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Four thin metal rods, each of mass M and length L, are welded to form a square. The moment of inertia of the composite structure about a line which bisects any two opposite rods is:

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Solution

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I1=I2=ML212

The MI of the rod BC(I3 )and AD(I4 ) about the axis PQ( as shown in the figure ) are same..

I3=I4=M(L2)2

AD||PQ and BC||PQ and all points on AD are at same distance from the axis PQ, all points on BC are at same distance from the axis PQ,

∴I=I1+I2+I3+I4=2×ML212+2×M(L2)2=23ML2

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