Question

A thin uniform rod of mass $5\text{kg}$ is rotating about an axis perpendicular to it's plane, passing through midpoint of the rod of length $4\text{m}$. Find the moment of inertia of the rod about this axis.

• A. $66.6{\text{kg.m}}^2$
• B. $6.66{\text{kg.m}}^2$
• C. $33.33{\text{kg.m}}^2$
• D. $3.33{\text{kg.m}}^2$

Answer 1

The correct option is B $6.66{\text{kg.m}}^2$

Mass of rod ($m$) = $5\text{kg}$
length of the rod ($l$) = $4\text{m}$
$\text{MI}$ of rod about an axis($z$), which is $\perp$ to the plane of rod i.e $x-y$ plane will be:
$I_z=\frac{m{l}^2}{12}$
$\Rightarrow I_z=\frac{5\times 4^2}{12}=\frac{80}{12}$
$\therefore I_z=6.66{\text{kg.m}}^2$