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 $=8 \times 10^{8} N / m ^{2}$
$Y=2 \times 10^{11} N / m ^{2}$
$L=1 \,m$
Substituting values
$\frac{8 \times 10^{8} \times 1}{2 \times 10^{11}}=\Delta L$
$4 \,mm =\Delta L$