The universal gravitational constant is dimensionally represented as:

1. ${\mathrm{ML}}^2{\mathrm{T}}^{-1}$

2. ${\mathrm{M}}^{-2}{\mathrm{L}}^3{\mathrm{T}}^{-2}$

3. ${\mathrm{M}}^{-2}{\mathrm{L}}^2{\mathrm{T}}^{-1}$

4. ${\mathrm{M}}^{-1}{\mathrm{L}}^3{\mathrm{T}}^{-2}$

Rohini satellite is at a height of 500 km and Insat-B is at a height of 3600 km from the surface of the earth. The relation between their orbital velocity (\(v_R,~v_i\)) is:

1. \(v_R>v_i\)

2. \(v_R<v_i\)

3. \(v_R=v_i\)

4. No relation 

For moon, its mass is 1/81 of Earth's mass and its diameter is 1/3.7 of Earth's diameter. If acceleration due to gravity at Earth's surface is 9.8 m/$s^2$, then at the moon, its value is: 

The acceleration due to gravity on 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 a jump by the same person on planet B?

Two spheres of masses \(m\) and \(M\) are situated in air and the gravitational force between them is \(F.\) If the space around the masses is filled with a liquid of specific density \(3,\) the gravitational force will become:
1. \(3F\)
2. \(F\)
3. \(F/3\)
4. \(F/9\)

The density of a newly discovered planet is twice that of the 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:

For a planet having mass equal to the mass of the earth but radius equal to one-fourth of the radius of the earth, its escape velocity will be:

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

A satellite is revolving in a circular orbit at a height \(h\) from the earth's surface (radius of earth \(R\); \(h<<R\)). The minimum increase in its orbital velocity required, so that the satellite could escape from the earth's gravitational field is close to: (Neglect the effect of the atmosphere.)
1. \(\sqrt{2gR}\)
2. \(\sqrt{gR}\)
3. \(\sqrt{\frac{gR}{2}}\)
4. \(\sqrt{gR}\left(\sqrt{2}-1\right)\)

The initial velocity \(v_i\) required to project a body vertically upwards from the surface of the earth to just reach a height of \(10R\), where \(R\) is the radius of the earth, described in terms of escape velocity \(v_e\) is:
1. \(\sqrt{\frac{10}{11}}v_e\)
2. \(\sqrt{\frac{11}{10}}v_e\)
3. \(\sqrt{\frac{20}{11}}v_e\)
4. \(\sqrt{\frac{11}{20}}v_e\)