Question

A satellite of mass $m$, revolving in a circular orbit of radius $r$ around the earth of mass $M$ has magnitude of total energy $E$. Then its angular momentum will be

• A. $\sqrt{2Em{r}^2}$
• B. $\sqrt{2Emr}$
• C. $\sqrt{Em{r}^2}$
• D. $\sqrt{4Em{r}^2}$

Answer 1

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


The orbital velocity is $V_0=\sqrt{\frac{GM}{r}}$
The magnitude of total energy $E=\frac{GMm}{2r}$
The angular momentum is $L=m{V}_{0}r$
$=m\sqrt{\frac{Gm}{r}}r$
$=\sqrt{\frac{GM{m}^2{r}^2}{r}}$
$=\sqrt{2m{r}^2\left(\frac{GMm}{2r}\right)}$
$=\sqrt{2Em{r}^2}$