Question

A wire increases by ${10}^{-3}$ times of its length when a stress of $1\times {10}^8{\text{Nm}}^{-2}$ is applied to it in the longitudinal direction. Ratio of longitudinal stress and longitudinal strain in the wire is

• A. ${10}^{11}{\text{Nm}}^{-2}$
• B. ${10}^8{\text{Nm}}^{-2}$
• C. $2\times {10}^6{\text{Nm}}^{-2}$
• D. $5.2\times {10}^4{\text{Nm}}^{-2}$

Answer 1

The correct option is A ${10}^{11}{\text{Nm}}^{-2}$

Given:
Longitudinal stress $=1\times {10}^8{\text{Nm}}^{-2}$
Longitudinal strain $=\frac{\Delta L}{L}=\frac{{10}^{-3}L}{L}={10}^{-3}$
Therefore, $\frac{\text{Longitudinal stress}}{\text{Longitudinal strain}}=\frac{{10}^8}{{10}^{-3}}={10}^{11}{\text{Nm}}^{-2}$