Q. Three 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 of the rod is at the origin. The moment of inertia of this system about $Z$ axis is
A) $\frac{2ML^{2}}{3}$
B) $\frac{4ML^{2}}{3}$
C) $\frac{5ML^{2}}{3}$
D) $\frac{ML^{2}}{3}$
Explanation
(a) M.I. of rod (1) about $Z -$ axis, $I_{1} = \frac{Ml^{2}}{3}$
M.I. of rod (2) about $Z -$ axis, $I_{2} = \frac{Ml^{2}}{3}$
M.I. of rod (3) about $Z -$ axis, $I_{3} = 0$
Because this rod lies on $Z$-axis
$\therefore I_{system} = I_{1} + I_{2} + I_{3} = \frac{2Ml^{2}}{3}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.