceleration due to gravity at the surface of earth)    JEE Main/MCQ/Medium/Gravitational potential and Potential Energy
  104. 104If a body of mass 11 kg falls on the earth from infinity, it attains velocity (v)(v) and kinetic energy (k)(k) on reaching the surface of earth. The values of vv and kk respectively are _______. (Take radius of earth to be 64006400 km and g=9.8g = 9.8 m/s2^2)JEE Main/MCQ/Medium/Gravitational potential and Potential Energy
  105. 105Three masses 200 kg,300 kg200 \mathrm{~kg}, 300 \mathrm{~kg} and 400 kg are placed at the vertices of an equilateral triangle with sides 20 m. They are rearranged on the vertices of a bigger triangle of side 25 m and with the same centre. The work done in this process ____\_\_\_\_ J. (Gravitational constant G=6.7×10−11 N m2/kg2\mathrm{G}=6.7 \times 10^{-11} \mathrm{~N} \mathrm{~m}^{2} / \mathrm{kg}^{2})JEE Main/MCQ/Medium/Gravitational potential and Potential Energy
  106. 106The escape velocity from a spherical planet AA is 10 km/s10 \mathrm{~km} / \mathrm{s}. The escape velocity from another planet BB whose density and radius are 10%10 \% of those of planet AA, is ____\_\_\_\_ m/s\mathrm{m} / \mathrm{s}.JEE Main/MCQ/Medium/Gravitational potential and Potential Energy
  107. 107An object is kept at rest at a distance of 3 R above the earth's surface where R is earth's radius. The minimum speed with which it must be projected so that it does not return to earth is :
    (Assume     M=\mathrm{M}= mass of earth, G=\mathrm{G}= Universal gravitational constant)    JEE Main/MCQ/Medium/Gravitational potential and Potential Energy
  108. 108Given below are two statements: one is labelled as Assertion A\mathrm{A} and the other is labelled as Reason R\mathrm{R} Assertion A : The kinetic energy needed to project a body of mass m from earth surface to infinity is 12mgR\frac{1}{2} \mathrm{mgR}, where R is the radius of earth.
    Reason     R\mathrm{R} : The maximum potential energy of a body is zero when it is projected to infinity from earth surface.
    In the light of the above statements, choose the correct answer from the option given below    JEE Main/MCQ/Medium/Gravitational potential and Potential Energy
  109. 109A satellite of mass 1000 kg is launched to revolve around the earth in an orbit at a height of 270 km from the earth's surface. Kinetic energy of the satellite in this orbit is ______ ×1010 J\times 10^{10} \mathrm{~J}.
    (Mass of earth     =6×1024 kg=6 \times 10^{24} \mathrm{~kg}, Radius of earth == 6.4×106 m6.4 \times 10^6 \mathrm{~m}, Gravitational constant ==
    6.67×10−11Nm2 kg−2)\left.6.67 \times 10^{-11} \mathrm{Nm}^2 \mathrm{~kg}^{-2}\right)    JEE Main/Numerical/Medium/Gravitational potential and Potential Energy
  110. 110Earth has mass 8 times and radius 2 times that of a planet. If the escape velocity from the earth is 11.2 km/s11.2 \mathrm{~km} / \mathrm{s}, the escape velocity in km/s\mathrm{km} / \mathrm{s} from the planet will be :JEE Main/MCQ/Medium/Gravitational potential and Potential Energy
  111. 111An astronaut takes a ball of mass mm from earth to space. He throws the ball into a circular orbit about earth at an altitude of 318.5 km318.5 \mathrm{~km}. From earth's surface to the orbit, the change in total mechanical energy of the ball is xGMem21Rex \frac{\mathrm{GM}_{\mathrm{e}} \mathrm{m}}{21 \mathrm{R}_{\mathrm{e}}}. The value of xx is (take Re=6370 km)\left.\mathrm{R}_{\mathrm{e}}=6370 \mathrm{~km}\right) :JEE Main/MCQ/Medium/Gravitational potential and Potential Energy
  112. 112To project a body of mass mm from earth's surface to infinity, the required kinetic energy is (assume, the radius of earth is RE,g=R_E, g= acceleration due to gravity on the surface of earth):JEE Main/MCQ/Medium/Gravitational potential and Potential Energy
  113. 113Match List I with List II :
    JEE Main/MCQ/Medium/Gravitational potential and Potential Energy/With diagram
  114. 114The mass of the moon is 1144\dfrac{1}{144} times the mass of a planet and its diameter 116\dfrac{1}{16} times the diameter of a planet. If the escape velocity on the planet is v, the escape velocity on the moon will be:JEE Main/MCQ/Medium/Gravitational potential and Potential Energy
  115. 115Escape velocity of a body from earth is 11.2kms−111.2km{s}^{-1}. If the radius of a planet be one-third the radius of earth and mass be one-sixth that of earth, the escape velocity from the plate is:JEE Main/MCQ/Medium/Gravitational potential and Potential Energy
  116. 116The gravitational potential at a point above the surface of earth is −5.12×107Jkg−1-5.12\times {10}^{7}J{kg}^{-1} and the acceleration due to gravity at that point is 6.4ms−26.4m{s}^{-2}. Assume that the mean radius of earth to be 6400km6400km. The height of this point above the earth's surface is:JEE Main/MCQ/Medium/Gravitational potential and Potential Energy
  117. 117Given below are two statements:
    Statement I : For a planet, if the ratio of mass of the planet to its radius increase, the escape velocity from the planet also increase.
