If $$g$$ is the acceleration due to gravity on the earth's surface, the gain in the potential energy of an object of mass $$m$$ raised from the surface of the earth to a height equal to the radius $$R$$ of the earth is

The time period of an earth satellite in circular orbit is independent of

Suppose the gravitational force varies inversely as the n^th power of distance. Then the time period of a planet in circular orbit of radius $$R$$ around the sun will be proportional to

A wire fixed at the upper end stretches by length $$l$$ by applying a force $$F.$$ The work done in stretching is