Two satellites, A and B, have masses m and 2,m respectively. A is in a circular orbit of radius R, a

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7.Gravitation

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Two satellites, $A$ and $B,$ have masses $m$ and $2\,m$ respectively. $A$ is in a circular orbit of radius $R,$ and $B$ is in a circular orbit of radius $2R$ around the earth. The ratio of their kinetic energies, $K.E._A / K.E._B ,$ is

A

$\frac {1}{2}$

B

$1$

C

$2$

D

$\sqrt {\frac {1}{2}}$

(JEE MAIN-2019)

Solution

$K{E_A} = \frac{1}{2}m\left( {\frac{{GM}}{R}} \right)$

$K{E_B} = \frac{1}{2}\left( {2m} \right)\left( {\frac{{GM}}{{2R}}} \right)$

$ \Rightarrow \frac{{K{E_A}}}{{K{E_B}}} = 1$

Standard 11

Physics

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