Question

The moment of inertia of a square plate of side $l$ about the axis passing through one of the corner and perpendicular to the plane of the square plate is given by:

• A. $\frac{M{l}^2}{12}$
• B. $M{l}^2$
• C. $\frac{M{l}^2}{6}$
• D. $\frac{2}{3}M{l}^2$

Answer 1

The correct option is D $\frac{2}{3}M{l}^2$

Moment of inertia of the square plate about an axis passing through its center of mass and perpendicular to its plane is :
$I_{com}=\frac{M{l}^2}{6}$
According to the parallel axis theorem, moment of inertia of the plate about the axis passing from the corner and perpendicular to its plane is :
$I=I_{com}+M{x}^2$
Here, the distance between this axis from com is equal to half the length of the diagonal of the square.
$i.e.x=\frac{l\sqrt{2}}{2}=\frac{l}{\sqrt{2}}$
$\Rightarrow I=\frac{M{l}^2}{6}+\frac{M{l}^2}{2}$
Or, $I=\frac{2M{l}^2}{3}$