Question

Four point masses, each of value $m$, are placed at the corners of a square ABCD of side $l$. The moment of inertia of this system about an axis passing through A and parallel to BD is

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

Answer 1

The correct option is C $3m{l}^2$


$I_{n{n}^{\prime }}=M.I$ due to the point mass at B +
M. I due to the point mass at D+
M.I due to the point mass at C,
$I_{n{n}^{\prime }}=2\times m{\left(\frac{l}{\sqrt{2}}\right)}^2+m(\sqrt{2}l{)}^2$
$=m{l}^2+2m{l}^2=3m{l}^2$

Why this question? "Understanding the concept that moment of inertia is an additive quantity and we can add moment of inertia of different bodies about a single axis to find out the moment of inertia of the system about that particular axis."