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Question

A material has poisson's ratio 0.50. If a uniform rod of it suffers a longitudinal strain of 2×10-3, then the percentage change in volume is


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Solution

Step 1. Given data:

Poisson's ratio α= 0.50

Longitudinal strain dll = 2×10-3

Step 2. Finding percentage change in volume

We know, Poisson's ratio = -drrdll

where r and l are the radius and length of the given rod respectively.

-drrdll=.50drr=-.50×dll=-.50×2×10-3=-10-3

Hence, drr=-10-3

Volume of the rod, V=πr2l

Differentiating partially, we get

dV=πr2dl+2l.rdr

Or dVV×100=πr2dl+2l.rdrπr2l×100=dll+2drr×100

dVV×100=2×10-3+2-10-3×100=0

Thus, the percentage change in volume is zero.


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