When a body of weight 72 N moves from the surface of the Earth at a height half of the radius of the earth, then the gravitational force exerted on it will be:

1. 36 N

2. 32 N

3. 144 N

4. 50 N

For a satellite moving in an orbit around the earth, the ratio of kinetic energy to potential energy is:
1. $\frac{1}{\sqrt{2}}$
2. \(2\)
3. $\sqrt{2}$
4. $\frac{1}{2}$

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:

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:

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:

If the radius of the earth shrinks by 1%, then for acceleration due to gravity, there would be:
1.  No change at the poles
2.  No change at the equator
3.  Maximum change at the equator
4.  Equal change at all locations

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: 

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

1. $\frac{\mathrm{mgR}}{4}$

2. $\frac{2}{3}\mathrm{mgR}$

3. $\frac{3}{4}\mathrm{mgR}$

4. $\frac{\mathrm{mgR}}{2}$

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

1.  ${\left(\frac{GM}{R}\right)}^{1/2}$

2. ${\left(\frac{8GM}{R}\right)}^{1/2}$

3.  ${\left(\frac{2GM}{R}\right)}^{1/2}$

4.  ${\left(\frac{4GM}{R}\right)}^{1/2}$