Question

A square sheet of side 'a' is of mass 'M'.Its moment of inertia about a diagonal is:

• A. $\frac{M{a}^2}{8}$
• B. $\frac{M{a}^2}{6}$
• C. $\frac{M{a}^2}{12}$
• D. $\frac{M{a}^2}{9}$

Answer 1

The correct option is C $\frac{M{a}^2}{12}$

Given,

Mass of square is $m$

Mass of each triangle is, $m_t=\frac{m}{2}$

Height of triangle = $a\sin {45}^o$

Moment of inertia of one triangle, $I=\frac{m_t{h}^2}{6}=\frac{1}{6}\times \left(\frac{m}{2}\right){\left(a\sin {45}^o\right)}^2=\frac{m{a}^2}{24}$

Total inertia, $I_{total}=2I=2\times \frac{m{a}^2}{24}=\frac{m{a}^2}{12}$

Hence, momet of inertia is $\frac{m{a}^2}{12}$