Question

A thin uniform rod of mass $10\text{kg}$ and length $6\text{m}$ is rotating about an axis perpendicular to its plane, passing through the midpoint of the rod. Find the moment of inertia of the rod about this axis.

• A. $120{\text{kg-m}}^2$
• B. $30{\text{kg-m}}^2$
• C. $60{\text{kg-m}}^2$
• D. $360{\text{kg-m}}^2$

Answer 1

The correct option is B $30{\text{kg-m}}^2$

Given,
Mass of the rod $\left(m\right)=10\text{kg}$
Length of the rod $\left(l\right)=6\text{m}$
Moment of inertia of the rod about $z-$ axis as shown in figure is
$I_z=\frac{m{l}^2}{12}$
$=\frac{10\times (6{)}^2}{12}=30{\text{kg-m}}^2$