Question

A metal ring of radius 20 cm is rotating about a transverse axis passing through its centre. What will be its radius of gyration about the same axis?

Answer 1

Given: R = 20 cm

For a ring, the moment of inertia about its central transverse axis is:

I = MR²   ...(i)

The radius of gyration (k) is defined by the relation:

I = Mk²   ...(ii)

From equations (i) and (ii), we get

Mk² = MR²

k² = R²

k = R

k = 20 cm

∴ The radius of gyration of a metal ring about its transverse central axis is exactly equal to its radius, which is 20 cm.