Question

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

• A. 2 mm
• B. 4 mm
• C. 1 mm
• D. 8 mm

Answer 1

Answer: (B)

At proportional limit
Stress $\propto$ strain
Stress $=Y\times$ strain
$\{Y=$ Young's Modulus $\}$
Stress $=Y\times \frac{\Delta }{L}$
Stress $=8\times 10^{8}N/m^2$
$Y=2\times 10^{11}N/m^2$
$L=1m$
Substituting values
$\frac{8\times 10^8\times 1}{2\times 10^{11}}=\Delta L$
$4mm=\Delta L$