A thin metal wire of length ‘ L ’ and uniform linear mass density ‘ Q ’ is bent into a circular coil with ‘ O ’ as centre. The moment of inertia of a coil about the axis X X ' is

Question

A thin metal wire of length ‘ L ’ and uniform linear mass density ‘ Q ’ is bent into a circular coil with ‘ O ’ as centre. The moment of inertia of a coil about the axis X X ' is, 3 Q L 3 / 8 π 2, Q L 3 / 4 π 2, 3 Q L 2 / 4 π 2, Q L 3 / 8 π 2

MARKS App · Accepted Answer

I x x ' = m R 2 2 + m R 2 = 3 2 . m R 2 ∴ 2 π R = L ∴ R = L 2 π So I x x ' = 3 2 Q . 2 π R . R 2 = 3 Q π R 3 = 3 Q π . L 3 8 π 3

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