Question

A square lamina of mass density $\left(\sigma \right)=10{\text{kg/m}}^2$ and side length $2\text{m}$ is rotated about an axis passing through one of it’s side as shown in figure. Find the moment of inertia of the lamina about this axis.

• A. ${\text{26.66 kg-m}}^2$
• B. ${\text{16.66 kg-m}}^2$
• C. ${\text{26.33 kg-m}}^2$
• D. ${\text{53.33 kg-m}}^2$

Answer 1

The correct option is D ${\text{53.33 kg-m}}^2$

Given, mass density $\left(\sigma \right)=10{\text{kg/m}}^2$
Side length of square lamina (a) = $2\text{m}$

From definition,
mass density $\left(\sigma \right)=\frac{\text{Mass of square lamina(M)}}{\text{Area of square lamina(A)}}$
$\Rightarrow$ Mass of square lamina, $\left(M\right)=\sigma \times a^2$
$=10\times 2^2=40\text{kg}$

Moment of inertia of square lamina about an axis passing through one of it’s side, $I=\frac{M{a}^2}{3}$

$=\frac{40\times (2{)}^2}{3}$
$=53.33{\text{kg-m}}^2$