    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    JEE Main/MCQ/Medium/Gravitational potential and Potential Energy
  118. 118A planet having mass 9Me9{M}_{e} and radius 4Re,4{R}_{e}, where Me{M}_{e} and Re{R}_{e} are mass and radius of earth respectively, has escape velocity in kms−1km{s}^{-1} given by: (Given escape velocity on earth Ve=11.2×103ms−1{V}_{e}=11.2\times {10}^{3}m{s}^{-1})JEE Main/MCQ/Medium/Gravitational potential and Potential Energy
  119. 119The ratio of escape velocity of a planet to the escape velocity of earth will be:-
    Given: Mass of the planet is     1616 times mass of earth and radius of the planet is 44 times the radius of earth.    JEE Main/MCQ/Medium/Gravitational potential and Potential Energy
  120. 120Two satellites AA and BB move round the earth in the same orbit. The mass of AA is twice the mass of BB. The quantity which is same for the two satellites will beJEE Main/MCQ/Medium/Gravitational potential and Potential Energy
  121. 121Given below are two statements:
    Statement I: If    EEbe the total energy of a satellite moving around the earth, then its potential energy will be E2\dfrac{E}{2}.
    Statement II: The kinetic energy of a satellite revolving in an orbit is equal to the half the magnitude of total energy     EE.
    In the light of the above statements, choose the most appropriate answer from the options given below.    JEE Main/MCQ/Medium/Gravitational potential and Potential Energy
  122. 122For a body projected at an angle with the horizontal from the ground, choose the correct statementJEE Main/MCQ/Medium/Gravitational potential and Potential Energy
  123. 123The escape velocities of two planets AandBAandB are in the ratio 1:21:2. If the ratio of their radii respectively is 1:31:3, then the ratio of acceleration due to gravity of planet AA to the acceleration of gravity of planet BB will be:JEE Main/MCQ/Medium/Gravitational potential and Potential Energy
  124. 124If earth has a mass nine times and radius twice to the of a planet PP. Then ve3xms−1\dfrac{{v}_{e}}{3}\sqrt{x}m{s}^{-1} will be the minimum velocity required by a rocket to pull out of gravitational force of PP, where ve is escape velocity on earth. The value of xx isJEE Main/MCQ/Medium/Gravitational potential and Potential Energy
  125. 125If the gravitational field in the space is given as (−Kr2)\left(-\dfrac{K}{{r}^{2}}\right). Taking the reference point to be at r=2cmr=2cm with gravitational potential V=10Jkg−1V=10J{kg}^{-1}. Find the gravitational potentials at r=3cmr=3cm in SI unit (Given, that K=6Jcmkg−1K=6Jcm{kg}^{-1})JEE Main/MCQ/Medium/Gravitational potential and Potential Energy
  126. 126A body of mass is taken from earth surface to the height hh equal to twice the radius of earth (Re)({R}_{e}), the increase in potential energy will be : (g=g= acceleration due to gravity on the surface of earth)JEE Main/MCQ/Medium/Gravitational potential and Potential Energy
  127. 127An object of mass 1kg1kg 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
    [If,     g=10ms−2g=10m{s}^{-2} and radius of earth =6400km=6400km]    JEE Main/MCQ/Medium/Gravitational potential and Potential Energy
  128. 128A body of mass mm is projected with velocity λve\lambda {v}_{e} in vertically upward direction from the surface of the earth into space. It is given that ve{v}_{e} is escape velocity and λ<1\lambda \lt 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 (RR : radius of earth)JEE Main/MCQ/Medium/Gravitational potential and Potential Energy
  129. 129A 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
    (Take radius of earth     =6400km=6400km and g=10ms−2g=10{ms}^{-2})    JEE Main/MCQ/Medium/Gravitational potential and Potential Energy
  130. 130The escape velocity of a body on a planet AA is 12kms−112km{s}^{-1}. The escape velocity of the body on another planet BB, whose density is four times and radius is half of the planet AA, isJEE Main/MCQ/Medium/Gravitational potential and Potential Energy
  131. 131Four spheres each of mass mm form aa square of side dd (as shown in figure). A fifth sphere of mass MM is situated at the centre of square. The total gravitational potential energy of the system is
    JEE Main/MCQ/Medium/Gravitational potential and Potential Energy/With diagram
  132. 132A mass of 50kg50kg is placed at the center of a uniform spherical shell of mass 100kg100kg and radius 50m50m. If the gravitational potential at a point, 25m25m from the center is Vkgm−1Vkg{m}^{-1}. The value of VV is:JEE Main/MCQ/Medium/Gravitational potential and Potential Energy
  133. 133A body of mass (2M)\left(2M\right) splits into four masses m,M−m,m,M−m,{m,M-m,m,M-m}, which are rearranged to form a square as shown in the figure. The ratio of Mm\dfrac{M}{m} for which, the gravitational potential energy of the system becomes maximum is x:1.x:1. The value of xx is ________.
