The energy required to shift a satellite from orbital radius ‘r’ to radius 2r is E. What energy will be required to shift the satellite from orbital radius 2r to 3r?

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E/2

3E/4

E/3

answer is D.

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Detailed Solution

$\begin{array}{l} E = GMm [\frac{1}{r_{1}} - \frac{1}{r_{2}}] = GMm [\frac{1}{r} - \frac{1}{2 r}] \\ E^{1} = GMm [\frac{1}{2 r} - \frac{1}{3 r}]; \frac{E^{1}}{E} = \frac{\frac{1}{6 r}}{\frac{1}{2 r}} = \frac{1}{3} \Rightarrow E^{1} = \frac{E}{3} \end{array}$

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