Question

About _____ axis in the following fig, the moment of inertia of the rectangular lamina is the maximum.

Answer 1

$I_1=\frac{1}{12}m(a^2+b^2)$

$\Rightarrow I_2=\frac{1}{3}m(a^2+b^2)$

$\Rightarrow I_3=\frac{1}{6}m\left(\frac{a^2{b}^2}{a^2+b^2}\right)$

$\Rightarrow I_4=\frac{1}{12}m(a^2+b^2)$

Clearly $I_2$ is larger than $I_1,I_3,I_4$

$\therefore$ About $2$ axis in the figure, the MOI of the rectangle is maximum.

Hence, the answer is $2.$