    JEE Main/Numerical/Medium/Gravitational potential and Potential Energy/With diagram
  134. 134The minimum and maximum distances of a planet revolving around the Sun are x1{x}_{1} and x2{x}_{2}. If the minimum speed of the planet on its trajectory is v0{v}_{0}, then its maximum speed will be:JEE Main/MCQ/Medium/Gravitational potential and Potential Energy
  135. 135A 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 hh is S.S.JEE Main/MCQ/Medium/Gravitational potential and Potential Energy
  136. 136The radius in kilometer to which the present radius of earth (R=6400km)(R=6400km) to be compressed so that the escape velocity is increased 1010 time is _______.JEE Main/Numerical/Medium/Gravitational potential and Potential Energy
  137. 137If one wants to remove all the mass of the earth to infinity in order to break it up completely. The amount of energy that needs to be supplied will be x5GM2R\dfrac{x}{5}\dfrac{G{M}^{2}}{R} where xx is ________.
    (Round off to the Nearest Integer)
    (    MM is the mass of earth, RR is the radius of earth, GG is the gravitational constant)    JEE Main/Numerical/Medium/Gravitational potential and Potential Energy
  138. 138The initial velocity vi{v}_{i} required to project a body vertically upward from the surface of the earth to reach a height of 10R10R, where RR is the radius of the earth, may be described in terms of escape velocity ve{v}_{e} such that vi=xy×ve{v}_{i}=\sqrt{\dfrac{x}{y}}\times {v}_{e}. The value of xx will beJEE Main/Numerical/Medium/Gravitational potential and Potential Energy
  139. 139Given below are two statements : one is labelled as Assertion AA and the other is labelled as Reason RR.
    Assertion     AA : The escape velocities of planet AA and BB are same. But AA and BB are of unequal mass.
    Reason     RR: The product of their mass and radius must be same. M1R1=M2R2{M}_{1}{R}_{1}={M}_{2}{R}_{2} In the light of the above statements, choose the most appropriate answer from the options given below :    JEE Main/MCQ/Medium/Gravitational potential and Potential Energy
  140. 140Two planets have masses MM and 16M16M and their radii are a and 2a2a, respectively. The separation between the centres of the planets is 10a10a. A body of mass mm is fired from the surface of the larger planet towards the smaller planet along the line joining their centres. For the body to be able to reach at the surface of smaller planet, the minimum firing speed needed is :JEE Main/MCQ/Medium/Gravitational potential and Potential Energy
  141. 141On the xx-axis and at a distance xx from the origin, the gravitational field due to a mass distribution is given by Ax(x2+a2)3/2\dfrac{Ax}{{\left({x}^{2}+{a}^{2}\right)}^{3/2}} in the xx-direction. The magnitude of the gravitational potential on the xx-axis at a distance xx, taking its value to be zero at infinity is:JEE Main/MCQ/Medium/Gravitational potential and Potential Energy
  142. 142Planet AA has mass MM and radius R.R. Planet BB has half the mass and half the radius of Planet A.A. If the escape velocities from the Planets AA and BB are vA{v}_{A} and vB,{v}_{B}, respectively, then vAvB=n4.\dfrac{{v}_{A}}{{v}_{B}}=\dfrac{n}{4}. The value of nn is:JEE Main/MCQ/Medium/Gravitational potential and Potential Energy
  143. 143An asteroid is moving directly towards the centre of the earth. When at a distance of 10R10R (RR is the radius of the earth) from the centre of the earth, it has a speed of 12kms−1.12km{s}^{-1}. Neglecting the effect of earth's atmosphere, what will be the speed of the asteroid when it hits the surface of the earth (escape velocity from the earth is 11.2kms−1)11.2km{s}^{-1}) ? Give your answer to the nearest integer in kms−1km{s}^{-1}__________.JEE Main/Numerical/Medium/Gravitational potential and Potential Energy
  144. 144A rocket has to be launched from earth in such a way that it never returns. If EE is the minimum energy delivered by the rocket launcher, what should be the minimum energy that the launcher should have, if the same rocket is to be launched from the surface of the moon? Assume that the density of the earth and the moon are equal and that the earth's volume is 6464 times the volume of the moon.JEE Main/MCQ/Medium/Gravitational potential and Potential Energy
  145. 145Two stars of masses 3×1031kg3\times {10}^{31}kg each, and at distance 2×1011m2\times {10}^{11}m rotate in a plane about their common centre of mass O.O. A meteorite passes through OO moving perpendicular to the stars,s rotation plane. In order to escape from the gravitational field of this double star, the minimum speed that meteorite should have at OO is ( Take Gravitational constant G=6.67×10−11Nm2kg−2G=6.67\times {10}^{-11}N{m}^{2}{kg}^{-2})JEE Main/MCQ/Medium/Gravitational potential and Potential Energy
