Question

What is the M.I. of a uniform circular ring of mass M and radius R
passing through its centre and perpendicular to its plane or transverse
axis?​

Answer 1

Explanation:

M.I of ring about an axis = mr²

Using perpendicular axis theorem;

iz = ix + iy

iz = 2ix    (since ix = iy)

we know that, iz = M.I

mr² = 2ix

ix = mr²/2

therefore,  M.I. of a uniform circular ring of mass M and radius R

passing through its centre and perpendicular to its plane is mr²/2 .