The elastic limit of steel is 8 10^8N/m^2 and its Young's modulus… - Vidyadip

Question

The elastic limit of steel is $8 \times 10^8N/m^2$ and its Young's modulus $2 \times 10^{11}N/m^2$. Find the maximum elongation of a half meter steel wire that can be given without exceeding the elastic limit.

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Answer

It means the maximum stress in the wire $\sigma =8\times 10^8\text{N}/\text{m}^2$
$Y = 2.0 \times 10^{11}N/ m^2$
Length of the wire L = 0.50m
Let corresponding maximum elongation = lm
Strain $\in=\frac{\text{l}}{\text{L}}=\frac{\text{l}}{0.50}=2\text{l}$
we have $\frac{\sigma}{\in}=\text{Y}$
$\Rightarrow\in=\frac{\sigma}{\text{Y}}$
$\Rightarrow2\text{l}=8\times\frac{10^8}{2.0}\times10^{11}$
$\Rightarrow\text{l}=\frac{2}{100}\text{m}=2\text{mm}$

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