question_answer

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) \[I>\frac{m{{a}^{2}}}{12}\]

B) \[\frac{m{{a}^{2}}}{24}<I<\frac{m{{a}^{2}}}{12}\]

C) \[I=\frac{m{{a}^{2}}}{24}\]

D) \[I=\frac{m{{a}^{2}}}{12}\]

Correct Answer: D

Solution :

[d] For a thin uniform square sheet       \[{{I}_{1}}={{I}_{2}}={{I}_{3}}=\frac{m{{a}^{2}}}{12}\]