Question

Find the MOI of a uniform square plate of mass $m$ and edge $a$ about one of its diagonals.

• A. $\frac{M{a}^2}{6}$
• B. $\frac{M{a}^2}{3}$
• C. $\frac{M{a}^2}{9}$
• D. $\frac{M{a}^2}{12}$

Answer 1

The correct option is D $\frac{M{a}^2}{12}$

Using perpendicular axis theorem,
$I_z=I_x+I_y=I_1+I_2=2I_x=2I_1$
$I_1=I_x$
Moment of inertia about diagonal is
$\therefore I_1=\frac{M{a}^2}{12}$