Question

The angular momentum of a planet of mass m having a real velocity $v_A$ is?

• A. $m{v}_A$
• B. $2m{v}_A$
• C. $3m{v}_A$
• D. $m+v_A$

Answer 1

Answer: (B)

$2m{v}_A$

$v_A=$ areal velocity
$=\frac{\text{area swept by radius vector}}{\text{time taken}}$
$\therefore v_A=\frac{\pi r^2}{T}$
Where, $T=$ period of revolution of planet $=\frac{2\pi }{\omega }$
$r=$ radius of planet
$\therefore v_A=\frac{\pi r^2}{2\pi /\omega }=\frac{r^2\omega }{2}$
$\Rightarrow =\omega =\frac{2v_A}{r^2}$
$L=I\omega =m{r}^2\cdot \omega$
$=m{r}^2\cdot \frac{2v_A}{I^2}$
$\therefore L=2m{v}_A$.