Question

A square plate of side $l$ has mass $M.$ What is its moment of inertia about one of its diagonals?

• A. $\frac{M{l}^2}{6}$
• B. $\frac{M{l}^2}{12}$
• C. $\frac{M{l}^2}{3}$
• D. $\frac{M{l}^2}{4}$

Answer 1

Answer: (B)

Moment of inertia of a square about an axis through
its centre and perpendicular to its plane
$I_O=\frac{M}{12}\left(l^2+l^2\right)=\frac{M{l}^2}{6}$
According to theorem of perpendicular
axes, we get
$I_1+I_2=I_O=\frac{M{l}^2}{6}$
But $I_1=I_2$ (By symmetry)
$\therefore 2I_1=\frac{M{l}^2}{6}$ or $I_1=\frac{M{l}^2}{12}$