Question

Two identical rods each of mass M and length L are kept according to the figure. Find the moment of inertia of the rods about an axis passing through O perpendicular to the plane of the rods.

• A. $\frac{M{L}^2}{6}$
• B. $\frac{M{L}^2}{3}$
• C. $\frac{2M{L}^2}{3}$
• D. $\frac{M{L}^2}{4}$

Answer 1

Answer: (C)

$\frac{2M{L}^2}{3}$

Let us take the figure as two rods $\left(1\right)$ and $\left(2\right)$

Now, moment of inertia of $\left(1\right)=I_1$

moment of inertia of $\left(2\right)=I_2$

$MOI$ of rod about any axis passing from are end and perpendicular to plane $=\frac{M{L}^2}{3}$

$\Rightarrow I_1=\frac{M{L}^2}{3}$

$MomentofInertia$ of rod about any axis passing from are end and perpendicular to plane $=\frac{M{L}^2}{3}$

$I_2=\frac{M{L}^2}{3}$

Total moment of inertia $I$

$I=I_1+I_2$

$I=\frac{M{L}^2}{3}+\frac{M{L}^2}{3}\Rightarrow I=\frac{2}{3}m{L}^2$