Question

Find the moment of inertia ($\text{MI}$) of an uniform rod of mass $3\text{kg}$ and length $2\text{m}$ about an axis ($y{y}^{\prime }$) perpendicular to the plane of rod and passing through it's one end ($A$) as shown in the figure.

• A. ${\text{1 kg-m}}^2$
• B. ${\text{3 kg-m}}^2$
• C. ${\text{4 kg-m}}^2$
• D. ${\text{12 kg-m}}^2$

Answer 1

The correct option is C ${\text{4 kg-m}}^2$

mass of rod, $m=3\text{kg}$
length of the rod, $l=2\text{m}$
The $\text{MI}$ of rod about an axis$\perp$ to rod's plane and passing through it's one end, given by:
$I=\frac{m{l}^2}{3}$
$I=\frac{\left(3\right)(2{)}^2}{3}=4{\text{kg-m}}^2$
$\therefore$ $\text{MI}$ of rod about axis $y{y}^{\prime }$ is $4{\text{kg-m}}^2$