A thin rod of length L and mass M is bent at the middle point O at an angle of 60 degree. The moment of inertia of the rod about an axis passing through O and perpendicular to the plane of the rod will be: (a) ML^2/6 (b) ML^2/12 (c) ML^2/24 (d) ML^2/3

The rod is bent at the middle, so each part of it will have same length (L/2) and mass (M/2)

Moment of inertia of each part through its one end

= (1/3) (M/2) (L/2)2

Therefore,

Net moment of inertia of complete structure through the middle point O is

I = (1/3) (M/2) (L/2)2 + (1/3) (M/2) (L/2)2

I = (1/3) [ML2/8 + ML2/8]

I = (1/3) [2ML2/8]

I = (1/3). ML2/4

We get,

I = ML2/12

So, the correct option is (b) 

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