Question

The Yogng's modulus of a material having area of $1cm$ is a cross-sectional $2\times {10}^{12}{\text{dyne/cm}}^2$. If the length is to be doubled the force required is

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

Answer 1

The correct option is B $2\times {10}^{7}N$

$\begin{array}{c}\text{Given length is doubled that means}\Delta L=L\\ \begin{array}{c}\text{Area of cross Section}=1{cm}^2\\ ={10}^{-4}{m}^2\end{array}\\ \text{Young's modulus}=\frac{2\times {10}^{12}\times {10}^{-5}}{{10}^{-4}}N/m^2\end{array}$

$\begin{array}{c}F=\frac{\Delta l}{l}\times A\times y\\ F=\frac{l}{l}\times {10}^{-4}\times \frac{2\times {10}^7}{{10}^{-14}}\\ F=2\times {10}^{7}N/m^2\end{array}$