Question

A satellite of mass $m$ is circulating around the earth with constant angular velocity. If radius of the orbit is $R_0$ and mass of earth is $M$, the angular momentum of the satellite is :

• A. $ M\sqrt{\frac{Gm}{R_{0}}} $
• B. $ m\sqrt{\frac{GM}{R_{0}}} $
• C. $ M\sqrt{GmR_{0}} $
• D. $ m\sqrt{GMR_{0}} $

Answer 1

Answer: (D)

Angular momentum of satellite
$L=m \nu R$
where $v$ is orbital velocity of satellite and $R$ is radius of earth.
Orbital velocity of satellite
$v=\sqrt{\frac{G M}{R}}=\sqrt{\frac{G M}{R_{0}}}$
(Here, $R=R_{0}$ )
Hence, angular momentum
$L=m \sqrt{\frac{G M}{R_{0}}} R_{0}=m \sqrt{G M R_{0}}$