Question

The fractional increase in volume of a wire of circular cross section, if its lingitudinal strain is 1% ($\sigma =0.3$)

• A. $0.4$
• B. $0.04$
• C. $0.004$
• D. $4$

Answer 1

Answer: (C)

$0.004$

Poisson's ratio $=\sigma =0.3$
$ϵ=0.01$
$L^1=\left(1.01\right)L$
i.e.
$\sigma =0.3=-\frac{\xi }{0.01}$
$ϵy=-0.003$
i.e. radius is decreased by this fraction
$R^1=\left(0.997\right)R.$
$\frac{\text{Now change in Volume}}{\text{initial Volume}}=\frac{\pi \left(1.01\right)(.997{)}^2{R}^{2}L-\pi L{R}^2}{\pi R^{2}L}$
$=-0.004$