Question

The Poisson's ratio of the material of a wire is$0.25.$ If it is stretched by a force F, the longitudinal strain produced in the wire is $5\times {10}^{-4}.$ What is the percentage increase in its volume?

• A. $0.2$
• B. $2.5\times {10}^{-2}$
• C. Zero
• D. $1.25\times {10}^{-6}$

Answer 1

The correct option is B $2.5\times {10}^{-2}$

$\sigma =.25$

$\Rightarrow \frac{-\Delta R1R}{\Delta l10}$

$\Rightarrow \frac{\Delta R}{R}=-.25\frac{\Delta l}{l}$

$=-.25\times 5\times {16}^4$

$v=\pi R^{2}l$

$\Rightarrow \frac{\Delta v}{v}\times 100(2\frac{\Delta R}{R}+\frac{\Delta l}{l})\times 100$

$=(2\times (-.25\times 5\times {10}^{-4})+5\times {10}^{-4})\times 150$

$=2.5\times {10}^{-2}=.025\%$