Question

A steel rod has a radius $10mm$ and a length $2m$. A force strtches it along its length and produes a strain of $0.30\%$. Youngs modulus of the steel is $2\times {10}^{11}N/m^2$. The magnitude of the force strething the rod is about

• A. $94kN$
• B. $188kN$
• C. $201kN$
• D. $402kN$

Answer 1

The correct option is B $188kN$

$\begin{array}{cc}\text{given,}& \text{steel rod of length}=2m\\ \text{and radius}& =10mm\end{array}$

Young's modulus of steel $=2\times {10}^{11}N/m^2$

$\begin{array}{c}\text{Strain}=0.3\%\\ \frac{\Delta l}{l}=0.003\\ F=YA\left(\frac{\Delta l}{l}\right)\\ =2\times {10}^{11}\times \pi \left({10}^{-4}\right)\left(0.003\right)\\ =6\pi \times {10}^{4}N\\ =188KN\end{array}$