A semicircular disc of mass M and radius R is free to rotate about...

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

$I = \dfrac{M^{'}R^{2}}{2}$

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

$I = \dfrac{2MR^{2}}{2}$

$I = MR^{2}... \left(i\right)$

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, $I = {I}_{1} + {I}_{1} ⇒ {I}_{1} = \dfrac{I}{2} = \dfrac{MR^{2}}{2}$