Question

A uniform sphere of mass M; radius R has a moment of inertia, I; about its symmetry axis. The shpere is reshaped into a uniform circular disc. The M.I of disc about a tangent perpendicular to plane of disc is 3/5 I . The radius of disc is

(1) R/2

(2) 3R/5

(3) 2R/3

(4) 3R/2

Answer 1

(3) 2R/3

The symmetry axis of sphere is any diameter of sphere. Therefore

I = 2/5 MR² ....(i)

Let r be radius of disc into which sphere is reshaped. Mass of disc is same as that of sphere i.e. M. The M.I, I; of disc about given axis is