Question

Two rods each of mass $m$ and length $l$ are joined at the centre to form a cross. The moment of inertia of this cross about an axis passing through the common centre of the rods and perpendicular to the plane formed by them, is :-

• A. $\frac{m{l}^2}{12}$
• B. $\frac{m{l}^2}{6}$
• C. $\frac{m{l}^2}{3}$
• D. $\frac{m{l}^2}{2}$

Answer 1

The correct option is B $\frac{m{l}^2}{6}$

$\begin{array}{c}\text{For a rod having length}\ell \text{and mass}m,\\ \text{its moment of inertia about the axis passing}\\ \text{perpendicularly through its centre is}\\ \frac{m{l}^2}{12}.\end{array}$

$\begin{array}{c}\text{Here, Inet}=\frac{m{l}^2}{12}+\frac{m{l}^2}{12}=\frac{m{l}^2}{6}\\ \text{so, correct answer is B.}\end{array}$