Question

Find the longitudinal stress applied to a steel wire to stretch it by $0.025\%$ of its original length, if the ratio of longitudinal stress and strain is $9\times {10}^{10}{\text{Nm}}^{-2}$.

• A. $2.25\times {10}^7{\text{Nm}}^{-2}$
• B. $2.5\times {10}^5{\text{Nm}}^{-2}$
• C. $2.25\times {10}^5{\text{Nm}}^{-2}$
• D. $2.5\times {10}^9{\text{Nm}}^{-2}$

Answer 1

The correct option is A $2.25\times {10}^7{\text{Nm}}^{-2}$

As we know,
Longitudinal strain $=\frac{\text{Change in length}}{\text{Original length}}=\frac{\Delta l}{l}=\frac{0.025\times {10}^{-2}\times l}{l}$
$=2.5\times {10}^{-4}$

Assume, Longitudinal stress $=\sigma$
$\frac{\text{Longitudinal stress}}{\text{Longitudinal strain}}=9\times {10}^{10}$ (given)
$\Rightarrow \frac{\sigma }{2.5\times {10}^{-4}}=9\times {10}^{10}$
$\Rightarrow \sigma =9\times 2.5\times {10}^6=2.25\times {10}^7{\text{Nm}}^{-2}$