Question

What force is required to stretch a steel wire $1c{m}^2$ in cross section to increase its length by $1\%$ given $[Y=2\times {10}^{11}N/m^2]$

• A. $2\times {10}^{7}N$
• B. $2\times {10}^{6}N$
• C. $2\times {10}^{5}N$
• D. $4\times {10}^{11}N$

Answer 1

The correct option is C $2\times {10}^{5}N$

$\begin{array}{c}A=1{cm}^2\\ \frac{\Delta l}{l}=0.01\end{array}$

$Y=2\times {10}^{11}N/m^2$

$\begin{array}{cc}& \text{To find: Force.}\\ & \begin{array}{c}\frac{F}{A}=Y\frac{\Delta l}{l}\\ \Rightarrow F=\frac{AY\Delta l}{l}\\ \Rightarrow F=(1\times {10}^{-4})\times 2\times {10}^{11}\times {10}^{-2}\\ \Rightarrow F=2\times {10}^{5}N\\ \text{Hence Answer}\to \left(C\right)\end{array}\end{array}$