Question

A square plate of mass $M$ and edge $L$ is shown in the fig. The moment of inertia of the plate about the axis in the plane of plate and passing through one of its vertex making an angle ${15}^0$ with the horizontal is

• A. $\frac{M{L}^2}{12}$
• B. $\frac{11M{L}^2}{24}$
• C. $\frac{7M{L}^2}{12}$
• D. none of these

Answer 1

The correct option is B $\frac{11M{L}^2}{24}$

From the figure we have $AO=\frac{L}{\sqrt{2}}$
Thus we get the perpendicular distance between the axis about which the plate is rotated and the center of mass as
$AN=\frac{L}{\sqrt{2}}cos{30}^o=\frac{L\sqrt{3}}{2\sqrt{2}}$
Now we have $I_{P{P}^{\prime }}=\frac{M{L}^2}{12}$
Thus using parallel axis theorem we get the moment of inertia about the given axis as
$\frac{11M{L}^2}{24}$