Question

Find the $M.I$. of a thin uniform rod about an axis perpendicular to tis length and passing through a point which is at a distance $"\frac{l}{3}"$ from one end. Then the radius of gyration about that axis.

• A. $\frac{l}{3}$
• B. $\frac{l}{2}$
• C. $\frac{l}{4}$
• D. $\frac{l}{6}$

Answer 1

The correct option is A $\frac{l}{3}$

Let R be radius of gyration

Moment of inertia through centre of rod is $\frac{M{l}^2}{12}$

Moment of inertia through a point at a distance is $\frac{l}{3}$ from one end is equal to a distance of $\frac{l}{6}$ from the centre of rod is

$\frac{M{l}^2}{12}+M(\frac{l}{6}{)}^2=\frac{M{l}^2}{9}$

$\frac{M{l}^2}{9}=M{R}^2$

$R=\frac{l}{3}$