A satellite is moving very close to a planet of density \(\rho.\) The time period of the satellite is:
1. \(\sqrt{\frac{3 \pi}{ρG}}\)
2. \(\left(\frac{3 \pi}{ρG}\right)^{3 / 2}\)
3. \(\sqrt{\frac{3 \pi}{2 ρG}}\)
4. \(\left(\frac{3 \pi}{2 ρG}\right)^{3 / 2}\)

Magnitude of potential energy (\(U\)) and time period \((T)\) of a satellite are related to each other as:
1. \(T^2\propto \frac{1}{U^{3}}\)
2. \(T\propto \frac{1}{U^{3}}\)
3. \(T^2\propto U^3\)
4. \(T^2\propto \frac{1}{U^{2}}\)

The time period of a simple pendulum on a freely moving artificial satellite is

1. Zero                           

2. 2 sec

3.  3 sec                          

4.  Infinite

Reason of weightlessness in a satellite is:

1. Zero gravity

2. Centre of mass

3. Zero reaction force by satellite surface

4. None

If r represents the radius of the orbit of a satellite of mass m moving around a planet of

mass M, the velocity of the satellite is given by: 

1. $v^2=g\frac{M}{r}$                     

2. $v^2=\frac{GMm}{r}$

3. $v=\frac{GM}{r}$                        

4. $v^2=\frac{GM}{r}$