# A satellite of mass m is circulating around the earth with constant angular velocity. If radius of the orbit is R0 and mass of the earth M, the angular momentum about the centre of the earth is Option 1) $M\sqrt{\left ( GmRo \right )}$ Option 2) $M\sqrt{\left ( \frac{Gm}{Ro }\right )}$ Option 3) $m\sqrt{\left ( \frac{GM}{Ro }\right )}$ Option 4) $m\sqrt{\left ( GMRo\right )}$

As we learnt in

Angular momentum of satellite -

$L=mvr$

$L=\sqrt{m^{2}GMr}$

$L=$ Angular momentum

$m\rightarrow$ mass of satellite

- wherein

$v$ depends on both the masses , mass of centre of body and mass of planet as well as radius of earth.

Centripetal force =$m\omega ^{2}R_{o}$

$m\omega ^{2}R_{o}=\frac{GmM}{R_{o}^{2}}$

$\Rightarrow \omega ^{2}=\frac{GM}{R_{o}^{3}}\ \: \: \: \: .........(1)$

$\therefore$ Angular momentum =$m\omega R_{o}^{2}$

$=m.\sqrt{\frac{GM}{R_{o}^{3}}}.R_{o}^{2} = m\sqrt{GMR_{o}}$

Option 1)

$M\sqrt{\left ( GmRo \right )}$

This is incorrect option

Option 2)

$M\sqrt{\left ( \frac{Gm}{Ro }\right )}$

This is incorrect option

Option 3)

$m\sqrt{\left ( \frac{GM}{Ro }\right )}$

This is incorrect option

Option 4)

$m\sqrt{\left ( GMRo\right )}$

This is correct option

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