Gravitation

Dependence of intensity of gravitational field (E) of earth with distance (r) from centre of earth is correctly represented by

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

Infinite number of bodies, each of mass 2 kg are situated on x-axis at distance 1 m, 2 m, 4 m, 8 m, . . . , respectively, from the origin. The resulting gravitational potential due to this system at the origin will be

1. - 43 G
2. - 4G
3. - G
4. - 83 G

A body of mass 'm' is taken from the earth's surface to the height equal to twice the radius (R) of the earth. The change in potential energy of body will be

1. 3mgR
2. 13mgR
3. mg2R
4. 23mgR

The radius of a planet is twice the radius of earth. Both have almost equal average mass densities. VP and VE are escape velocities of the planet and the earth, respectively, then

1. VP = 1.5 VE
2. VP = 2 VE
3. VE = 3 VP
4. VE = 1.5 VP

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