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 \[E=-\frac{GMm}{r}\] where, \[M=\] mass of the earth, \[m=\] mass of the body, \[r=\] radius of the earth. At \[r=2\,R\], \[{{E}_{1}}=-\frac{GMm}{(2R)}\] At \[r=3R\], \[{{E}_{2}}=-\frac{GMm}{(3R)}\] Energy required to move a body of mass m from an orbit of radius 2 R to 3R is \[\Delta E=\frac{GMm}{R}\left[ \frac{1}{2}-\frac{1}{3} \right]\] \[=\frac{GMm}{6R}\]
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