Question

The satellite of mass $m$ revolving in a circular orbit of radius $r$ around the earth has kinetic energy $E$. Then its angular momentum will be:

• A. $\sqrt{\frac{E}{{mr}^2}}$
• B. $\frac{E}{{2mr}^2}$
• C. $\sqrt{{2Emr}^2}$
• D. $\sqrt{2Emr}$

Answer 1

The correct option is C $\sqrt{{2Emr}^2}$

KE of a satellite,
$E=\frac{1}{2}{mv}^2$
or $mv=\sqrt{2Em}$
Angular momentum,
$L=mvr=\left(\sqrt{2Em}\right)\times r$
$=\sqrt{2mE{r}^2}$