Question

If $A$ is the areal velocity of a planet of mass $M$ , then its angular momentum about the centre of the circular orbit is

• A. $MA$
• B. $2MA$
• C. $A^{2}M$
• D. $A{M}^2$

Answer 1

Answer: (B)

Areal velocity is area swept per unit time.
$A=\frac{\frac{1}{2}r\left(rd\theta \right)}{dt}=\frac{1}{2}{r}^2\frac{d\theta }{dt}=\frac{1}{2}{r}^2\omega =\frac{1}{2}\frac{\left(M{r}^2\right)\omega }{M}=\frac{L}{2M}$
$\Rightarrow L=2MA$