A satellite of mass \(m\) is orbiting the earth (of radius \(R\)) at a height \(h\) from its surface. What is the total energy of the satellite in terms of \(g_0?\)
(\(g_0\) is the value of acceleration due to gravity at the earth's surface)
1. \(\frac{mg_0R^2}{2(R+h)}\)
2. \(-\frac{mg_0R^2}{2(R+h)}\)
3. \(\frac{2mg_0R^2}{(R+h)}\)
4. \(-\frac{2mg_0R^2}{(R+h)}\)

If the mass of the sun were ten times smaller and the universal gravitational constant were ten times larger in magnitude, which of the following statements would not be correct?

The kinetic energies of a planet in an elliptical orbit around the Sun, at positions \(A,B~\text{and}~C\) are \(K_A, K_B~\text{and}~K_C\) respectively. \(AC\) is the major axis and \(SB\) is perpendicular to \(AC\) at the position of the Sun \(S\), as shown in the figure. Then:
                 

A satellite S is moving in an elliptical orbit around the earth. If the mass of the satellite is very small as compared to the mass of the earth, then:

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 average distance \(r\) between the sun and planet i.e. \(T^2 = Kr^3\), 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 \(F = \frac{GMm}{r^2},\) here \(G\) is the gravitational constant. The relation between \(G\) and \(K\) is described as:
1. \(GK = 4\pi^2\)
2. \(GMK = 4\pi^2\)
3. \(K =G\)
4. \(K = \frac{1}{G}\)

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 the collision is:

A black hole is an object whose gravitational field is so strong that even light cannot escape from it. To what approximate radius would Earth (mass \(= 5.98\times 10^{24}~\text{kg}\)) have to be compressed to be a black hole?
1. \(10^{-9}~\text{m}\)
2. \(10^{-6}~\text{m}\)
3. \(10^{-2}~\text{m}\)
4. \(100​~\text{m}\)

A body of mass \(m\) is taken from the Earth’s surface to the height equal to twice the radius \((R)\) of the Earth. The change in potential energy of the body will be: 

A body projected vertically from the earth reaches a height equal to earth’s radius before returning to the earth. The power exerted by the gravitational force:

The figure shows the elliptical orbit of a planet \(m\) about the sun \(\mathrm{S}.\) The shaded area \(\mathrm{SCD}\) is twice the shaded area \(\mathrm{SAB}.\) If \(t_1\) is the time for the planet to move from \(\mathrm{C}\) to \(\mathrm{D}\) and \(t_2\) is the time to move from \(\mathrm{A}\) to \(\mathrm{B},\) then: