A) \[GMm/12{{R}^{2}}\]
B) \[GMm/3{{R}^{2}}\]
C) \[GMm/8R\]
D) \[GMm/6R\]
Correct Answer: D
Solution :
Gravitational potential energy of body will be \[E=\frac{G{{M}_{e}}m}{r}\] where \[{{m}_{e}}=\]mass of earth, \[m=\]mass of the body, \[R=\]radius of earth At \[r=2R,\] \[{{E}_{1}}=-\frac{G{{M}_{e}}m}{r}\] At\[r=2R,\] \[{{E}_{2}}=-\frac{G{{M}_{e}}m}{(3R)}\] Energy required to move a body of mass m from an orbit of radius 2R to 3R is \[\Delta E=\frac{G{{M}_{e}}m}{R}\left[ \frac{1}{2}-\frac{1}{3} \right]\] \[=\frac{G{{M}_{e}}m}{6R}\]
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