Question

Consider a uniform square plate of side $a$ and mass $m$. The moment of inertia of this plate about an axis perpendicular to its plane and passing through one of its corner is

• A. $\frac{5}{6}m{a}^2$
• B. $\frac{1}{12}m{a}^2$
• C. $\frac{7}{12}m{a}^2$
• D. $\frac{2}{3}m{a}^2$

Answer 1

The correct option is A $\frac{5}{6}m{a}^2$

The moment of inertia of square plate about an axis through its centre of mass passing perpendicular to the plane is given by $I_{CM}=m{a}^2/6$

The moment of inertia about parallel axis through one corner $O$ is given by,

$I=I_{CM}+m(a/\sqrt{2}{)}^2$

$\therefore I=m{a}^2/6+m{a}^2/2=\left(2/3\right)m{a}^2$

Hence correct option is $D$.