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 proportional limit is

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

Answer 1

The correct option is B 4 mm

The correct option is B

Given,

Proportional limits of steel are $8\times {10}^{8}N/m^2$

Young's modulus is $2\times {10}^{11}N/m^2$

So, Stress up to which stress and strain are proportional.

So $\frac{stress}{strain}=\frac{8\times {10}^8}{strain}$

Since

$strain=\frac{stress}{modulus}$

$\Rightarrow strain=\frac{4\times {10}^8}{2\times {10}^{11}}$

$=4\times {10}^{-3}$

Thus,

$\frac{\Delta L}{L}=4\times {10}^{-3}$ Where $\Delta L$ is stress

But, $L=1m$

So,

$\Delta L=4\times {10}^{-3}m$

$=4mm$