Question

Four equal masses, $m$ each are placed at the corners of a square of length $(l)$ as shown in the figure. The moment of inertia of the system about an axis passing through $A$ and parallel to $DB$ would be :

• A. $ml l^{2}$
• B. $2 m l^{2}$
• C. $3 m l^{2}$
• D. $\sqrt{3} m l^{2}$

Answer 1

Answer: (C)

Moment of inertia of point mass
$=$ mass $\times(\text { Perpendicular distance from axis })^{2}$

Moment of Inertia
$= m (0)^{2}+ m (l \sqrt{2})^{2}+ m \left(\frac{l}{\sqrt{2}}\right)^{2}+ m \left(\frac{l}{\sqrt{2}}\right)^{2}$
$=3 \,ml^2$