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A thin rod of length L and mass m is bent at the middle point 'O' at an angle of 60⁰. The moment of inertia of the rod about an axis passing through 'O' and perpendicular to the plane of the rod will be

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a

$\frac{{ML}^{2}}{6}$

b

$\frac{{ML}^{2}}{12}$

c

$\frac{{ML}^{2}}{24}$

d

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

answer is B.

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Detailed Solution

Each half of a bent rod has a mass of $m = \frac{M}{2}$ and a length of $l = \frac{L}{2}$ .

The road's MI around point O is

$I = 2 \frac{m l^{2}}{3} = 2 \frac{(\frac{M}{2}) {(\frac{L}{2})}^{2}}{3} = \frac{{ML}^{2}}{12}$

Hence the correct answer is $\frac{{ML}^{2}}{12}$ .

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