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)

1.	\(g\)	2.	\(2g\)
3.	\(\dfrac{g}{2}\)	4.	\(3g\)

A planet of mass \(m\) is moving around a star of mass \(M\) and radius \(R\) in a circular orbit of radius \(r.\) The star abruptly shrinks to half its radius without any loss of mass. What change will be there in the orbit of the planet?

A planet is orbiting the sun in an elliptical orbit. Let \(U\) denote the potential energy and \(K\) denote the kinetic energy of the planet at an arbitrary point in the orbit.
Choose the correct statement from the given ones:

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. \(v_e\propto \frac{1}{\sqrt{\rho} R}\)

The law of gravitation states that the gravitational force between two bodies of mass \(m_1\) $\mathrm{and}$ \(m_2\) is given by:
\(F=\dfrac{Gm_1m_2}{r^2}\)
$\mathrm{}$\(G\) (gravitational constant) \(=7\times 10^{-11}~\text{N-m}^2\text{kg}^{-2}\)$\mathrm{.}$
\(r\) (distance between the two bodies) in the case of the Earth and Moon $\mathrm{}$\(=4\times 10^8~\text{m}\)
\(m_1~(\text{Earth})=6\times 10^{24}~\text{kg}\)
\(m_2~(\text{Moon})=7\times 10^{22}~\text{kg}\)
${\mathrm{}}_{}$What is the gravitational force between the Earth and the Moon?
1. \(1.8375 \times 10^{19}~\text{N}\)
2. \(1.8375 \times 10^{20}~\text{N}\)
3. \(1.8375 \times 10^{25}~\text{N}\)
4. \(1.8375 \times 10^{26}~\text{N}\)

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

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?