Question

Three thin uniform rods each of mass $m$and length $l$ are placed along the three axes of a Cartesian co-ordinate system with their one end at the origin. The moment of inertia of the system about $z-axis$ is

• A. $\frac{m{l}^2}{3}$
• B. $\frac{2m{l}^2}{3}$
• C. $\frac{m{l}^2}{6}$
• D. $m{l}^2$

Answer 1

The correct option is B $\frac{2m{l}^2}{3}$

Moment of Inertia $I$ of system about $z-axis$,
$I=I_x+I_y+I_z$
$I_x=I_y=\frac{m{l}^2}{3}$(Moment of Inertia of a rod about corner)
$I_z=0$ (Moment of Inertia of a rod along the length)
$I=\frac{m{l}^2}{3}+\frac{m{l}^2}{3}+0$

= $\frac{2m{l}^2}{3}$