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  4. 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 square plate is given by:

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Q. 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 square plate is given by:

JEE MainJEE Main 2021System of Particles and Rotational Motion

Solution:

According to perpendicular Axis theorem.
image
$I _{ x }+ I _{ y }= I _{ z }$
$I _{ z }$
$ \Rightarrow \frac{ m \ell^{2}}{3}+\frac{ m \ell^{2}}{3}$
$=\frac{2 m \ell^{2}}{3}$