Question

The ratio $\frac{\text{stress}}{\text{strain}}$ remains constant for small deformation of a metal wire. When the deformation increases, then the ratio will -

• A. Increase
• B. Decrease
• C. Remains constant
• D. First increases then decreases.

Answer 1

The correct option is B Decrease

We know,
Stress versus strain curve for a metal wire is


For small deformations as seen in the region OA
$\frac{\text{stress}}{\text{strain}}=\text{tan}{\theta }_1=\text{constant}$
When deformation is increased,
$\frac{\text{stress}}{\text{strain}}=\text{tan}{\theta }_2\left(\text{at point B}\right)$
From the curve, it is evident that${\theta }_2<{\theta }_1\Rightarrow \text{tan}{\theta }_2<\text{tan}{\theta }_1$
Therefore, the ratio will decrease when deformation increases.