  146. 146The energy required to take a satellite to a height hh above the Earth surface (radius of Earth =6.4×103km=6.4\times {10}^{3}km ) is E1{E}_{1}, and the kinetic energy required for the satellite to be in a circular orbit at this height is E2.{E}_{2}. The value of hh for which E1{E}_{1} and E2{E}_{2} are equal, isJEE Main/MCQ/Medium/Gravitational potential and Potential Energy
  147. 147A body of mass mm is moving in a circular orbit of radius RR about a planet of mass MM. At some instant, it splits into two equal masses. The first mass moves in a circular orbit of radius R2\dfrac{R}{2} . And the other mass, in a circular orbit of radius 3R2.\dfrac{3R}{2}. The difference between the final and the initial total energies isJEE Main/MCQ/Medium/Gravitational potential and Potential Energy
  148. 148A body of mass mm is moving in a circular orbit of radius RR about a planet of mass MM. At some instant, it splits into two equal masses. The first mass moves in a circular orbit of radius R2\frac{R}{2}, and the other mass, in a circular orbit of radius 3R2\frac{3 R}{2}. The difference between the final and initial total energies is:JEE Main/MCQ/Medium/Gravitational potential and Potential Energy
  149. 149Which of the following most closely depicts the correct variation of the gravitation potential, V(r)V(r) with distance rr due to a large planet of radius RR and uniform mass density? (figures are not drawn to scale)JEE Main/MCQ/Medium/Gravitational potential and Potential Energy
  150. 150From a solid sphere of mass MM and radius R,R\text{,} a spherical portion of radius (R2)\left(\dfrac{R}{2}\right) is removed as shown in the figure. Taking gravitational potential V=0V=0 at r=∞,r=\infty , the potential at the centre of the cavity thus formed is (G=G=gravitational constant)
    JEE Main/MCQ/Medium/Gravitational potential and Potential Energy/With diagram
  151. 151The gravitational field in a region is given by g⃗=(5i^+12j^)Nkg−1\vec{g}=\left(5\hat{\text{i}}+12\hat{j}\right)N{kg}^{-1}. The change in the gravitational potential energy of a particle of mass 2kg2kg when it is taken from the origin to a point (7m,−3m)\left(7m,-3m\right) isJEE Main/MCQ/Medium/Gravitational potential and Potential Energy
  152. 152

    Two hypothetical planets of masses     m1\mathrm{m}_1 and m2\mathrm{m}_2 are at rest when they are infinite distance apart. Because of the gravitational force they move towards each other along the line joining their centres. What is their speed when their separation is ' dd '?
    (Speed of     m1\mathrm{m}_1 is v1\mathrm{v}_1 and that of m2\mathrm{m}_2 is v2\mathrm{v}_2 )    JEE Main/MCQ/Medium/Gravitational potential and Potential Energy/With diagram
  153. 153From a sphere of mass MM and radius R\mathrm{R}, a smaller sphere of radius R2\frac{\mathrm{R}}{2} is carved out such that the cavity made in the original sphere is between its centre and the periphery (See figure). For the configuration in the figure where the distance between the centre of the original sphere and the removed sphere is 3R, the gravitational force between the two sphere is:
    JEE Main/MCQ/Medium/Gravitational potential and Potential Energy/With diagram
  154. 154What is the minimum energy required to launch a satellite of mass m\text{m} from the surface of a planet of mass M\text{M} and radius R\text{R} in a circular orbit at an altitude of 2R\text{2R}?JEE Main/MCQ/Medium/Gravitational potential and Potential Energy
  155. 155A point particle is held on the axis of a ring of mass mm and radius rr at a distance rr from its centre CC. When released, it reaches CC under the gravitational attraction of the ring. Its speed at CC will beJEE Main/MCQ/Medium/Gravitational potential and Potential Energy
  156. 156The mass of a spaceship is 1000 kg1000 \mathrm{~kg}. It is to be launched from the earth's surface out into free space. The value of ' g\mathrm{g} ' and ' RR ' (radius of earth) are 10 m/s210 \mathrm{~m} / \mathrm{s}^2 and 6400 km6400 \mathrm{~km} respectively. The required energy for this work will be ;JEE Main/MCQ/Medium/Gravitational potential and Potential Energy
  157. 157Two bodies of masses m\mathrm{m} and 4 m4 \mathrm{~m} are placed at a distance r\mathrm{r}. The gravitational potential at a point on the line joining them where the gravitational field is zero is:JEE Main/MCQ/Medium/Gravitational potential and Potential Energy
