The elastic limit of steel is $8 imes 10^{8} \mathrm{~N} \mathrm{~m}^{-2}$ and its Young modulus $

Question

The elastic limit of steel is $8 	imes 10^{8} \mathrm{~N} \mathrm{~m}^{-2}$ and its Young modulus $2 	imes 10^{11} \mathrm{~N} \mathrm{~m}^{-2}$. The maximum elongation of a half-metre steel wire (in mm) that can be given without exceeding the elastic limit.

Professor PC Thomas Classes · Answer

Elastic limit (maximum stress) $=8 	imes 10^8 \mathrm{~N} / \mathrm{m}^2$
Young's modulus $E=2 	imes 10^{11} \mathrm{~N} / \mathrm{m}^2$
Length of wire $L=0.5 \mathrm{~m}$
Maximum strain
$$	ext { Strain }=\frac{	ext { Stress }}{E}=\frac{8 	imes 10^8}{2 	imes 10^{11}}
$$$$
	ext { Strain }=4 	imes 10^{-3}
$$Maximum elongation
$$\Delta L=	ext { Strain } 	imes L=4 	imes 10^{-3} 	imes 0.5
$$$$
\begin{gathered}
4 	imes 0.5=2 \
\Delta L=2 	imes 10^{-3} \mathrm{~m}=0.002 \mathrm{~m}=2 \mathrm{~mm}
\end{gathered}
$$