Question

Two thin rod of mass $m$ and length $l$ are joined together to make a ${}^{\prime }{L}^{\prime }$ shaped structure. Find out moment of inertia of structure about an axis passing through their common joining point and perpendicular to the plane of structure.

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

Answer 1

The correct option is C $\frac{2m{l}^2}{3}$

Both rod $oa$ and $ob$ are joined at common point $o$.
So, moment of Inertia of rod $oa$ about $x{x}^{\prime }$
$I_{oa}=\frac{m{l}^2}{3}$
and moment of inertia of rod $ob$ about $x{x}^{\prime }$
$I_{ob}=\frac{m{l}^2}{3}$

Moment of inertia of $L$ shaped structure is given by $I_{net}=I_{oa}+I_{ob}$
$I_{net}=\frac{m{l}^2}{3}+\frac{m{l}^2}{3}$
$I_{net}=\frac{2}{3}m{l}^2$