= Solution
Let $O$ be the original disk centre and $C$ the hole centre. The source geometry has $OS=a$, $OC=CS=a/2$, all collinear. The removed disk has <mass> $m/4$, since its <area> is one quarter of the original disk's. Use the <parallel axis theorem> for both the original disk and the removed disk:
$$
I_S^{\rm full}=\frac12ma^2+ma^2=\frac32ma^2,
\qquad
I_S^{\rm hole}=\frac12\frac m4\left(\frac a2\right)^2+\frac m4\left(\frac a2\right)^2
=\frac{3ma^2}{32}.
$$
Subtracting the missing material's <moment of inertia> gives
$$
\boxed{I_S=\frac{45ma^2}{32}.}
$$
Here $m$ continues to denote the original unperforated disk <mass>; the earring itself has <mass> $3m/4$.
\Image[/past-exam-of-the-physics-1-paper-of-the-university-of-oxford/2017-resit-perforated-pendulum.png]
{title=Equilibrium geometry and mass subtraction for a perforated-disk physical pendulum}
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