  158. 158A planet in a distant solar system is 10 times more massive than the earth and its radius is 10 times smaller. Given that the escape velocity from the earth is 11kms−111 \mathrm{kms}^{-1}, the escape velocity from the surface of the planet would beJEE Main/MCQ/Medium/Gravitational potential and Potential Energy
  159. 159A particle of mass 10 g10 \mathrm{~g} is kept on the surface of a uniform sphere of mass 100 kg100 \mathrm{~kg} and radius 10 cm10 \mathrm{~cm}. Find the work to be done against the gravitational force between them to take the particle far away from the sphere (you may take G=6.67×10−11Nm2/kg2\mathrm{G}=6.67 \times 10^{-11} \mathrm{Nm}^2 / \mathrm{kg}^2 )JEE Main/MCQ/Medium/Gravitational potential and Potential Energy
  160. 160If g\mathrm{g} is the acceleration due to gravity on the earth's surface, the gain in the potential energy of object of mass mm raised from the surface of the earth to a height equal to the radius RR of the earth isJEE Main/MCQ/Medium/Gravitational potential and Potential Energy
  161. 161The escape velocity for a body projected vertically upwards from the surface of earth is 11 km/s11 \mathrm{~km} / \mathrm{s}. If the body is projected at an angle of 45∘45^{\circ} with the vertical, the escape velocity will beJEE Main/MCQ/Medium/Gravitational potential and Potential Energy
  162. 162The escape velocity of a body depends upon mass asJEE Main/MCQ/Medium/Gravitational potential and Potential Energy
  163. 163Energy required to move a body of mass m from an orbit of radius 2R to 3R isJEE Main/MCQ/Medium/Gravitational potential and Potential Energy
  164. 164The kinetic energy needed to project a body of mass mm from the earth surface (radius RR ) to infinity isJEE Main/MCQ/Medium/Gravitational potential and Potential Energy
  165. 165Given below are two statements:
    Statement I: A satellite is moving around earth in the orbit very close to the earth surface. The time period of revolution of satellite depends upon the density of earth.
    Statement II: The time period of revolution of the satellite is     T=2πRegT=2 \pi \sqrt{\frac{R_{e}}{g}} (for satellite very close to the earth surface), where ReR_{\mathrm{e}} radius of earth and gg acceleration due to gravity.
    In the light of the above statements, choose the correct answer from the options given below :    JEE Main/MCQ/Medium/Motion of satellite
  166. 166Initially a satellite of 100 kg is in a circular orbit of radius 1.5RE1.5 \mathrm{R}_{\mathrm{E}}. This satellite can be moved to a circular orbit of radius 3RE3 R_{E} by supplying α×106 J\alpha \times 10^{6} \mathrm{~J} of energy. The value of α\alpha is ____\_\_\_\_. (Take Radius of Earth RE=6×106 mR_{E}=6 \times 10^{6} \mathrm{~m} and g=10 m/s2\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2})JEE Main/MCQ/Medium/Motion of satellite
  167. 167A satellite is launched into a circular orbit of radius ' R ' around the earth. A second satellite is launched into an orbit of radius 1.03 R . The time period of revolution of the second satellite is larger than the first one approximately byJEE Main/MCQ/Medium/Motion of satellite
  168. 168A satellite of mass M2\frac{M}{2} is revolving around earth in a circular orbit at a height of R3\frac{R}{3} from earth surface. The angular momentum of the satellite is MGMRxM \sqrt{\frac{G M R}{x}}. The value of xx is ______ , where MM and RR are the mass and radius of earth, respectively. ( G is the gravitational constant)JEE Main/Numerical/Medium/Motion of satellite
  169. 169A satellite of 103 kg10^3 \mathrm{~kg} mass is revolving in circular orbit of radius 2R2 R. If 104R6J\frac{10^4 R}{6} J energy is supplied to the satellite, it would revolve in a new circular orbit of radius
    (use     g=10 m/s2,R=g=10 \mathrm{~m} / \mathrm{s}^2, R= radius of earth)    JEE Main/MCQ/Medium/Motion of satellite
  170. 170Two satellite AA and BB go round a planet in circular orbits having radii 4R4 R and RR respectively. If the speed of A\mathrm{A} is 3v3 v, the speed of B\mathrm{B} will be :JEE Main/MCQ/Medium/Motion of satellite
  171. 171Correct formula for height of a satellite from earths surface is:JEE Main/MCQ/Medium/Motion of satellite
  172. 172Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R).
    Assertion (A) : The angular speed of the moon in its orbit about the earth is more than the angular speed of the earth in its orbit about the sun.
    Reason (R): The moon takes less time to move around the earth than the time taken by the earth to move around the sun.
