Question

A steel wire AB of length 100 cm is fixed rigidly at points A and B in an aluminium frame as shown in the figure If the temperature of the system increases through 100C, then the excess stress produced in the steel wire relative to the aluminium? ${\alpha }_{\mu }=22\times {10}^{-6}{/}^{0}Cand{\alpha }_{stret}=11\times {10}^{-6}{/}^{0}C$ young 's modulus of steel is $2\times {10}^{31}{Nm}^{-2}$

• A. $2.2\times {10}^5$Pa
• B. $22\times {10}^{27}$Pa
• C. $2.2\times {10}^2$Pa
• D. $220\times {10}^2$Pa

Answer 1

The correct option is B $22\times {10}^{27}$Pa

$\Delta l=l\alpha .\Delta T$

$\begin{array}{cc}\Delta l_{\text{Btul}}=1\times 11\times {10}^{-6}\times 100& =11\times {10}^{-4}m\\ \Delta l_{\text{Al}}=& 1\times 22\times {10}^{-6}\times 100=22\times {10}^{-4}m\\ \text{Net Elongation}\left(\Delta l\right)=& \Delta l_{A\ell }-\Delta l_{\text{stul}}\\ & =11\times {10}^{-4}m.\end{array}$ $\begin{array}{cc}\text{Therefore Excess Streess}& =\gamma \times \text{strain}\\ & =Y\times \frac{\Delta \ell }{l}\\ & =2\times {10}^{31}\times \frac{11\times {10}^{-4}}{1}\\ & =22\times {10}^{27}Pa\end{array}$