Question

Three identical thin rods, each of mass m and length l are joined to form an equilateral triangle. Find the moment of inertia of the triangle about one of its sides.

• A. $\frac{M{l}^2}{2}$
• B. $\frac{M{l}^2}{3}$
• C. $\frac{M{l}^2}{9}$
• D. $\frac{M{l}^2}{12}$

Answer 1

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

$MOIofsystem=I_{AB}+I_{BC}+I_{AC}{I}_{AB}=0\left(itisattheaxis\right)I_{BC}=\frac{1}{3}m(l_{eff.}{)}^2=\frac{1}{3}m(l\sin 60{)}^2=\frac{1}{3}m{l}^2\times \frac{3}{4}\therefore MOI=0+\frac{m{l}^2}{4}+\frac{m{l}^2}{4}=\frac{m{l}^2}{2}$