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. \(R^{-4}\)

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. \(2F\)

Radii and densities of two planets are \(R_1, R_2\) and \(\rho_1, \rho_2\) respectively. The ratio of accelerations due to gravity on their surfaces is:
1. \(\frac{\rho_1}{R_1}:\frac{\rho_2}{R_2}\)
2. \(\frac{\rho_1}{R^2_1}: \frac{\rho_2}{R^2_2}\)
3. \(\rho_1 R_1 : \rho_2R_2\)
4. \(\frac{1}{\rho_1R_1}:\frac{1}{\rho_2R_2}\)

\(1\) kg of sugar has maximum weight:
1. at the pole.
2. at the equator.
3. at a latitude of \(45^{\circ}.\)
4. in India.

A body is thrown vertically upwards with an initial speed \(\sqrt{gR}\), where \(R\) is the radius of the earth. The maximum height reached by the body from the surface of the earth is:
1. \(\frac{R}{2}\)
2. \(\frac{3R}{2}\)
3. \(R\)
4. \(\frac{R}{4}\)

A particle is located midway between two point masses each of mass \(M\) kept at a separation \(2d.\) The escape speed of the particle is:
(neglecting the effect of any other gravitational effect)
1. \(\sqrt{\frac{2 GM}{d}}\)
2. \(2 \sqrt{\frac{GM}{d}}\)
3. \(\sqrt{\frac{3 GM}{d}}\)
4. \(\sqrt{\frac{GM}{2 d}}\)

Three identical particles each of mass \(M\) are located at the vertices of an equilateral triangle of side \(a\). The escape speed of one particle will be:
1. \(\sqrt{\frac{4 GM}{a}}\)
2. \(\sqrt{\frac{3 GM}{a}}\)
3. \(\sqrt{\frac{2 GM}{a}}\)
4. \(\sqrt{\frac{GM}{a}}\)