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. $\frac{T^2}{R^3}$

A satellite moves round the earth in a circular orbit of radius R making one revolution per day. A second satellite moving in a circular orbit, moves round the earth once in 8 days. The radius of the orbit of the second satellite is -

1. 8 R                           

2. 4 R

3. 2 R                             

4. R

A satellite moves in a circle around the earth. The radius of this circle is equal to one half of the radius of the moon’s orbit. The satellite completes one revolution in

1. $\frac{1}{2}$ lunar month                   

2. $\frac{2}{3}$ lunar month

3. $2^{\raisebox{1ex}{$-3$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}$ lunar month               

4. $2^{\raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}$ lunar month

If the acceleration due to gravity at a height \(1\) km above the earth is similar to a depth \(d\) below the surface of the earth, then: 
1. \(d= 0.5\) km
2. \(d=1\) km
3. \(d=1.5\) km
4. \(d=2\) km

Two astronauts are floating in a gravity free space after having lost contact with their spaceship. The two will:

Starting from the centre of the earth having radius R, the variation of g (acceleration  due to gravity) is shown by:

1.  

2. 

3. 

4.