The proportional limit of steel is $8 \times 10^8 \,N / m ^2$ and its Young's modulus is $2 \times 10^{11} \,N / m ^2$. The maximum elongation, a one metre long steel wire can be given without exceeding the elastic limit is $......mm$
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At proportional limit
Stress $\propto$ strain
Stress $=Y \times$ strain $\{Y=$ Young's Modulus $\}$
Stress $=Y \times \frac{\Delta L}{L} $
Stress $=8 \times 10^8 \,N / m ^2 Y$
$=2 \times 10^{11} \,N / m ^2L=1 \,m $
Substituting values
$\frac{8 \times 10^8 \times 1}{2 \times 10^{11}}=\Delta L$
$4 \,mm=\Delta L$
Stress $\propto$ strain
Stress $=Y \times$ strain $\{Y=$ Young's Modulus $\}$
Stress $=Y \times \frac{\Delta L}{L} $
Stress $=8 \times 10^8 \,N / m ^2 Y$
$=2 \times 10^{11} \,N / m ^2L=1 \,m $
Substituting values
$\frac{8 \times 10^8 \times 1}{2 \times 10^{11}}=\Delta L$
$4 \,mm=\Delta L$
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