Energy required in moving a body of mass `m` from a distance 2R to 3R from centre of earth of mass M is

Options

A. mgR
B. `(mgR)/(3)`
C. `(mgR)/(2)`
D. `(mgR)/(12)`

Answer

D

Explanation

Energy of the satellite in an orbit of radius r is
`E = - (GMm)/(2r)`
where M and m are the masses of the earth and satellite respectively. Initial energy of the satellite is `E_i = - (GMm)/(2(2R))`
Final energy of the satellite is `E_f = = (GMm)/(2(3R))`
Amount of energy required is
`Delta E = E_f - E_i = - (GMm)/(2(3R)) - ( - (GMm)/(2(2R)) ) = - (GMm)/(2(3R)) + (GMm)/(2(2R))`
` = (GMm)/(2R) [ 1/2 - 1/3] = (GMm)/(12R) = (mg R)/(12) ( because g = (GM)/(R^2))`