Q. A rod, of length L at room temperature and uniform area of cross section A, is made of a metal having coefficient of linear expansion $\alpha / {^{\circ}C}$. It is observed that an external compressive force F, is applied on each of its ends, prevents any change in the length of the rod, when its temperature rises by $\Delta T K$. Young's modulus, Y, for this metal is :

Solution:

Young's modulus $y = \frac{\text{Stress}}{\text{Strain}} $
$ =\frac{F/A}{\left(\Delta \ell/\ell\right)} $
$ = \frac{F}{A\left(\alpha \Delta T\right)}$

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