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  4. A metal rod of Young's modulus Y and coefficient of thermal expansion α is held at its two ends such that its length remains invariant. If its temperature is raised by t°C, the linear stress developed in its is :

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Q. A metal rod of Young's modulus Y and coefficient of thermal expansion $\alpha$ is held at its two ends such that its length remains invariant. If its temperature is raised by t$^{\circ}$C, the linear stress developed in its is :

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Solution:

$\frac{\Delta\ell}{\ell} = \alpha.\Delta T$
and $\quad Y = \frac{F/ A}{\Delta\ell/\ell}$
So,$\quad F = AY\alpha t$
Thermal stress $\left(\frac{F}{A}\right) = Y\alpha t.$

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