A circular ring of radius `10 cm` is made of a wire of mass `0.02 g//cm`. Calculate its radius of gyration and moment of inertia about an axis passing perpendicular to its plane through the centre of the ring.

Explanation

Here, `r = 10 cm = 0.1 m`
Length of wire `= 2 pi r = 2 pi xx 10 = 20 pi cm`
Mass of ring, `m = 0.02 xx 20pi kg = 0.4 pi kg`
About an axis passing perpendicular to its plane, through centre of the ring,
`K = r = 0.1 m`
Moment of inertia of the ring about the given axis, `I = mK^(2) = mr^(2)`
`= 0.4 pi (0.1)^(2) = 4pi xx 10^(-3) kg m^(2)`