JEE Questions for Physics Gravitation Quiz 16 - MCQExams.com

A solid sphere of uniform density and radius 4 units is located with its centre at the origin O. Two spheres of equal radii 1 unit with their centres at A (–2, 0,and B (2, 0,respectively are taken out of the solid leaving behind cavities as shown in fig. Then
Physics-Gravitation-75120.png
  • the gravitational field due to this object at the origin is zero.
  • the gravitational potential is the same at all points on the circle, y2 + z2 = 36.
  • the gravitational potential is the same at all points on the circle y2 + z2 = 4.
  • all of these are true.
The spherical hole of radius R/2 is made in a solid sphere of radius R. The mass of the sphere before hollowing was M. The gravitational field at the centre O1 of the hole due to the remaining mass is
Physics-Gravitation-75121.png
  • zero
  • 2)
    Physics-Gravitation-75122.png

  • Physics-Gravitation-75123.png

  • Physics-Gravitation-75124.png
A point P lies on the axis of a ring of mass M and radius r, at a distance r from its centre O. A small particle starts from P and reaches O under gravitational attraction only. Its speed at O will be
Physics-Gravitation-75126.png
  • zero
  • 2)
    Physics-Gravitation-75127.png

  • Physics-Gravitation-75128.png

  • Physics-Gravitation-75129.png
The masses and radii of the earth and moon are M1, R1 and M2, R2 respectively. Their centres are distance d apart. The minimum velocity with which a particle of mass m should be projected from a point midway between their centres so that it escapes to infinity is

  • Physics-Gravitation-75131.png
  • 2)
    Physics-Gravitation-75132.png

  • Physics-Gravitation-75133.png

  • Physics-Gravitation-75134.png
The escape velocity of an object from the earth depends upon the mass Of the earth (M), its mean density (ρ), its radius (R) and the gravitational constant (G). Thus, the formula for escape velocity is

  • Physics-Gravitation-75136.png
  • 2)
    Physics-Gravitation-75137.png

  • Physics-Gravitation-75138.png

  • Physics-Gravitation-75139.png
Choose the correct statement from the following : The radius of the orbit of a geostationary satellite depends upon
  • Mass of the satellite, its time period and the gravitational constant
  • Mass of the satellite, mass of the earth and the gravitational constant
  • Mass of the earth, mass of the satellite, time period of the satellite and the gravitational constant
  • Mass of the earth, time period of the satellite and the gravitational constant
In the following four periods
(i) Time of revolution of a satellite just above the earth\'s surface (Tst)
(ii) Period of oscillation of mass inside the tunnel bored along the diameter of the earth (Tma)
(iii) Period of simple pendulum having a length equal to the earth\'s radius in a uniform field of 9.8 N/kg (Tsp)
(W) Period of an infinite length simple pendulum in the earth\'s real gravitational field (Tis)
  • Tst > Tma
  • Tma > Tst
  • Tsp > Tis
  • Tst = Tma = Tsp = Tis
Three identical bodies of mass M are located at the vertices of an equilateral triangle of side L. They revolve under the effect of mutual gravitational force in a circular orbit, circumscribing the triangle while preserving the equilateral triangle. Their orbital velocity is

  • Physics-Gravitation-75142.png
  • 2)
    Physics-Gravitation-75143.png

  • Physics-Gravitation-75144.png

  • Physics-Gravitation-75145.png

  • Physics-Gravitation-75146.png
The earth E moves in an elliptical orbit with the sun S at one of the foci as shown in figure. Its speed of motion will be maximum at the point
Physics-Gravitation-75148.png
  • C
  • A
  • B
  • D
A planet is revolving around the sun as shown in elliptical path
The correct option is
Physics-Gravitation-75149.png
  • The time taken in travelling DAB is less than that for BCD
  • The time taken in travelling DAB is greater than that for BCD
  • The time taken in travelling CDA is less than that for ABC
  • The time taken in travelling CDA is greater than that for ABC
A thin uniform annular disc (see figure) of mass M has outer radius 4R and inner radius 3R. The work required to take a unit mass from point P on its axis to infinity is
Physics-Gravitation-75150.png

