A satellite is moving with a constant speed v in circular orbit around earth. An object of mass &lsq

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7.Gravitation

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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

A

$2\,mv^2$

B

$mv^2$

C

$\frac{1}{2}\,m{v^2}$

D

$\frac{3}{2}\,m{v^2}$

(JEE MAIN-2019)

Solution

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

By conservation of $M.E$.,

$\frac{{ – G{M_e}m}}{r} + KE = 0$

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

Standard 11

Physics

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