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
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
- [JEE MAIN 2017]
- A
${l^2}\,Y\alpha \Delta T$
- B
$lA\,Y\alpha \Delta T$
- C
$A\,Y\alpha \Delta T$
- D
$\frac{{AY}}{{\alpha \Delta T}}$
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- [JEE MAIN 2022]