Q 11-08-103JEE MainJEE Main 2017 (8 Apr)Easy
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 $l$ 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:
Answer: (B) $AY\alpha\,\Delta T$
The compression must cancel the thermal expansion:
$$\frac{Fl}{AY} = l\alpha\,\Delta T \;\Rightarrow\; F = AY\alpha\,\Delta T$$
Solution by Sreeraj P, M.Sc Physics