Question

Four point objects of mass $m$ are located at the corners of a square of side $\text{S}$ as shown in the figure below. Determine the moment of inertia of this system about $\text{cd}$ as shown in the figure.

• A. $4m{S}^2$
• B. $m{S}^2$
• C. $2m{S}^2$
• D. $0.5m{S}^2$

Answer 1

The correct option is B $m{S}^2$

Here, two masses lie on the axis. Hence moment of inertia about $\text{cd}$ for those two masses is zero.
Other two masses are $\frac{S\sqrt{2}}{2}$ away from the axis.

Hence, $I=\sum r^2\cdot m$
$I=m{\left(\frac{S}{\sqrt{2}}\right)}^2+m{\left(\frac{S}{\sqrt{2}}\right)}^2$
$I=m{S}^2$