Question

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

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

Answer 1

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

Moment of inertia of system $I=I_A+I_B+I_C+I_D$
$\Rightarrow I=0+m(AO{)}^2+m(AO{)}^2+m(AC{)}^2$
AO cos ${45}^o=\frac{l}{2}\Rightarrow AO=\frac{1}{\sqrt{2}}$

or $I=\frac{2m{l}^2}{2}+m{\left(\frac{2l}{\sqrt{2}}\right)}^2=\frac{2m{l}^2}{2}+\frac{4m{l}^2}{2}$
or $I=\frac{6m{l}^2}{2}=3m{l}^2$