Question

Find the MOI about AB axis.

• A. $\frac{2}{3}M{L}^2$
• B. $\frac{4}{3}M{L}^2$
• C. $\frac{3}{2}M{L}^2$
• D. $\frac{3}{4}M{L}^2$

Answer 1

The correct option is D $\frac{3}{4}M{L}^2$

$I_{AB}=I_A+I_B+I_C$

$\Rightarrow I_{AB}=M{\left(o\right)}^2+M{\left(o\right)}^2+M{\left(OC\right)}^2$

$OC=AC\sin {60}^o=\frac{\sqrt{3}}{2}AC=\frac{\sqrt{3}}{2}L$

So,$I_{AB}=m{\left(\frac{\sqrt{3}}{2}L\right)}^2$

$I_{AB}=\frac{3m}{4}{L}^2$

Option -$D$ is correct.