Physics - Rotation Question with Solution | TestHub

Given plate has mass M and area$3a^2$

A square plate of side$2a$(made of the same material) has mass$\frac{4M}{3}$and

Therefore moment of inertia about its axis is

$I_1=\frac{1}{6}\left(\frac{4M}{3}\right){\left(2a\right)}^2$

A square plate of side$a$(made of the same material) has mass$\frac{M}{3}$and

Therefore moment of inertia about its axis is$I_2=\frac{1}{6}\left(\frac{M}{3}\right)a^2$

Moment of inertia of the given plate is

$I=I_1-I_2=\frac{5}{6}M{a}^2$