Question
Energy required to move a body of mass $$m$$ from an orbit of radius $$2R$$ to $$3R$$ is-
A.
$$\frac{{GMm}}{{12{R^2}}}$$
B.
$$\frac{{GMm}}{{3{R^2}}}$$
C.
$$\frac{{GMm}}{{8R}}$$
D.
$$\frac{{GMm}}{{6R}}$$
Answer :
$$\frac{{GMm}}{{6R}}$$
Solution :
Energy required $$=$$ (Potential energy of the Earth $$-$$ mass system when mass is at distance $$3R$$ ) $$-$$ (Potential energy of the Earth $$-$$ mass system when mass is at distance $$2R$$ )
$$\eqalign{
& = \frac{{ - GMm}}{{3R}} - \left( {\frac{{ - GMm}}{{2R}}} \right) \cr
& = \frac{{ - GMm}}{{3R}} + \frac{{GMm}}{{2R}} \cr
& = \frac{{ - 2GMm + 3GMm}}{{6R}} \cr
& = \frac{{GMm}}{{6R}} \cr
& \cr} $$