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

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

(a) $\displaystyle \frac{m L^2}{6}$

(b) $\displaystyle \frac{3 m L^2}{2}$

(c) $\displaystyle \frac{m L^2}{3}$

(d) $\displaystyle \frac{m L^2}{2}$

Sol: Using formula , $\displaystyle I = \frac{m L^2}{3}sin^2 \alpha$
Required Moment of Inertia , $\displaystyle I = \frac{m L^2}{3}sin^2 60 + \frac{m L^2}{3}sin^2 60$
$\displaystyle I = 2 \times \frac{m L^2}{3} \times \frac{3}{4}$
$\displaystyle I = \frac{m L^2}{2}$