Question

In planetary motion the areal velocity of position vector of a planet depends on angular velocity $\left(\omega \right)$ 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. $\frac{dA}{dt}\propto \sqrt{\omega r}$

Answer 1

The correct option is C

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

$\frac{dA}{dt}=\frac{L}{2m}=\frac{mvr}{2m}=\frac{1}{2}\omega r^2[AsangularmomentumL=mvrandv=r\omega ]\therefore \frac{dA}{dt}\propto \omega r^2$