The energy required to move a satellite of mass \(m\) from an orbit of radius \(2R\) to \(3R\) around the Earth having mass \(M\) is:

1.	\(\frac{GMm}{12R} \)	2.	\(\frac{GMm}{R} \)
3.	\(\frac{GMm}{8 R} \)	4.	\(\frac{GMm}{2R}\)

Three equal masses \(m\) are placed at the three vertices of an equilateral triangle of sides \(r.\) The work required to double the separation between masses will be:

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 centripetal force acting on a satellite orbiting around the earth and the gravitational force of the earth acting on the satellite, both are equal to \(F\). The net force on the satellite is:
1. zero
2. \(F\)
3. \(F\sqrt{2}\)
4. \(2F\)

Two identical solid copper spheres of radius \(R\) are placed in contact with each other. The gravitational attraction between them is proportional to:
1. \(R^2\)
2. \(R^{-2}\)
3. \(R^4\)
4. \(R^{-4}\)

Mass \(M\) is divided into two parts \(xM\) and \((1-x)M.\) For a given separation, the value of \(x\) for which the gravitational attraction between the two pieces becomes maximum is:

Two particles of equal masses go around a circle of radius \(R\) under the action of their mutual gravitational attraction. The speed of each particle is:
1. \(v = \frac{1}{2 R} \sqrt{\frac{1}{Gm}}\)
2. \(v = \sqrt{\frac{Gm}{2 R}}\)
3. \(v = \frac{1}{2} \sqrt{\frac{G m}{R}}\)
4. \(v = \sqrt{\frac{4 Gm}{R}}\)