Question

In planetary motion the areal velocity of position vector of a planet depends on angular velocity ( $ \omega $ ) and distance of the planet from the 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

The Correct Option is C

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