A geostationary satellite is orbiting the earth at a height of \(5R\) above the surface of the earth, \(R\) being the radius of the earth. The time period of another satellite in hours at a height of \(2R\) from the surface of the earth is:

1. \(5\)

2. \(10\)

3. \(6\sqrt2\)

4. \(\dfrac{6}{\sqrt{2}}\)

The radii of circular orbits of two satellites A and B of the earth are \(4R\) and \(R\) respectively. If the speed of satellite A is \(3v,\) then the speed of satellite B will be:
1. \(3v/4\)
2. \(6v\)
3. \(12v\)
4. \(3v/2\)

The additional kinetic energy to be provided to a satellite of mass \(m\) revolving around a planet of mass \(M,\) to transfer it from a circular orbit of radius \(R_1\) to another of radius \(R_2\) (\(R_2>R_1\)) is:

1. \(GmM\) $\left(\frac{1}{R_1}-\frac{1}{R_2}\right)$

2. \(2GmM\) $\left(\frac{1}{R_1}-\frac{1}{R_2}\right)$

3. $\frac{1}{2}GmM$ $\left(\frac{1}{R_1}-\frac{1}{R_2}\right)$

4. \(GmM\) $\left(\frac{1}{R_1^2}-\frac{1}{R_2^2}\right)$

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?

For a satellite moving in an orbit around the earth, the ratio of kinetic energy to potential energy is:
1. $\frac{1}{\sqrt{2}}$
2. \(2\)
3. $\sqrt{2}$
4. $\frac{1}{2}$