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Question

Poisson`s ratio of a material is 0.5 applied to wire of this material, these in the cross-section area increase in the length is.

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Solution

Given Poisson's ratio$ () = 0.5.$

Here, density is constant and hence change in volume is 0.

Given that there is a decrease in cross-sectional area by 4

So, (dAA)=4.

We know that dA/A=2(dr/r).

4=2×(drr)

2=(drr).

Hence,

=dll

$= (\dfrac{dr}{r})/⊂$

=20.5

=4.

Therefore, the % increase in length =4


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