The kinetic energy needed to project a body of mass m from the earth surface (radius R) to infinity is -

1.   mgR/2                 

2.  2 mgR

3.   mgR                   

4.   mgR/4

A satellite is to revolve round the earth in a circle of radius 8000 km. The speed at which this satellite be projected into an orbit, will be 
1. $3 km/s$                     

2. 16 km/s

3. 7.15 km/s                   

4. 8 km/s

If the mass of a body is M on the earth surface, then the mass of the same body on the moon surface is:

1.  M/6       
2.  Zero
3.  M         
4.  None of these

Radius of orbit of satellite of earth is R. Its kinetic energy is proportional to -

1. $\frac{1}{R}$                      

2. $\frac{1}{\sqrt{R}}$

3. R                         

4.  $\frac{1}{R^{3/2}}$

A particle falls towards earth from infinity. It’s velocity on reaching the earth would be -

1.   Infinity                   

2. $\sqrt{2gR}$

3.  $2\sqrt{gR}$                   

4.  Zero

Two satellite A and B, ratio of masses 3 : 1 are in circular orbits of radii r and 4r. Then ratio of total mechanical energy of A to B is 

1. 1 : 3                             

2. 3 : 1

3. 3 : 4                             

4. 12 : 1

The orbital velocity of a planet revolving close to earth's surface is 

1. $\sqrt{2gR}$              

2. $\sqrt{gR}$

3. $\sqrt{\frac{2g}{R}}$               

4. $\sqrt{\frac{g}{R}}$  

If the gravitational force between two objects were proportional to \(\frac{1}{R}\) (and not as\(\frac{1}{R^2}\)${\mathrm{}}^{}$) where \(R\) is the separation between them, then a particle in circular orbit under such a force would have its orbital speed \(v\) proportional to:
1. \(\frac{1}{R^2}\)
2. \(R^{0}\)
3. \(R^{1}\)
4. \(\frac{1}{R}\)

When a satellite going round the earth in a circular orbit of radius r and speed v loses some of its energy, then r and v change as 

1. r and v both will increase

2. r and v both will decrease

3. r will decrease and v will increase

4. r will decrease and v will decrease

Which of the following quantities does not depend upon the orbital radius of the satellite ?

1.  $\frac{T}{R}$                            

2.  $\frac{T^2}{R}$

3. $\frac{T^2}{R^2}$                           

4. $\frac{T^2}{R^3}$