What is the depth at which the value of acceleration due to gravity becomes \(\dfrac{1}{{n}}\) times it's value at the surface of the earth? (radius of the earth = \(\mathrm{R}\))  

1.	\(\dfrac R {n^2}\)	2.	\(\dfrac {R~(n-1)} n\)
3.	\(\dfrac {Rn} { (n-1)}\)	4.	\(\dfrac R n\)

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: 

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. \(F/9\)

A planet moves around the sun. At a point \(P,\) it is closest to the sun at a distance \(d_1\) and has speed \(v_1.\) At another point \(Q,\) when it is farthest from the sun at distance \(d_2,\) its speed will be:

Two satellites \(S_1\)​ and \(S_2\)​ move in the same direction in coplanar, concentric circular orbits of radii \(R_1\)​ and \(R_2.\) Their orbital periods are \(1~\text{hr}\) and \(8~\text{hr}\) respectively. If \(R_1=10^4~\text{km},\) what is their relative speed when they are closest to each other?