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. $\frac{dA}{dt} \propto \omega r$
• B. $\frac{dA}{dt} \propto \omega^2 r$
• C. $\frac{dA}{dt} \propto \omega r^2$
• D. $\frac{dA}{dt} \propto \sqrt{\omega r}$

Answer 1

Answer: (C)

$\frac{dA}{dt} = \frac{L}{2m} = \frac{dA}{dt} \propto vr \propto \omega r^2$