The escape velocity of a particle of mass \(m\) varies as:

1.	\(m^{2}\)	2.	\(m\)
3.	\(m^{0}\)	4.	\(m^{-1}\)

If the radius of a planet is \(R\) and its density is \(\rho,\) the escape velocity from its surface will be:
1. \(v_e\propto \rho R\)
2. \(v_e\propto \sqrt{\rho} R\)
3. \(v_e\propto \frac{\sqrt{\rho}}{R}\)
4. \(v_e\propto \frac{1}{\sqrt{\rho} R}\)

A planet whose density is double of earth and radius is half of the earth, will produce gravitational field on its surface:
(\(g=\) acceleration due to gravity at the surface of earth)

A body weighs \(200\) N on the surface of the earth. How much will it weigh halfway down the centre of the earth?

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 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: 

Dependence of intensity of gravitational field \((\mathrm{E})\) of the earth with distance \((\mathrm{r})\) from the centre of the earth is correctly represented by: (where \(\mathrm{R}\) is the radius of the earth)

1.		2.
3.		4.

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\(m=5.98\times 10^{24}~\text{kg})\) 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. \(100​~\text{m}\)