A satellite of mass 'm' is revolving in an orbit of radius 2 R. The minimum energy required to lift it into another orbit of radius 3R is
(R is radius of the earth and g is acceleration due to gravity on its surface. )

Options

A. `(gRm)/(4)`
B. `(gRm)/(8)`
C. `(gRm)/(12)`
D. `(gRm)/(18)`

Answer

c

Explanation

`E_(2)-E_(1)=-("GMm")/(2xx3R)+("GMm")/(2xx2R)`
`=("GMm")/(R)[(1)/(4)-(1)/(6)]`
`=("GMm")/(12R)=(gR^(2)m)/(12R)=(1)/(2)gRm`
`=(1)/(2)mgR.`