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) $\dfrac{dA}{dt} \propto \omega r^2$
In time $dt$ the radius vector sweeps a thin triangle of area $dA = \dfrac{1}{2}r^2\,d\theta$:
$$\frac{dA}{dt} = \frac{1}{2}r^2\omega \propto \omega r^2$$
Solution by Sreeraj P, M.Sc Physics