Question

The moment of inertia of the plate about its base parallel to the x-axis is

• A. $\frac{M{L}^2}{18}$
• B. $\frac{M{L}^2}{36}$
• C. $\frac{M{L}^2}{24}$
• D. None of these

Answer 1

The correct option is C $\frac{M{L}^2}{24}$

From geometry, $OA=OB=\frac{L}{\sqrt{2}}$

Moment of inertia about an axis passing through C and perpendicular to plane, $I_C=\frac{M{a}^2}{6}$

$I_C=\frac{M(\frac{L}{\sqrt{2}}{)}^2}{6}=\frac{M{L}^2}{12}$

Using perpendicular axis theorem, $I_y+I_{AB}=I_C$

But due to symmetry $I_{AB}=I_y$

$⟹I_{AB}=\frac{I_C}{2}=\frac{M{L}^2}{24}$