A compressive force, F is applied at the two ends of a long thin steel rod. It is heated, simultaneously, such that its temperature increases by $\Delta $T. The net change in its length is zero. Let $\ell $ be the length of the rod, A its area of cross-section,Y its Young’s modulus, and $\alpha $ its coefficient of linear expansion. Then, F is equal to :
$\ell $2 Y$\alpha $ $\Delta $T
$\ell $A Y$\alpha $ $\Delta $T
A Y$\alpha $ $\Delta $T
${{AY} \over {\alpha \,\Delta T}}$
Solution
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