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Question

Two rods of length L1 and L2 are welded together to make a composite rod of length ((L1+L2)). If the coefficient of linear expansion of the materials of the rods are α1 and α2 respectively, the effective coefficient of linear expansion of the composite rod is:

A
L1α1L2α2L1+L2
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B
L1α1+L2α2L1+L2
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C
α1α2
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D
α1+α22
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Solution

The correct option is B L1α1+L2α2L1+L2
The new length of rod 1 will be L1=L1(1+α1ΔT) and that of rod 2 will be L2=L2(1+α2ΔT)

Hence, for the combined rod,

L1+L2=(L1+L2)(1+αΔT)=(L1+L2)+(L1α1+L2α2)ΔT

Hence, α=L1α1+L2α2L1+L2



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