    In the light of the above statements, choose the most appropriate answer from the options given below :    JEE Main/MCQ/Medium/Motion of satellite
  173. 173A space ship of mass 2×104kg2\times {10}^{4}kg is launched into a circular orbit close to the earth surface. The additional velocity to be imparted to the space ship in the orbit to overcome the gravitational pull will be (if g=10ms−2g=10m{s}^{-2} and radius of earth =6400km=6400km ):JEE Main/MCQ/Medium/Motion of satellite
  174. 174The time period of a satellite, revolving above earth's surface at a height equal to RR will be (Given g=π2ms−2,R=g={\pi }^{2}m{s}^{-2},R= radius of earth)JEE Main/MCQ/Medium/Motion of satellite
  175. 175Two satellites of masses mm and 3m3m revolve around the earth in circular orbits of radii r&3r respectively. The ratio of orbital speeds of the satellites respectively isJEE Main/MCQ/Medium/Motion of satellite
  176. 176Given 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 statements, choose the correct answer from the options given below:    JEE Main/MCQ/Medium/Motion of satellite
  177. 177The time period of a satellite of earth is 2424 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.JEE Main/MCQ/Medium/Motion of satellite
  178. 178Every 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 :    JEE Main/MCQ/Medium/Motion of satellite
  179. 179If the distance of the earth from Sun is 1.5×106km1.5\times {10}^{6}km, then the distance of an imaginary planet from Sun, if its period of revolution is 2.832.83 years is:JEE Main/MCQ/Medium/Motion of satellite
  180. 180Two satellites AA and BB having masses in the ratio 4:34:3 are revolving in circular orbits of radii 3r3r and 4r4r respectively around the earth. The ratio of total mechanical energy of AA to BB isJEE Main/MCQ/Medium/Motion of satellite
  181. 181Two satellites S1{S}_{1} and S2{S}_{2} are revolving in circular orbits around a planet with radius RI=3200km{R}_{I}=3200km and R2=800km{R}_{2}=800km respectively. The ratio of speed of satellite S1{S}_{1} to the speed of satellite S2{S}_{2} in their respective orbits would be 1x\dfrac{1}{x} where x=x=JEE Main/Numerical/Medium/Motion of satellite
  182. 182Two identical particles of mass 1kg1kg each go round a circle of radius RR, under the action of their mutual gravitational attraction. The angular speed of each particle is:JEE Main/MCQ/Medium/Motion of satellite
  183. 183Suppose two planets (spherical in shape) of radii RR and 2R,2R, but mass MM and 9M9M respectively have a centre to centre separation 8R8R as shown in the figure. A satellite of mass mm is projected from the surface of the planet of mass MM directly towards the centre of the second planet. The minimum speed vv required for the satellite to reach the surface of the second planet is a7GMR\sqrt{\dfrac{a}{7}\dfrac{GM}{R}}, then the value of aa is
    [Given : The two planets are fixed in their position]
    JEE Main/Numerical/Medium/Motion of satellite/With diagram
  184. 184A geostationary satellite is orbiting around an arbitrary planet PP at a height of 11R11R above the surface of PP, RR being the radius of PP. The time period of another satellite in hours at a height of 2R2R from the surface of PP is ________ has the time period of 24hours.24hours.JEE Main/MCQ/Medium/Motion of satellite
  185. 185Two satellites AA and BB of masses 200kg200kg and 400kg400kg are revolving round the earth at height of 600km600km and 1600km1600km respectively. If TA{T}_{A} and TB{T}_{B} are the time periods of AA and BB respectively then the value of TB−TA{T}_{B}-{T}_{A} :
    [ Given : radius of earth     =6400km,=6400km, mass of earth =6×1024kg=6\times {10}^{24}kg ]    JEE Main/MCQ/Medium/Motion of satellite/With diagram
  186. 186Consider two satellites S1{S}_{1} and S2{S}_{2} with periods of revolution 1hr1hr and 8hr8hr respectively revolving around a planet in circular orbits. The ratio of angular velocity of satellite S1{S}_{1} to the angular velocity of satellite S2{S}_{2} is:JEE Main/MCQ/Medium/Motion of satellite
  187. 187A body is moving in a low circular orbit about a planet of mass MM and radius RR. The radius of the orbit can be taken to be RR itself. Then the ratio of the speed of this body in the orbit to the escape velocity from the planet is:JEE Main/MCQ/Medium/Motion of satellite
  188. 188A satellite is moving in a low nearly circular orbit around the earth. Its radius is roughly equal to that of the earth's radius Re.{R}_{e}. By firing rockets attached to it, its speed is instantaneously increased in the direction of its motion so that it become 32\sqrt{\dfrac{3}{2}} times larger. Due to this the farthest distance from the centre of the earth that the satellite reaches is RR. Value of RR is :JEE Main/MCQ/Medium/Motion of satellite
  189. 189A body A of mass mm is moving in a circular orbit of radius RR about a planet. Another body B of mass m2\dfrac{m}{2} collides with A with a velocity which is half (v⃗2)\left(\dfrac{\vec{v}}{2}\right) the instantaneous velocity v⃗\vec{v} of A. The collision is completely inelastic. Then, the combined body:JEE Main/MCQ/Medium/Motion of satellite
  190. 190A spaceship orbits around a planet at a height of 20km20km from its surface. Assuming that only gravitational field of the planet acts on the spaceship, what will be the number of complete revolutions made by the spaceship in 2424 hours around the planet?
