First slide

Moment of intertia

Question

A square is made by joining four rods each of mass M and length L. Its moment of inertia about an axis PQ, in its plane and passing through one of its corner is

Moderate

A

$6 M L^{2}$
B

$\frac{4}{3} M L^{2}$
C

$\frac{8}{3} M L^{2}$
D

$\frac{10}{3} M L^{2}$

Solution

By theorem of parallel axes, $I_{1} = I_{2} + (4 M) r^{2}$
$= 4 [\frac{M L^{2}}{3} \sin^{2} 45 °] + 4 M {[\frac{\sqrt{2} L}{2}]}^{2} = \frac{8}{3} M L^{2}$

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