Question

the moment of inertia of a uniform ring of mass M and radius r about and tangent lying in it's on plane is​

Answer 1

Here is the answer with explanation

Answer 2

Moment of inertia of a uniform ring is 3/2 mr²

Mass of the ring = m (Given)

Radius of the ring = r (Given)

Let the tangent of the ring = AB

Let the diameter of the ring = XY

According to the parallel axis theorem -

I (AB) = I (XY) + mr²

Moment of inertia about its diameter = 1/2 mr²

Substituting the value -

I (AB) = 1/2 mr² + mr²

= 3/2 mr²

Thus, the moment of inertia is 3/2 mr²