In planetary motion the areal velocity of position vector of a planet depends on angular velocity $\left(\mathrm{\omega }\right)$ and the distance of the planet from sun (r). If so the correct relation for areal velocity is

• A

  $\frac{\mathrm{dA}}{\mathrm{dt}}\propto \mathrm{\omega r}$

• B

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

• C

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

• D

  $\frac{\mathrm{dA}}{\mathrm{dt}}\propto \sqrt{\mathrm{\omega r}}$