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

Answer: (C)

$\frac{da}{dt}\propto \omega {{r}^{2}}$

Answer 2

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