Question

In planetary motion the areal velocity of position vector of a planet depends on angular velocity $(\omega)$ and the distance of the planet from sun $(r)$. If so the correct relation for areal velocity is

• A. $\frac{d A}{d t} \propto \omega r$
• B. $\frac{d A}{d t} \propto \omega^{2} r$
• C. $\frac{d A}{d t} \propto \omega r^{2}$
• D. $\frac{d A}{d t} \propto \sqrt{\omega r}$

Answer 1

Answer: (C)

$\frac{d A}{d t}=\frac{L}{2 m}$
$=\frac{d A}{d t} \propto v r \propto \omega r^{2}$