Time period of a satellite revolving above Earth’s surface at a height equal to \(R\) (the radius of Earth) will be:
(\(g\) is the acceleration due to gravity at Earth’s surface)
1. \(2 \pi \sqrt{\frac{2 R}{g}}\)
2. \(4 \sqrt{2} \pi \sqrt{\frac{R}{g}}\)
3. \(2 \pi \sqrt{\frac{R}{g}}\)
4. \(8 \pi \sqrt{\frac{R}{g}}\)

A rocket of mass \(M\) is launched vertically from the surface of the earth with an initial speed \(v\). Assuming the radius of the earth to be \(R\) and negligible air resistance, the maximum height attained by the rocket above the surface of the earth is:
1. \(\frac{R}{\left(\frac{gR}{2v^2}-1\right)}\)
2. \(R\left({\frac{gR}{2v^2}-1}\right)\)
3. \(\frac{R}{\left(\frac{2gR}{v^2}-1\right)}\)
4. \(R{\left(\frac{2gR}{v^2}-1\right)}\)

If two planets are at mean distances \(d_1\) and \(d_2\) from the sun and their frequencies are \(n_1\) and \(n_2\) respectively, then:
1. \(n^2_1d^2_1= n_2d^2_2\)
2. \(n^2_2d^3_2= n^2_1d^3_1\)
3. \(n_1d^2_1= n_2d^2_2\)
4. \(n^2_1d_1= n^2_2d_2\)

The distance of a planet from the sun is \(5\) times the distance between the earth and the sun. The time period of the planet is: 

Two satellites \(A\) and \(B\) go around the earth in circular orbits at heights of \(R_A ~\text{and}~R_B\) respectively from the surface of the earth. Assuming earth to be a uniform sphere of radius \(R_e\)${}_{}$, the ratio of the magnitudes of their orbital velocities is:

A body of mass \(m\) kg starts falling from a point \(2R\) above the Earth’s surface. Its kinetic energy when it has fallen to a point \(R\) above the Earth’s surface, is:
[\(R\text-\) Radius of Earth, \(M\text-\) Mass of Earth, \(G\text-\) Gravitational Constant]
1. \(\frac{1}{2} \frac{G M m}{R}\)
2. \(\frac{1}{6} \frac{G M m}{R}\)
3. \(\frac{2}{3} \frac{G M m}{R}\)
4. \(\frac{1}{3} \frac{G M m}{R}\)

A body is projected vertically upwards from the surface of a planet of radius \(R\) with a velocity equal to half the escape velocity for that planet. The maximum height attained by the body is:
1. \(\frac{R}{3}\)
2. \(\frac{R}{2}\)
3. \(\frac{R}{4}\)
4. \(\frac{R}{5}\)

A satellite is launched into a circular orbit of radius \(R\) around the Earth while a second satellite is launched into an orbit of radius \(1.02~\text{R}\). The percentage difference in the time periods of the two satellites is: