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.

Find the moment of inertia of a thin uniform rod about an axis perpend

1.	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.
Answer» Solution :(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)`