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The rods A and B are heated.If $\alpha_1 : \alpha_2=5 : 7$,the thermal stresses develpoed on the two rods are equal if $Y_1 : Y_2$ is

$\begin{array}{1 1}(A)\;5 : 7\\(B)\;1 : 1\\(C)\;7 : 5\\(D)\;25 : 49\end{array} $

1 Answer

$\large\frac{\Delta l}{l}=$$\alpha_1\Delta \theta$
Stress =$Y\times \large\frac{\Delta l}{l}$
So $Y_1\times \large\frac{\Delta l_1}{l_1}$$=Y_2\times \large\frac{\Delta l_2}{l_2}$
As stress is same
$\Rightarrow Y_1\alpha_1\Delta \theta=Y_2\alpha_2\Delta \theta$
$\Rightarrow \large\frac{Y_1}{Y_2}=\frac{\alpha_2}{\alpha_1}=\frac{7}{5}$
Hence (C) is the correct answer.
answered May 8, 2014 by sreemathi.v

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