Question

Three identical rods, each of mass $m$ and length $l$, form an equaliteral triangle. Moment of intertia about one of the side is

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

Answer 1

Answer: (B)

$\frac{m{l}^2}{2}$

MI of CA$=\frac{m{l}^2}{3}{sin}^2\theta$, where $\theta$ is the angle between rod and the axis of rotation.

MI of the system = $2\frac{m{l}^2}{3}{sin}^2\theta =\frac{2m{l}^2}{3}{sin}^2{60}^0=\frac{m{l}^2}{2}$