Question

The moment of inertia of a semi-circular ring of mass M and radius R about an axis passing through centre and perpendicular to the plane of ring is

(1) MR²

(2) 1/2 MR²

(3) 2MR²

(4) 3/4 MR²

Answer 1

Correct option is (1) MR²

Distance of mass from centre is same so,

\(I = \int dmR^2\)

\(= R^2\int dm\)

\(= MR^2\)