From a circular disc of radius $R$ and mass $9M$,a small disc of radius $\frac{R}{3}$ is removed. The moment of inertia of the remaining disc about an axis perpendicular to the plane of the disc and passing through $O$ is:

  • A
    $4 MR^2$
  • B
    $\frac{40}{9} MR^2$
  • C
    $10 MR^2$
  • D
    $\frac{37}{9} MR^2$

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$A$ uniform circular disc of radius $R$ and mass $M$ is rotating about an axis perpendicular to its plane and passing through its centre. $A$ small circular part of radius $R/2$ is removed from the original disc as shown in the figure. Find the moment of inertia of the remaining part of the original disc about the axis as given above.

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