First slide

Moment of intertia

Question

A thin rod AB of mass 1 kg and length 1m is bent as its mid point c at an angle $60^{o}$ as shown in figure. PQ is the bisector of the angle ACB. Then moment of inertia of the bent rod about the line PQ is

Difficult

A

$\frac{1}{96} kg - m^{2}$
B

$\frac{1}{48} kg - m^{2}$
C

$\frac{1}{24} kg - m^{2}$
D

$\frac{1}{12} kg - m^{2}$

Solution

$I_{PQ} = (\frac{1}{3} \times 0 .5 \times {(0 .5)}^{2} \times \sin^{2} 30^{o}) \times 2 kg - m^{2} = \frac{1}{48} kg - m^{2}$

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