In planetary motion the areal velocity of position vector of a planet depends on angular velocity (r) and the distance of the planet from sun (r). If so the correct relation for areal velocity is :
Answer & explanation
Correct answer: option 3
\(\frac{dA}{dt} = \frac{L}{2m}\)
=\(\frac{mvr}{2m}\)
=\(\frac{1}{2}\omega r^2\)
[As Angular momentum L = mvr and v = rω]
\(\Rightarrow \frac{dA}{dt} \propto \omega r^2\)