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 $∆T$. 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 $α$ its coefficient of linear expansion. Then, $F$ is equal to :

Question

$\begin{array}{1 1}(1)\; l^2 Y \alpha \Delta \\ (2)\; I A Y \alpha \Delta T \\ (3)\; A Y \alpha \Delta T \\ (4)\; \frac{AY}{\alpha \Delta T} \end{array} $