    [Given: Mass of planet     =8×1022kg=8\times {10}^{22}kg ,
    Radius of planet     =2×106m,=2\times {10}^{6}m,
    Gravitational constant     G=6.67×10−11Nm2/kg2G=6.67\times {10}^{-11}N{m}^{2}/k{g}^{2} ]    JEE Main/MCQ/Medium/Motion of satellite
  191. 191Two satellites, AA and BB, have masses mm and 2m2m respectively. AA is in a circular orbit of radius RR and BB is in a circular orbit of radius 2R2R around the earth. The ratio of their kinetic energies, KAKB\dfrac{{K}_{A}}{{K}_{B}} is:JEE Main/MCQ/Medium/Motion of satellite
  192. 192A satellite of mass MM is in a circular orbit of radius RR about the center of the earth. A meteorite of the same mass, falling towards the earth, collides with the satellite completely inelastic. The speeds of the satellite and the meteorite are the same, just before the collision. The subsequent motion of the combined body will be:JEE Main/MCQ/Medium/Motion of satellite
  193. 193A satellite is revolving in a circular orbit at a height h from the carth surface, such that h<<R\mathrm{h}\lt \lt \mathrm{R} where R\mathrm{R} is the radius of the earth. Assuming that the effect of earth"s atmosphere can be neglected the minimum increase in the speed required so that the satellite could escape from the gravitational field of earth isJEE Main/MCQ/Medium/Motion of satellite
  194. 194A satellite is moving with a constant speed vv in circular orbit around the earth. An object of mass 'm' is ejected from the satellite such that it just escapes from the gravitational pull of the earth. At the time of ejection, the kinetic energy of the object is:JEE Main/MCQ/Medium/Motion of satellite
  195. 195A satellite is revolving in a circular orbit at a height hh from the earth's surface (radius of earth RR; h\lt\ltR\text{h}\text{\lt \lt }\text{R} ). The minimum increase in its orbital velocity required, so that the satellite could escape from the earth's gravitational field, is close to (Neglect the effect of atmosphere.)JEE Main/MCQ/Medium/Motion of satellite
  196. 196The time period of an earth satellite in circular orbit is independent ofJEE Main/MCQ/Medium/Motion of satellite
  197. 197A satellite of mass mm revolves around the earth of radius RR at a height xx from its surface. If gg is the acceleration due to gravity on the surface of the earth, the orbital speed of the satellite isJEE Main/MCQ/Medium/Motion of satellite
  198. 198The time period of a satellite of earth is 5 hours. If the separation between the earth and the satellite is increased to 4 times the previous value, the new time period will becomeJEE Main/MCQ/Medium/Motion of satellite
  199. 199A planet (P1)(P_1) is moving around the star of mass 2M2M in the orbit of radius RR. Another planet (P2)(P_2) is moving around another star of mass 4M4M in a orbit of radius 2R2R. Ratio of time periods of revolution of P2P_2 and P1P_1 is _______.JEE Main/MCQ/Medium/Kepler laws
  200. 200Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
    Assertion (A) : The radius vector from the Sun to a planet sweeps out equal areas in equal intervals of time and thus areal velocity of planet is constant.
    Reason (R) : For a central force field the angular momentum is a constant.
    In the light of the above statements, choose the most appropriate answer from the options given below :    JEE Main/MCQ/Medium/Kepler laws
  201. 201Two planets, AA and BB are orbiting a common star in circular orbits of radii RAR_A and RBR_B, respectively, with RB=2RAR_B=2 R_A. The planet BB is 424 \sqrt{2} times more massive than planet AA. The ratio (LBLA)\left(\frac{L_B}{L_A}\right) of angular momentum (LB)\left(L_B\right) of planet BB to that of planet A(LA)A\left(L_A\right) is closest to integer ________.JEE Main/Numerical/Medium/Kepler laws
  202. 202If a satellite orbiting the Earth is 9 times closer to the Earth than the Moon, what is the time period of rotation of the satellite? Given rotational time period of Moon =27=27 days and gravitational attraction between the satellite and the moon is neglected.JEE Main/MCQ/Medium/Kepler laws
  203. 203Two planets AA and BB having masses m1m_1 and m2m_2 move around the sun in circular orbits of r1r_1 and r2r_2 radii respectively. If angular momentum of AA is LL and that of BB is 3 L3 \mathrm{~L}, the ratio of time period (TATB)\left(\frac{T_A}{T_B}\right) is:JEE Main/MCQ/Medium/Kepler laws
  204. 204A satellite revolving around a planet in stationary orbit has time period 6 hours. The mass of planet is one-fourth the mass of earth. The radius orbit of planet is :
    (\left(\right. Given == Radius of geo-stationary orbit for earth is 4.2×104 km4.2 \times 10^4 \mathrm{~km} )    JEE Main/MCQ/Medium/Kepler laws
  205. 205A light planet is revolving around a massive star in a circular orbit of radius RR with a period of revolution T.T. If the force of attraction between planet and star is proportional to R−3/2{R}^{-3/2} then choose the correct option :JEE Main/MCQ/Medium/Kepler laws
  206. 206A planet takes 200200 days to complete one revolution around the Sun. If the distance of the planet from Sun is reduced to one fourth of the original distance, how many days will it take to complete one revolution?JEE Main/MCQ/Medium/Kepler laws
