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. $M\sqrt{Gm{R}_0}$
• D. $m\sqrt{GM{R}_0}$

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
$v=\sqrt{\frac{GM}{R}}=\sqrt{\frac{GM}{R_0}}$
(Here, $R=R_0$ )
Hence, angular momentum
$L=m\sqrt{\frac{GM}{R_0}}{R}_0=m\sqrt{GM{R}_0}$