Question

Consider a thin uniform square sheet made of a rigid material. If its side is '$a$', mass $m$ and moment of inertia $I$ about one of its diagonals, then :

• A. $I > \frac{ma^{2}}{12}$
• B. $\frac{ma^{2}}{24} < I < \frac{ma^{2}}{12}$
• C. $ I = \frac{ma^{2}}{12}$
• D. $ I = \frac{ma^{2}}{24}$

Answer 1

The Correct Option is B

$I_{z}=\frac{m a^{2}}{6}$ Using perpendicular axis theorem
$2 I_{d}=I_{z} \Rightarrow I_{d}=\frac{m a^{2}}{12}$