  207. 207If the earth suddenly shrinks to 164th\dfrac{1}{64}th of its original volume with its mass remaining the same, the period of rotation of earth becomes 24xh\dfrac{24}{x}h. The value of xx is ________JEE Main/Numerical/Medium/Kepler laws
  208. 208The orbital angular momentum of a satellite is LL, when it is revolving in a circular orbit at height hh 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 beJEE Main/MCQ/Medium/Kepler laws
  209. 209Choose the incorrect statement from the following:JEE Main/MCQ/Medium/Kepler laws
  210. 210The time period of a satellite revolving around earth in a given orbit is 77 hours. If the radius of orbit is increased to three times its previous value, then approximate new time period of the satellite will beJEE Main/MCQ/Medium/Kepler laws
  211. 211Two planets AA and BB of equal mass are having their period of revolutions TA{T}_{A} and TB{T}_{B} such that TA=2TB{T}_{A}=2{T}_{B}. These planets are revolving in the circular orbits of radii rA{r}_{A} and rB{r}_{B} respectively. Which out of the following would be the correct relationship of their orbits?JEE Main/MCQ/Medium/Kepler laws
  212. 212The distance between Sun and Earth is RR. The duration of year if the distance between Sun and Earth becomes 3R3R will be :JEE Main/MCQ/Medium/Kepler laws
  213. 213When a body slides down from rest along a smooth inclined plane making an angle of 30∘30^{\circ} with the horizontal, it takes time T.T. When the same body slides down from the rest along a rough inclined plane making the same angle and through the same distance, it takes time αT,\alpha T, where α\alpha is a constant greater than 1.1. The co-efficient of friction between the body and the rough plane is 1x(α2−1α2)\dfrac{1}{\sqrt{x}}\left(\dfrac{{\alpha }^{2}-1}{{\alpha }^{2}}\right) where x=__________.JEE Main/Numerical/Medium/Kepler laws
  214. 214A satellite is launched into a circular orbit of radius RR around earth, while a second satellite is launched into a circular orbit of radius 1.02R.1.02R. The percentage difference in the time periods of the two satellites is:JEE Main/MCQ/Medium/Kepler laws
  215. 215The angular momentum of a planet of mass MM moving around the sun in an elliptical orbit is L⃗\vec{L}. The magnitude of the areal velocity of the planet is :JEE Main/MCQ/Medium/Kepler laws
  216. 216The time period of a satellite in a circular orbit of the radius RR is T.T. The period of another satellite in a circular orbit of the radius 9R9R is:JEE Main/MCQ/Medium/Kepler laws
  217. 217A planet revolving in elliptical orbit has :
    A. a constant velocity of revolution.
    B. has the least velocity when it is nearest to the sun.
    C. its areal velocity is directly proportional to its velocity.
    D. areal velocity is inversely proportional to its velocity.
    E. to follow a trajectory such that the areal velocity is constant.
    Choose the correct answer from the options given below:    JEE Main/MCQ/Medium/Kepler laws
  218. 218A satellite is in an elliptical orbit around a planet P.P. It is observed that the velocity of the satellite when it is farthest from the planet is 6 times less than that when it is closest to the planet. The ratio of distances between the satellite and the planet at closest and farthest points is :JEE Main/MCQ/Medium/Kepler laws
  219. 219If the angular momentum of a planet of mass m,m, moving around the Sun in a circular orbit is L,L, about the center of the Sun, its areal velocity is:JEE Main/MCQ/Medium/Kepler laws
  220. 220The relative uncertainty in the period of a satellite orbiting around the earth is 10−2{10}^{-2} . If the relative uncertainty in the radius of the orbit is negligible, the relative uncertainty in the mass of the earth is:JEE Main/MCQ/Medium/Kepler laws
  221. 221The figure shows an elliptical path ABCDABCD of a planet around the sun SS such that the area of triangle CSACSA is 14\dfrac{1}{4} the area of the ellipse. (see figure) with DBDB as the major axis, and CACA as the minor axis. If t1{t}_{1} is the time taken for the planet to go over path ABCABC and t2{t}_{2} for path taken over CDACDA then:

    JEE Main/MCQ/Medium/Kepler laws/With diagram
  222. 222A very long (length LL) cylindrical galaxy is made of uniformly distributed mass and has radius R(R<<L)R(R\lt \lt L). A star outside the galaxy is orbiting the galaxy in a plane perpendicular to the galaxy and passing through its centre. If the time period of the star is TT and its distance from the galaxy's axis is rr, thenJEE Main/MCQ/Medium/Kepler laws
  223. 223India's Mangalyan was sent to the Mars by launching it into a transfer orbit EOM around the sun. It leaves the earth at EE and meets Mars at MM. If the semi-major axis of Earth's orbit is ae=1.5×1011m{\text{a}}_{\text{e}}=\text{1.5}\times 1{0}^{11}\text{m} , that of Mar's orbit am=2.28×1011m{\text{a}}_{\text{m}}=\text{2.28}\times 1{0}^{11}\text{m}, taking Kepler's laws, give the estimate of time for Mangalyan to reach Mars from Earth.
    JEE Main/MCQ/Medium/Kepler laws/With diagram

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