In planetary motion the areal velocity of possition vector of a planet depends of angular velocity `(omega)` and the distance of the planet from sun (r). If so the correct relation for areal velocity is

Options

A. `(dA)/(dt)prop omega r^(2)`
B. `(dA)/(dt)prop omega r`
C. `(dA)/(dt) prop sqrt(omega r)`
D. `(dA)/(dt)prop omega^(2)r`

Answer

A

Explanation

The areal velocity `(dA)/(dt)prop vr` but `v = r omega`
`therefore (dA)/(dt)prop (r omega)r` or `(dA)/(dt)prop omega r^(2)`