The moment of inertia of disc of radius R about its axis is I=
M′R2
2
where, M′= mass of complete disc =2M ∴I=
2MR2
2
I=MR2 .......(i) If I1 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=I1+I1⇒I1=