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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
