Question

Angular momentum of a planet of mass $m$ orbiting around sun is $J$. Areal velocity of its radius vector will be:

• A. $\frac{J}{2M}$
• B. $\frac{J}{M}$
• C. $\frac{m}{2J}$
• D. $\frac{1}{2mJ}$

Answer 1

The correct option is A $\frac{J}{2M}$

The areal velocity of radius vector
$=\frac{1}{2}r\left(r\frac{d\theta }{dt}\right)=\frac{1}{2}\omega r^2$

Angular momentum, $J=I\omega =m{r}^2\omega$
$\therefore$ Areal velocity $=\frac{J}{2m}$