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Question

The volume of a wire remains constant, when subjected to tensile stress is applied on it. If the percentage change in lateral strain is 2 %, then percentage change in longitudinal strain is

A
2 %
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B
4 %
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C
6 %
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D
8 %
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Solution

The correct option is B 4 %
Let us suppose length of wire is L and radius is r then it's volume is
V=πr2L
On differentiating both side
ΔV=π(2rΔr)L+πr2ΔL
As, V= constant, then ΔV=0
2πrLΔr+πr2ΔL=0
2πrLΔr=πr2ΔL
Δrr=12×ΔLL
ΔLL=2Δrr
ΔLL×100=2Δrr×100


ΔLL×100=2×2
[Δrr×100=2%, given, Negative sign in percentage lateral strain shows radius will decrease due to tensile stress.]
ΔLL×100=+4 %
Percentage change in longitudnal strain is +4 %

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