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((I)/(M))=sqrt((Ml^(2))/(9M))=(l)/(3)`