A satellite is moving with a constant speed v in circular orbit a… - Vidyadip

Question

A satellite is moving with a constant speed $v$ in circular orbit around the earth. An object of mass $‘m’$ is ejected from the satellite such that it just escapes from the gravitational pull of the earth. At the time of ejection, the kinetic energy of the object is

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Answer

$Initially,\,kinetic\,energy = \frac{1}{2}m{v^2} = \frac{1}{2}m\frac{{G{M_e}}}{r}$

By conservation of $M.E$.,

$\frac{{ - G{M_e}m}}{r} + KE = 0$

$KE = \frac{{G{M_e}m}}{r} = m{v^2}$

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