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