A satellite of mass $$m$$ revolves around the earth of radius $$R$$ at a height $$x$$ from its surface. If $$g$$ is the acceleration due to gravity on the surface of the earth, the orbital speed of the satellite is-

Solution :
Gravitational force provides the necessary centripetal force
$$\eqalign{ & \therefore \frac{{m{v^2}}}{{\left( {R + x} \right)}} = \frac{{GmM}}{{{{\left( {R + x} \right)}^2}}}{\text{ also }}g = \frac{{GM}}{{{R^2}}} \cr & \therefore {v^2} = \frac{{g{R^2}}}{{R + x}} \Rightarrow v = {\left( {\frac{{g{R^2}}}{{R + x}}} \right)^{\frac{1}{2}}} \cr} $$