Question

# 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:

A
ML26
B
ML23
C
ML22
D
2ML23
Solution
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#### The MI of the rod AB(I1 )and CD(I2 ) about the axis PQ( as shown in the figure ) are same.I1=I2=ML212The MI of the rod BC(I3 )and AD(I4 ) about the axis PQ( as shown in the figure ) are same..I3=I4=M(L2)2AD||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

2
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