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. \(T^2\propto \frac{1}{U^{2}}\)

Weightlessness experienced while orbiting the earth in a space-ship is the result of:

1. Inertia                        
2. Acceleration
3. Zero gravity
4. Freefall towards the earth

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

1. Zero                           

2. 2 sec

3.  3 sec                          

4.  Infinite

The centripetal force acting on a satellite orbiting round the earth and the gravitational

force of earth acting on the satellite both equal F. The net force on the satellite is

1. Zero                                  

2. F

3. $F\sqrt{2}$                                 

4. 2 F

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. $v^2=\frac{GM}{r}$

A satellite which is geostationary in a particular orbit is taken to another orbit. Its

distance from the centre of earth in new orbit is 2 times that of the earlier orbit. The time

period in the second orbit is:

1. 4.8 hours                         

2. $48\sqrt{2}$ hours

3. 24 hours                           

4. $24\sqrt{2}$ hours

An astronaut orbiting the earth in a circular orbit 120 km above the surface of earth, gently drops a spoon out of space-ship. The spoon will

1. Fall vertically down to the earth

2. Move towards the moon

3. Will move along with space-ship

4. Will move in an irregular way then fall down