Question

$\begin{array}{c}\text{Three identical uniform rods each of length}1m\text{and}\\ \text{mass}2kg\text{are arranged to form an equilateral triangle.}\\ \text{What is the moment of inertia of the system about an to}\\ \text{axis passing through one corner and perpendicular to}\\ \text{the plane of the triangle:}\end{array}$

• A. $4kg-m^2$
• B. $3kg-m^2$
• C. $2kg-m^2$
• D. $3/2kg-m^2$

Answer 1

The correct option is B $3kg-m^2$

$\begin{array}{c}I=\frac{m{l}^2}{3}+\frac{m{l}^2}{3}+\left[\frac{m{l}^2}{12}+m{\left(\frac{\sqrt{3}l}{2}\right)}^2\right]\\ =\frac{2m{c}^2}{3}+\left[\frac{m{c}^2}{12}+\frac{3m{l}^2}{4}\right]\\ =\frac{2m{l}^2}{3}+\frac{10m{l}^2}{12}\\ =\frac{18m{l}^2}{12}\\ =\frac{3m{l}^2}{2}\\ =3kg-m^2\\ Hence,theoptionBisthecorrectanswer.\end{array}$