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. $\sqrt{\frac{E}{m{r}^2}}$
• B. $\frac{E}{2m{r}^2}$
• C. $\sqrt{2Em{r}^2}$
• D. $\sqrt{2Emr}$

Answer 1

Answer: (C)

If $m$ is the mass and $v$ is the orbital velocity of the satellite, then kinetic energy.
$E=\frac{1}{2}m{v}^2$
$orEm=\frac{1}{2}{m}^2{v}^2$
$or{m}^2{v}^2=2Em$
$ormv=\sqrt{2Em}\dots .\left(i\right)$
If $r$ is the radius of the orbit of the satellite, then its angular momentum
$L=mvr$
Using Eq. $(i)$ ,
$L=\left(\sqrt{2Em}\right)r=\sqrt{{\left(2Emr\right)}^2}$