Q80 / 105 · JEE Main 2008 · Physics

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

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

Solution

$$ I=I_{c m}+m\left(\frac{a \sqrt{2}}{2}\right)^2=\frac{m a^2}{6}+\frac{m a^2}{2}=\frac{2}{3} m a^2 $$

Hence, the correct answer is option: 'D'.

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