From a disc of radius R and mass M, a circular hole of diameter R, whose rim passes through the centre is cut. What is the moment of inertia of the remaining part of the disc about a perpendicular axis, passing through the centre?

13 MR² /32

I = \(\frac{MR^2}{2} - \frac{3\sigma}{2} \pi (\frac{R}{2})^2 (\frac{R}{2})^2\)

where \(\sigma\) = \(\frac{M}{\pi R^2}\)

I = \(\frac{MR^2}{2} - \frac{3\sigma}{2} MR^2\)

  = 13 MR² /32