Find the moment of inertia of a thin uniform rod about an axis perpendicular to its length and passing through a point which is at a distance of `1/3` from one end. Also find radius of gyration about that axis.

Explanation

Let P be the point at a distance `l/3` from one end . It is distance of `(l/2-l/3)=l/6` from the centre as shown in the figure .

By parallel axes theorem `I = I_(c ) +Mr^(2)`
`(Ml^(2))/(12) + M(l/6)^(2) = (Ml^(2))/9`
(ii) The radius of gyration
`K = sqrt(I/M)= sqrt((Ml^(2))/(9M)) = l/3 `