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 `l/3` from one end. Also find radius of gyration about that axis.

Explanation

(i) Let P be the point at a distance `(l)/(3)` from one end. It is at a 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)`
(ii) The radius of gyration,
`K = sqrt((l)/(M))=sqrt((Ml^(2))/(9M))=(l)/(3)`