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

Answer 1

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

$I_A=0$ (on the Axis .)
$I_B=I_D=m{r}^2$
$=m{\left(\frac{l}{\sqrt{2}}\right)}^2$
$=\frac{m{l}^2}{2}$
$I_C=m(\sqrt{2}l{)}^2$
$I_C=2m{l}^2$
$I=I_A+I_B+I_C+I_D$
$I=0+\frac{m{l}^2}{2}+\frac{m{l}^2}{2}+2m{l}^2$
$I=3m{l}^2$