The change in length of a wire of a circular cross section is found to be 0.01% due to longitudinal stress, IF the poisson's ratio for the material is 0.2, what is the percentage change in volume?

Explanation

Let the length of the wire be l, its radius be r and volume be V.
So, `V=pir^2l`
`thereforedV=pir^2dl+2pilrdr[becausesigma=(-dr//r)/(dl//l),dr=-rsigma(dl)/l]`
`=pir^2dl-2pir^2sigma dl`
`=pir^2dl(l-2sigma)`
`therefore` Volume strain
`=(dV)/V=(pir^2dl(1-2sigma))/(pir^2l)`
`=(dl)/l(1-2sigma)[Here,(dl)/l=0.01%=0.0001]`
`=0.0001(1-2times0.2)=6times10^-5`
`therefore` Percentage change in volume
`=(dV)/Vtimes100=6times10^-5times100=0.006%`