Question

Three thin rods each of length $L$ and mass $M$ are placed along $X,Y$ and $Z$ axes in such a way that one end of each rod is at the origin as shown. The moment of inertia of this system about $Z-$ axis is

• A. $\frac{2M{L}^2}{3}$
• B. $\frac{4M{L}^2}{3}$
• C. $\frac{5M{L}^2}{3}$
• D. $\frac{M{L}^2}{3}$

Answer 1

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

$I_z=I_1+I_2+I_3$
$=\frac{M{L}^2}{3}+\frac{M{L}^2}{3}+0$
$=2\frac{M{L}^2}{3}$