A thin circular plate of mass \( M \) and radius \( R \) has its density varying as \( \rho(r)=\...

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A thin circular plate of mass \( M \) and radius \( R \) has its density varying as \( \rho(r)=\rho_{0} r \) with \( \rho_{0} \) as constant and \( r \) is the distance from its center. The moment of inertia of the circular plate about an axis perpendicular to the plate and passing through its edge is \( I=a M R^{2} \). The value of the coefficient \( a \) is
[JEE (Main) 2019]
(a) \( \frac{3}{5} \)
(b) \( \frac{8}{5} \)
(c) \( \frac{3}{2} \)
(d) \( \frac{1}{2} \)
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