The moment of inertia of a thin uniform semicircular wire of mass ‘M’ and radius ‘r’ about a line perpendicular to the plane of the wire through the centre is:

for a semi-circular uniform ring of mass M and radius R, moment of inertia about the axis perpendicular to the plane of ring and passing through the centre, is given as,

  $\mathrm{I}={\mathrm{MR}}^2$