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Question

A material has Poisson's ratio 0.5. If a uniform rod made of the material suffers a longitudinal strain of 2×103, what is the percentage increase in volume?

A
2 %
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B
4 %
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C
0 %
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D
5 %
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Solution

The correct option is C 0 %
Given,
Longitudinal strain(ΔLL)=2×103
Poisson's ratio (σ)=0.5
Fractional change in volume of the cylindrical wire is given by,
ΔVV=Δ(πr2L)πr2L=ΔLL+2Δrr ......(1)
σ=(Δr/r)(ΔL/L)
or Δrr=σΔLL .....(2)
Using (2) in (1), we can write
ΔVV=(12σ)ΔLL
ΔVV=2×1032×103=0
Hence, there is no fractional change in volume of the cylindrical wire.
Thus, option (c) is the correct answer.

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