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 $10^{6}Nm^{- 2}$

Answer 1

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 $=2\times 10^{11}\times \frac{0 . 196}{100}=392\times 10^{6}Nm^{- 2}$