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Question

Coefficient of linear expansion of brass and steel rods are α1and α2 . Length of brass and steel rods are l1 and l2 respectively. If l2l1 is maintained same at all temperatures, then find the ratio of α1 to α2.

A
l2l1
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B
l1l2
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C
α2l1
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D
l2α1
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Solution

The correct option is A l2l1
Let l1 and l2 be length of the rods at temperature T.
For any temperature t, length of rods can be given as
l1=l1(1+α1ΔT)
l2=l2(1+α2ΔT)
Given:
l2l1= constant
l2(1+α2ΔT)l1(1+α1ΔT)=constant
l2(1+α2×(tT))l1(1+α1×(tT))=constant
Differetiating both side w.r.t. t
l2α2=l1α1
i.e α1α2=l2l1

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