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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:

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a

$\frac{2}{3} {Ml}^{2}$

b

$\frac{{Ml}^{2}}{6}$

c

$\frac{{Ml}^{2}}{12}$

d

${Ml}^{2}$

answer is D.

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Detailed Solution

Question Image

From the figure according to the perpendicular axis theorem

$I_{X} + I_{Y} = I_{Z}$

$I_{Z} = \frac{{ml}^{2}}{3} + \frac{{ml}^{2}}{3} = \frac{2 {ml}^{2}}{3}$

Hence the correct answer is $\frac{2 {ml}^{2}}{3} .$

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