Question

The moment of inertia of a semicircular ring about its centre is

Answer 1

The moment of inertia of a uniform semicircular wire of mass m and radius r about a line perpendicular to the plane of the wire through the center

Using Parallel Axis Theorem

I0=ICM+Md^2

where Io= Moment of inertia about centre=MR^2

and ICM= Moment of inertia about centre of mass

d=2R/π(distance between centre of mass and centre)

ICM=I0−M(2R/π)^2

=MR^2[1−4/π^2]