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 specific relation 

For moon, its mass is \(\frac{1}{81}\) of Earth's mass and its diameter is \(\frac{1}{3.7}\) of Earth's diameter. If acceleration due to gravity at Earth's surface is \(9.8~\text{m/s}^2,\) then at the moon, its value is: 

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

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

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. $\frac{\mathrm{mgR}}{2}$

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 Earth. If the acceleration due to gravity on its surface is the same as that on Earth, and the radius of Earth is \(R,\) what will be the radius of the new planet?
1. \(4R\)
2. \(\dfrac{1}{4}R\)
3. \(\dfrac{1}{2}R\)
4. \(2R\)