Gravitation · Question 37

A particle of mass 'm' is kept at rest at a height 3R from the surface of earth, where 'R' is radius of earth and 'M' is mass of earth. The minimum speed with which it should be projected, so that it does not return back, is (g is acceleration due to gravity on the surface of earth)

1. ( GM2R )1/2
2. ( gR4 )1/2
3. ( 2gR )1/2
4. ( GMR )1/2

If ve is escape velocity and vo is orbital velocity of a satellite for orbit close to the earth's surface, then these are related by

1. vo = 2ve
2. vo = ve
3. ve = 2vo
4. ve = 2 vo

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 )