Question

If an earth satellite of mass $m$ orbiting at a distance $2\,R$ from the centre of earth has to be transferred into the orbit of radius $3\,R$, the amount of energy required is (R = radius of earth)

• A. $ mgR $
• B. $ \frac{mgR}{3} $
• C. $ \frac{mgR}{2} $
• D. $ \frac{mgR}{12} $
• E. $ \frac{mgR}{9} $

Answer 1

Answer: (D)

Energy require = Final energy - initial energy
$ =-\frac{GMm}{2(3R)}-\left[ \frac{GMm}{2(2R)} \right] $
$ =\frac{GMm}{2(3R)}-\left[ -\frac{1}{2}-\frac{1}{3} \right] $
$ =\frac{GMm}{12R}=\frac{g{{R}^{2}}m}{12R} $
$ =\frac{mgR}{12} $