The moment of inertia of disc of radius $R$ about its axis is

$I=\frac{M^{\text{'}}{R}^2}{2}$

where, $M^{\text{'}}=$ mass of complete disc $=2M$

$I=\frac{2M{R}^2}{2}$

$I=M{R}^2 ...\left(\mathrm{i}\right)$

If $I_1$ be the moment of inertia of semicircular disc about its. axis, then disc may be assumed as combination of two semi-circular parts,

Thus, $I=I_1+I_1\Rightarrow I_1=\frac{I}{2}=\frac{M{R}^2}{2}$