A thin circular plate of mass $M$ and radius $R$ has its density varying as $p(r)\, = \,{p_0}r$ with ${p_0}$ as constant and $r$ is the distance from its centre. The moment of inertia of the circular plate about an axis perpendicular to the plate about an axis perpendicular to the plate and passing through its edge is $I\, = \,aM{R^2}$. The value of the coefficient $a$ is