Q 11-07-020NEETJEE MainEAMCET 2003 (Engineering)Easy
In planetary motion, the areal velocity of the position vector of a planet depends on the angular velocity ($\omega$) and the distance of the planet from the sun ($r$). If so, the correct relation for the areal velocity is
Answer: (C) $\dfrac{dA}{dt} \propto \omega r^2$
Concept. In time $dt$ the radius vector sweeps $dA = \dfrac12r^2\,d\theta$.
Step 1. Rate. $\dfrac{dA}{dt} = \dfrac12r^2\omega \propto \omega r^2$.
Answer. $\dfrac{dA}{dt} \propto \omega r^2$ (Option C).
Solution by Sreeraj P, M.Sc Physics