Consider a uniform square plate of side ' $a$ ' and mass ' $m$ '. The moment of inertia of this plate about…
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 corners is
$\frac{5}{6} m a^2$
$\frac{1}{12} m a^2$
$\frac{7}{12} m a^2$
$\frac{2}{3} m a^2$
Solution
$
I=I_{c m}+m\left(\frac{a \sqrt{2}}{2}\right)^2=\frac{m a^2}{6}+\frac{m a^2}{2}=\frac{2}{3} m a^2
$