Q. 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) $\frac{dA}{dt} \propto \sqrt{\omega r}$
Explanation
(c) $\frac{dA}{dt} = \frac{L}{2m} \Rightarrow \frac{dA}{dt} \propto vr \propto \omega r^{2}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.