Question

What is the moment of inertia of a square sheet of slide $\ell$ and mass per unit area $\mu$ unit area $\mu$ about an axis. Passing through the center and perpendicular to its plane:

• A. $\frac{\mu l^2}{12}$
• B. $\frac{\mu l^2}{6}$
• C. $\frac{\mu l^4}{12}$
• D. $\frac{\mu l^4}{6}$

Answer 1

The correct option is D $\frac{\mu l^4}{6}$

Given that,

Side = $l$

Mass per unit area = $\mu$

Total mass $M=\mu l^2$

Now, the moment of inertia is

$I=\frac{M{R}^2}{12}$

By perpendicular axis theorem

$I=I_x+I_y$

$I=2I_x$

$I=2\times \frac{\mu l^2\times l^2}{12}$

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

Hence, the moment of inertia of a square sheet is $\frac{\mu l^4}{6}$