Gravitation

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]

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

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

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

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

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

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

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 )

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)

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