Question

Overall changes in volume and radii of a uniform cylindrical steel wire $\left(Y=2.0\times {\left(10\right)}^{11}N{m}^{-2}\right)$ are $0.2\%$ and $0.002\%$ respectively when subjected to some suitable force. Obtain the longitudinal tensile stress acting on the wire in the multiple of $10^{6}N{m}^{-2}$

Answer 1

Answer: 392

Volume of a cylinder, $V=\pi r^{2}l$
Percentage change in volume, $\frac{\Delta V}{V}=2\frac{\Delta r}{r}+\frac{\Delta l}{l}$
Percentage change in length, $\frac{\Delta l}{l}=\frac{\Delta V}{V}-2\frac{\Delta r}{r}=0.196\%$
$\therefore$ Stress $=2\times 10^{11}\times \frac{0.196}{100}=392\times 10^{6}N{m}^{-2}$