A satellite is moving with a constant speed v in circular orbit...

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:

Options

A $\dfrac{3}{2}m{v}^{2}$
B $m{v}^{2}$
C $\dfrac{1}{2}m{v}^{2}$
D $2m{v}^{2}$

Correct answer

B. $m{v}^{2}$

Step-by-step solution

At height $r$ from the centre of the Earth, orbital velocity is given as:

$orbitalvelocity = \sqrt{\dfrac{GM}{r}}$

${V}_{e} = \sqrt{2}v$

$K . E = \dfrac{1}{2}m{\left(\sqrt{2}v\right)}^{2} = m{v}^{2}$

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