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Question

A metal wire is stretched by a load. Then the fractional change in its volume ΔVV is proportional to

A
ΔLL
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B
(ΔL2)2
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C
ΔLL
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D
(ΔLL)3
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Solution

The correct option is A ΔLL
From the data given in the question, a load F acting on the metallic wire is as shown in figure.


It is given that, the wire will stretch.
The length of wire will increase
We know, Poisson's ratio, e=ΔddΔLL(1)
Volume of wire, V=A×L=πd2L4 where d is the diameter of the wire.
ΔV=πd24ΔL+πL4×2dΔd
ΔVV=ΔLL+2Δdd
ΔVV=(12e)ΔLL
[using (1)]
Therefore, ΔVVΔLL

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