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

Difficult

A

$6 {ML}^{2}$
B

$\frac{4}{3} {ML}^{2}$
C

$\frac{8}{3} {ML}^{2}$
D

$\frac{10}{3} {ML}^{2}$

Solution

$\begin{array}{l} I = I_{cm} + M_{tot} r^{2} \\ = 4 [\frac{{ML}^{2}}{3} \sin^{2} 45^{0}] + 4 M {[\frac{L}{\sqrt{2}}]}^{2} \\ = \frac{8}{3} {ML}^{2} \end{array}$

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