A thin circular plate of mass $M$ and radius $R$ has its density varying as $\mathit{\text{ρ}}\left(r\right){\text{=ρ}}_{\text{0}}\mathit{\text{r}}$ with ${\rho }_0$ 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 and passing through its edge is $I=aM{R}^2$. The value of the coefficient $a$ is:

• A

  $\frac{3}{5}$
• B

  $\frac{1}{2}$
• Correct answer
  C

  $\frac{8}{5}$
• D

  $\frac{3}{2}$

Hence, the correct answer is option: 'C'.