In planetary motion the areal velocity of position vector of a planet depends on angular velocity and the distance of the planet from sun r . The correct relation for areal velocity is

Step-by-step solution

Areal velocity d A d t depends on angular velocity ( ) and distance of the planet from sun. d A d t w^a r^b d A d t =K ^a r^b Writing the dimensional formula on both sides, [ L ^2 ~T ⁻¹ ]=k [ ~T ⁻¹ ]^a[ ~L ]^b On comparing, -a=-1 a=1b=2 d A d t r^2