What is the moment of inertia of a square she | vedclass

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(B) Side length $= l$. Mass per unit area $= \mu$. Total mass $M = \mu l^2$. For a square sheet,the moment of inertia about an axis passing through it

Vedclass · Accepted Answer

$\frac{\mu l^4}{6}$

Vedclass · Answer

(B) Side length $= l$. Mass per unit area $= \mu$. Total mass $M = \mu l^2$. For a square sheet,the moment of inertia about an axis passing through its centre and parallel to one of its sides is $I_x = I_y = \frac{M l^2}{12}$. By the perpendicular axis theorem,the moment of inertia about an axis passing through the centre and perpendicular to its plane is $I_z = I_x + I_y$. $I_z = \frac{M l^2}{12} + \frac{M l^2}{12} = \frac{2 M l^2}{12} = \frac{M l^2}{6}$. Substituting $M = \mu l^2$,we get $I_z = \frac{(\mu l^2) l^2}{6} = \frac{\mu l^4}{6}$. Thus,the correct option is $B$.

What is the moment of inertia of a square sheet of side $l$ and mass per unit area $\mu$ about an axis passing through the centre and perpendicular to its plane?

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