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Gravitation · Question 40

AIPMT 2012 (Mains)MCQEasy📈 Topic in 38% papers+4−1
1

Which one of the following plots represents the variation of gravitational field on a particle with distance r due to a thin spherical shell of radius R? (r is measured from the centre of the spherical shell)

  1. [figure]
  2. [figure]
  3. [figure]
  4. [figure]

Answer

(2) [figure]

Solution

Inside a thin spherical shell (r < R): gravitational field F = 0.

Outside (r R): the shell behaves as a point mass at its centre F = GMr2

So F is zero up to R, jumps to GMR2 at the surface and then falls as 1r2.

Answer: (2)

AIPMT 2012 (Mains)

Keep practising — Gravitation

2

The height at which the weight of a body becomes ( 116 )th of its weight on the surface of earth (radius R), is

  1. 5R
  2. 15R
  3. 3R
  4. 4R
AIPMT 2012 (Prelims)
3

A spherical planet has a mass MP and diameter DP. A particle of mass m falling freely near the surface of this planet will experience an acceleration due to gravity, equal to

  1. 4GMPDP2
  2. GMP mDP2
  3. GMPDP2
  4. 4GMP mDP2
AIPMT 2012 (Prelims)
4

A geostationary satellite is orbiting the earth at a height of 5R above the surface of the earth, R being the radius of the earth. The time period of another satellite in hours at a height of 2R from the surface of the earth is

  1. 5
  2. 10
  3. 6 2
  4. 6 2
AIPMT 2012 (Prelims)
5

A particle of mass m is thrown upwards from the surface of the earth, with a velocity u. The mass and the radius of the earth are, respectively, M and R. G is gravitational constant and g is acceleration due to gravity on the surface of the earth. The minimum value of u so that the particle does not return back to earth, is

  1. 2GMR2
  2. 2GMR
  3. 2gMR2
  4. 2gR2
AIPMT 2011 (Mains)
6

A particle of mass M is situated at the centre of a spherical shell of same mass and radius a. The magnitude of the gravitational potential at a point situated at a2 distance from the centre, will be :

  1. GMa
  2. 2GMa
  3. 3GMa
  4. 4GMa
AIPMT 2011 (Mains)
7

A planet moving along an elliptical orbit is closest to the sun at a distance r1 and farthest away at a distance of r2. If v1 and v2 are the linear velocities at these points respectively, then the ratio v1v2 is

  1. (r1/r2)2
  2. r2/r1
  3. (r2/r1)2
  4. r1/r2
AIPMT 2011 (Prelims)
8

The additional kinetic energy to be provided to a satellite of mass m revolving around a planet of mass M, to transfer it from a circular orbit of radius R1 to another of radius R2 (R2 > R1) is

  1. GmM ( 1R12- 1R22 )
  2. GmM ( 1R1- 1R2 )
  3. 2GmM ( 1R1- 1R2 )
  4. 12GmM ( 1R1- 1R2 )
AIPMT 2010 (Mains)
9

The dependence of acceleration due to gravity g on the distance r from the centre of the earth, assumed to be a sphere of radius R of uniform density is as shown in figures below [figure] The correct figure is

  1. (4)
  2. (1)
  3. (2)
  4. (3)
AIPMT 2010 (Mains)
10

A particle of mass M is situated at the centre of a spherical shell of same mass and radius a. The magnitude of the gravitational potential at a point situated at a/2 distance from the centre, will be :

  1. GMa
  2. 2GMa
  3. 3GMa
  4. 4GMa
AIPMT 2010 (Prelims)
11

The radii of circular orbits of two satellites A and B of the earth, are 4R and R, respectively. If the speed of satellite A is 3V, then the speed of satellite B will be

  1. 3V4
  2. 6V
  3. 12V
  4. 3V2
AIPMT 2010 (Prelims)

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