A geostationary satellite is taken to a new orbit, such that its distance from centre of the earth is doubled. Then, find the time period of this satellite in the new orbit.

The distance through which one has to dig the Earth from its surface, so as to reach the point where the acceleration due to gravity is reduced by 40% of that at the surface of the Earth, is (radius of Earth is 6400 km)

Infinite number of masses each of 3kg are placed along a straight line at the distances of 1 m, 2m, 4m, 8m, ...... from a point O on the same line. If G is the universal gravitational constant, then the magnitude of gravitational field intensity at O is

A particle is kept on the surface of a uniform sphere of mass 1000 kg and radius 1 m. The work done per unit mass against the gravitational force between them is

[G = 6.67 $$\times$$ 10$$^{-11}$$ Nm$$^2$$ kg$$^{-2}$$]