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Three identical thin rods each of mass m and length L are joined together to form an equilateral triangular frame. The moment of inertia of frame about an axis perpendicular to the plane of frame and passing through a corner is:

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Solution

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For the third rod, the distance between center of the rod and the axis is d=√3L/2

Using parallel axis theorem, its MI is mL2/12+3mL2/4=5mL2/6

So total MI of the system is 2mL2/3+5mL2/6=3mL2/2

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