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

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

Spherical balls of radius $$R$$ are falling in a viscous fluid of viscosity $$\eta $$ with a velocity $$v.$$ The retarding viscous force acting on the spherical ball is