Question

The figure shows a rod of length Land
mass M lying in the x - y plane passing
through the origin at its centre. The
moment of inertia of the rod about the x-
axis is
Y
M
L​

Answer 1

Moment of inertial of a rod of about an axis passing through centre and perpendicular to length :

I=12Ml2

moment of inertia of the rod about an axis inclined an angle θ to the original axis:

I′=Isin2θ

The line x=y makes an angle of 45∘ about x and y axes.

Hence I′=Isin245∘=2I

moment of inertia of both rods about the line passing through x=y

Itwo/,rods=2I′

=2×2I=I

=12Ml2