A material has a Poisson's ratio 0.3. It suffers a uniform longitudinal strain `4.5 xx 10^(-3)`, calculate the percentage change in its volume.

Options

A. `0.15%`
B. `0.02%`
C. `0.24%`
D. `0.48%`

Answer

C

Explanation

As `sigma = (Delta R//R)/(Delta l//l)`
`therefore (DeltaR)/(R) = - sigma (Deltal)/(l) = - 0.2 xx 4.0 xx 10^(-3) = - 0.8 xx 10^(-3)`
`V =piR^(2)l`
`therefore (DeltaV)/(V) xx 100= (2(DeltaR)/(R) +(Deltal)/(l))xx 100`
`=[2xx(-0.8xx10^(-3)) + 0.4 xx 10^(-3)] xx 100`
`= 2.4 xx 10^(-3) xx 100 = 0.24%`