Additional kinetic energy to be provided to a satellite of mass m revolving around a planet of mass

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7.Gravitation

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The additional kinetic energy to be provided to a satellite of mass $m$ revolving around a planet of mass $M$, to transfer it from a circular orbit of radius $R_1$ to another of radius $R_2\,(R_2 > R_1)$ is

A

$GmM\,\left( {\frac{1}{{{R_1}}} - \frac{1}{{{R_2}}}} \right)$

B

$2GmM\,\left( {\frac{1}{{{R_1}}} - \frac{1}{{{R_2}}}} \right)$

C

$\frac{1}{2}GmM\,\left( {\frac{1}{{{R_1}}} - \frac{1}{{{R_2}}}} \right)$

D

$GmM\,\left( {\frac{1}{{R_1^2}} - \frac{1}{{R_2^2}}} \right)$

Solution

Additional kinetic energy $=\mathrm{TE}_{2}-\mathrm{TE}_{1}$

$ = – \frac{{{\rm{GMm}}}}{{2{{\rm{R}}_2}}} – \left( { – \frac{{{\rm{GMm}}}}{{2{{\rm{R}}_1}}}} \right)$

$ = \frac{1}{2}{\rm{GmM}}\left( {\frac{1}{{{{\rm{R}}_1}}} – \frac{1}{{{{\rm{R}}_2}}}} \right)$

Standard 11

Physics

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