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. 

At what height from the surface of earth the gravitation potential and the value of g are $-5.4\times {10}^{7}J$ $k{g}^{-2}$ and $6.0$ $m{s}^{-2}$ respectively? (Take, the radius of earth as 6400 km.)

1. 1600 km             
2. 1400 km 
3. 2000 km             
4. 2600 km

Kepler's third law states that the square of the period of revolution (T) of a planet around the sun, is proportional to the third power of the average distance r between the sun and planet i.e. T²=Kr^3, here K is constant. If the masses of the sun and planet are M and m respectively, then as per Newton's law of gravitation, the force of attraction between them is F=GMm/r², here G is gravitational constant. The relation between G and K is described as

(1) GK=4π² 

(2) GMK=4π²
 

(3) K=G
 

(4) K=l/G
 

Two spherical bodies of masses M and 5M and radii R and 2R are released in free space with initial separation between their centres equal to 12R. If they attract each other due to gravitational force only, then the distance covered by the smaller body before collision is

(1)2.5 R

(2)4.5 R

(3)7.5 R

(4)1.5 R

A remote sensing satellite of the earth revolves in a circular orbit at a height of \(0.25\times 10^{6}\) m above the surface of the earth. If the earth’s radius is \(6.38\times 10^{6}\) m and \(g = 9.8\) ms^-1, then the orbital speed of the satellite is:
1. \(7.76\) kms^-1
2. \(8.56\) kms^-1
3. \(9.13\) kms^-1
4. \(6.67\) kms^-1