Question

Three thin uniform rods each of mass $M$ and length $L$ are placed along the three axes of a cartesian coordinate system. The moment of inertia of the system about $z$ -axis is

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

Answer 1

Answer: (B)

The moment of inertia of a thin rod of mass $M$ and
length $L$ about an axis passing through one end of the rod and
perpendicular to the length of the rod is $\frac{1}{3} M L^{2}$
Moment of inertia of the rod
about $z$ -axis is zero.
Therefore, moment of inertia of
the system about the $z$ -axis

$=\frac{1}{3} M L^{2}+\frac{1}{3} M L^{2}+0=\frac{2}{3} M L^{2}$
Note : For rods along $x$ and $y$ -axes, $z$ -axis is an axis passing
through one end of the rod and perpendicular to the length of the rod.