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…
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 of the rods is at the
origin. The moment of inertia of this system about Z-axis is
$\frac{2 M L^2}{3}$
$\frac{4 M L^2}{3}$
$\frac{5 M L^2}{3}$
$\frac{ M L^2}{3}$
Solution
The moment of inertia about Z-axis is given by
$\begin{aligned} I & =I_x+I_y+I_z \\ I_x & =I_y=\frac{1}{3} M L^2\end{aligned}$
( $\because$ Moment of inertia of $a$ rod of mass $M$ and length $L$ about its one end $=\frac{M L^2}{3}$ ) $I_z=0$, as the rod lies in the Z-axis
So, $I=\frac{M L^2}{3}+\frac{M L^2}{3}+0=\frac{2 M L^2}{3}$
