Two satellites of Earth, \(S_1\)_, and \(S_2\), are moving in the same orbit. The mass of \(S_1\) is four times the mass of \(S_2\). Which one of the following statements is true?

A planet is revolving around a massive star in a circular orbit of radius R. If the gravitational force of attraction between the planet and the star is inversely proportional to ${\mathrm{R}}^3$, then the time period of revolution T is proportional to:

1. ${\mathrm{R}}^5$

2. ${\mathrm{R}}^3$

3. ${\mathrm{R}}^2$

4. R

A satellite is moving very close to a planet of density $\mathrm{\rho }$. The time period of the satellite is:

1.  $\sqrt{\frac{3\mathrm{\pi }}{\mathrm{\rho G}}}$

2.  ${\left(\frac{3\mathrm{\pi }}{\mathrm{\rho G}}\right)}^{3/2}$

3.  $\sqrt{\frac{3\mathrm{\pi }}{2\mathrm{\rho G}}}$

4.  ${\left(\frac{3\mathrm{\pi }}{2\mathrm{\rho G}}\right)}^{3/2}$

Magnitude of potential energy (U) and time period (T) of a satellite are related to each other as:

1. $T^2$ $\alpha$ $\frac{1}{U^3}$

2. $T$ $\alpha$ $\frac{1}{U^3}$

3. $T^2$ $\alpha$ $U^3$

4. $T^2$ $\alpha$ $\frac{1}{U^2}$

A satellite of mass m revolving around the earth in a circular orbit of radius r has its angular momentum equal to L about the centre of the earth. The potential energy of the satellite is: 

If the speed of an artificial satellite revolving around the earth in a circular orbit be \(2 \over 3\) of the escape velocity from the surface of earth then its altitude above the surface of the earth is

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

The orbital angular momentum of a satellite revolving at a distance \(r\)from the centre is \(L\). If the distance is increased to 16r, then the new angular momentum will be:

A planet is moving in an elliptical orbit. If T, V, E, and L stand, respectively, for its kinetic energy, gravitational potential energy, total energy and angular momentum about the center of the orbit, then:

The centripetal force acting on a satellite orbiting around the earth and the gravitational force of the earth acting on the satellite, both are equal to F. The net force on the satellite is:

1. Zero                                  

2. F

3. $F\sqrt{2}$                                 

4. 2 F