Question

There is some change in length when a $33000N$ tensile force is applied on a steel rod of area of cross-section ${10}^{-3}{m}^2$ . The change of temperature required to produce the same elongation of the steel rod when heated is
$(Y=3\times {10}^{11}N/m^2,\alpha =1.1\times {10}^{-5/0}C)$

• A. ${20}^{\circ }C$
• B. ${15}^{\circ }C$
• C. ${10}^{\circ }C$
• D. $0^{\circ }C$

Answer 1

The correct option is C ${10}^{\circ }C$

$\begin{array}{c}\text{Area of cross - section}\left(A\right)={10}^{-3}{m}^2\\ \text{load}\left(F\right)=33\times {10}^{3}N\\ y=3\times {10}^{11}\\ \alpha =1.1\times {10}^{-5}/cc\end{array}$

By Hooke's law \& Thermal Expansion

$\Delta l=\frac{Fl}{AY}=l\alpha \Delta T$

$\Delta T=\frac{F}{\alpha AY}$

$=\frac{33\times {10}^3}{1.1\times {10}^{-5}\times {10}^{-3}\times 3\times {10}^{11}}$

$\Delta T={10}^{\circ }C$