Gravitation

The figure shows elliptical orbit of a planet m about the sun S. The shaded area SCD is twice the shaded area SAB. If t1 is the time for the planet to move from C to D and t2 is the time to move from A to B then [figure]

1. t1 = 4t2
2. t1 = 2t2
3. t1 = t2
4. t1 > t2

Two satellites of earth, S1 and S2 are moving in the same orbit. The mass of S1 is four times the mass of S2. Which one of the following statements is true?

1. The potential energies of earth and satellite in the two cases are equal.
2. S1 and S2 are moving with the same speed.
3. The kinetic energies of the two satellites are equal.
4. The time period of S1 is four times that of S2.

The earth is assumed to be a sphere of radius R. A platform is arranged at a height R from the surface of the earth. The escape velocity of a body from this platform is fv, where v is its escape velocity from the surface of the Earth. The value of f is

1. 1/2
2. 2
3. 1/ 2
4. 1/3

Imagine a new planet having the same density as that of earth but it is 3 times bigger than the earth in size. If the acceleration due to gravity on the surface of earth is g and that on the surface of the new planet is g', then

1. g' = g/9
2. g' = 27g
3. g' = 9g
4. g' = 3g

For a satellite moving in an orbit around the earth, the ratio of kinetic energy to potential energy is

1. 1/2
2. 1/ 2
3. 2
4. 2

The density of a newly discovered planet is twice that of earth. The acceleration due to gravity at the surface of the planet is equal to that at the surface of the earth. If the radius of the earth is R, the radius of the planet would be

1. 2R
2. 4R
3. 14R
4. 12R

Two spheres of masses m and M are situated in air and the gravitational force between them is F. The space around the masses is now filled with a liquid of specific gravity 3. The gravitational force will now be

1. 3F
2. F
3. F/3
4. F/9

The acceleration due to gravity on the planet A is 9 times the acceleration due to gravity on planet B. A man jumps to a height of 2 m on the surface of A. What is the height of jump by the same person on the planet B?

1. (2/9) m
2. 18 m
3. 6 m
4. (2/3) m

A body of mass m is placed on earth's surface which is taken from earth surface to a height of h = 3R, then change in gravitational potential energy is

1. mgR4
2. 23mgR
3. 34mgR
4. mgR2

With what velocity should a particle be projected so that its height becomes equal to radius of earth?

1. ( GMR )1/2
2. ( 8GMR )1/2
3. ( 2GMR )1/2
4. ( 4GMR )1/2