Question

An artificial satellite of mass $m$ is revolving around Earth in a circular orbit of radius $r$. If the mass of Earth is $M$, angular momentum of the satellite with respect to the centre of earth is :
($G$-Universal Gravitational constant)

• A. $\sqrt{GM{m}^{2}r}$
• B. $2m\sqrt{GMr}$
• C. $2M\sqrt{GMr}$
• D. $\sqrt{\frac{GM}{r}}$

Answer 1

The correct option is A $\sqrt{GM{m}^{2}r}$

By equating centripetal force to gravitational force, we get,

$\frac{GMm}{r^2}=\frac{m{v}^2}{r}$

$v=\sqrt{\frac{GM}{r}}$

Thus, angular momentum with respect to the center of the earth is

$L=mvr=m\sqrt{\frac{GM}{r}}r=\sqrt{GM{m}^{2}r}$