  • Physics-Gravitation-75151.png
  • 2)
    Physics-Gravitation-75152.png

  • Physics-Gravitation-75153.png

  • Physics-Gravitation-75154.png
A satellite S is moving in an elliptical orbit around the earth. The mass of the satellite is very small compared to the mass of earth
  • The acceleration of S is always directed towards the centre of the earth
  • The angular momentum of S about the centre of the earth changes in direction but its magnitude remains constant
  • The total mechanical energy of S varies periodically with time
  • The linear momentum of S remains constant in magnitude
A rocket of mass M is launched vertically from the surface of the earth with an initial speed V. Assuming the radius of the earth to be R and negligible air resistance, the maximum height attained by the rocket above the surface of the earth is

  • Physics-Gravitation-75156.png
  • 2)
    Physics-Gravitation-75157.png

  • Physics-Gravitation-75158.png

  • Physics-Gravitation-75159.png
A sphere of mass M and radius R2 has a concentric cavity of radius R1 as shown in figure. The force F exerted by the sphere on a particle of mass m located at a distance r from the centre of sphere varies as (0 ≤ r ≤ ∞)
Physics-Gravitation-75161.png

  • Physics-Gravitation-75162.png
  • 2)
    Physics-Gravitation-75163.png

  • Physics-Gravitation-75164.png

  • Physics-Gravitation-75165.png
The correct graph representing the variation of total energy (E) kinetic energy (K) and potential energy (U) of a satellite with its distance from the centre of earth is

  • Physics-Gravitation-75167.png
  • 2)
    Physics-Gravitation-75168.png

  • Physics-Gravitation-75169.png

  • Physics-Gravitation-75170.png

Physics-Gravitation-75172.png

  • Physics-Gravitation-75173.png
  • 2)
    Physics-Gravitation-75174.png

  • Physics-Gravitation-75175.png

  • Physics-Gravitation-75176.png
The magnitudes of the gravitational force at distances r1 and r2 from the centre of a uniform sphere of radius R and mass M are F1 and F2 respectively. Then

  • Physics-Gravitation-75178.png
  • 2)
    Physics-Gravitation-75179.png

  • Physics-Gravitation-75180.png

  • Physics-Gravitation-75181.png
  • Both (and (2)
A solid sphere of uniform density and radius 4 units is located with its centre at the origin O of coordinates. Two spheres Of equal radii 1 unit with their centres at A(- 2, 0,and B(2, 0,respectively are taken out of the solid leaving behind spherical cavities as shown in figure
Physics-Gravitation-75183.png
  • The gravitational force due to this object at the origin is zero
  • The gravitational force at the point B (2, 0,is zero
  • The gravitational potential is the same at all points of the circle y2 + z2 = 36
  • The gravitational potential is the same at all points of the circle y2 + z2 = 4
  • All (1), (and (4)
Two spherical planets P and Q have the same uniform density ρ , masses MP and MQ , and surface areas A and 4A, respectively. A spherical planet R also has uniform density ρ and its mass is (MP + MQ ). The escape velocities from the planets P, Q and R, are VP , VQ and VR respectively. Then,
  • VQ > VR > VP
  • VR > VQ > VP
  • VR / VP = 3
  • VP /VQ = 1/2
  • Both 2 and 4
Statement I An astronaut in an orbiting space station above the Earth experiences weightlessness.
Statement II An object moving around the Earth under the influence of earth\'s gravitational force is in a State of \'free-fall\'.
  • Statement I is true, statement II is true ; statement II is a correct explanation for statement I
  • Statement I is true, statement II is true ; statement II is not a correct explanation for statement I
  • Statement I is true, statement II is false
  • Statement I is false, statement II is true
Statement I For a mass M kept at the centre of a cube of side \'a\' ,the flux of gravitational field passing through its sides is 4 π GM.
Statement II If the direction of a field due to a point source is radial and its dependence on the distance \' r\' from the source is given as 1/r2 , 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.
  • Statement I is true, statement II is true ; statement II is a correct explanation for statement I
  • Statement I is true, statement II is true ; statement II is not a correct explanation for statement I
  • Statement I is true, statement II is false
  • Statement I is false, statement II is true
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