question_answer

Figure shows a thin metallic triangular sheet ABC. The sides AB and BC are of equal lengths l. The mass of the sheet is M. What is its moment of inertia about AC?

A) \[\frac{M{{l}^{2}}}{18}\]       

B)   \[\frac{M{{l}^{2}}}{12}\]

C) \[\frac{M{{l}^{2}}}{6}\]                     

D) \[\frac{M{{l}^{2}}}{4}\]

Correct Answer: B

Solution :

\[h\,\,=\,\,l\,cos 45{}^\circ =\frac{1}{\sqrt{2}}\] \[{{I}_{AC}}=\frac{1}{6}M{{h}^{2}}=\frac{1}{6}M\,{{\left( \frac{1}{\sqrt{2}} \right)}^{2}}\,\,=\,\,\frac{M{{l}^{2}}}{12}\]