Question

The proportional limit of steel is $8\times {10}^8{\text{N/m}}^2$ and its young modulus is $2\times {10}^{11}{\text{N/m}}^2.$ The maximum elongation, a one meter long steel wire can be given without exceeding the proportional limit is

• A. $2\text{mm}$
• B. $4\text{mm}$
• C. $1\text{mm}$
• D. $8\text{mm}$

Answer 1

The correct option is B $4\text{mm}$

From the Hook's law, at proportional limit stress is directly proportional to the strain within the elastic limit.
stress $=Y\times$ strain
[$\because Y=$ Young's Modulus ]
We know,
Strain$=\frac{\Delta L}{L}$
$\therefore$Stress $=Y\times \frac{△L}{L}$
Or
$\Delta L=\frac{\text{Stress}\times L}{Y}$

Given:
proportional limit of steel is $8\times {10}^8{\text{N/m}}^2$
$\therefore$ Stress at proportional limit of steel is $8\times {10}^8{\text{N/m}}^2$

$\Rightarrow \Delta L=\frac{(8\times {10}^8)\times 1}{2\times {10}^{11}}$
$=4\text{mm}$