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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 coefficients of linear expansion of the rod are α1 and α2 respectively, the effective coefficient of linear expansion of the composite rod will be

A
L1α1+L2α26(L1+L2)
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B
L1α1+L2α24(L1+L2)
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C
L1α1+L2α2L1+L2
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D
L1α1+L2α22(L1+L2)
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Solution

The correct option is C L1α1+L2α2L1+L2
Given:
Lengths of the two rods are L1 and L2
Length of composite rod =L1+L2
Coefficients of linear expansion =α1 and α2 respectively
To find:
Effective coefficient of linear expansion of composite rod, α=?
Let us assume:
Change in temperature =ΔT
We know that, for end to end connection of rod,
effective expansion = expansion in rod 1 + expansion in rod 2
(L1+L2)αΔT=L1α1ΔT+L2α2ΔT
α=L1α1+L2α2L1+L2
is the effective coefficient of linear expansion.

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