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Moment of inertia

Question:

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 :

  1. $\frac{\mathrm{M} l^{2}}{6}$

  2. $\mathrm{M} l^{2}$

  3. $\frac{\mathrm{M} l^{2}}{12}$

  4. $\frac{2}{3} \mathrm{M} l^{2}$


Correct Option: , 4

Solution:

According to perpendicular Axis theorem.

$\mathrm{I}_{\mathrm{x}}+\mathrm{I}_{\mathrm{y}}=\mathrm{I}_{\mathrm{z}}$

$\mathrm{I}_{\mathrm{z}} \Rightarrow \frac{\mathrm{m} \ell^{2}}{3}+\frac{\mathrm{m} \ell^{2}}{3}$

$=\frac{2 m \ell^{2}}{3}$

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