Question

Four thin rods of same mass 'M' and same length 'l', form a square as shown in the figure. Moment of inertia of this system about an axis through centre O and perpendicular to its plane is

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

Answer 1

The correct option is A $\frac{4}{3}M{l}^2.$

Moment of inertia of rod AB about point $P=\frac{1}{12}M{l}^2$
M.I. of rod AB about point $O=\frac{M{l}^2}{12}+M{\left(\frac{1}{2}\right)}^2=\frac{1}{3}M{l}^2$ [by the theorem of parallel axis]
and the system consists of 4 rods of similar type so by the symmetry $I_{System}=\frac{4}{3}M{l}^2.$