The ratio of the energy required to raise a satellite upto a height h above the surface of earth to that the kinetic energy of the satellite into the orbit there is (R=radius of earth)

Options

A. `R:h`
B. `h:R`
C. `R:2h`
D. `2h:R`

Answer

D

Explanation

Energy required to raise the satellite to a height h from the surface of earth is
`U = - (GMm)/((R + h)) - (- (GMm)/(R)) = (GMmh)/(R(R + h))`
Kinetic energy of satellite is
`K = 1/2 mv_0^2 = 1/2 m (GM)/((R + h)) therefore U/K = (2h)/( R)`