A compressive force, \( F \) is applied at the two ends of a long thin steel rod. It is heated, ....

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A compressive force, \( F \) is applied at the two ends of
P
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:
(1) \( l^{2} Y \alpha \Delta T \)
(2) \( l A Y \alpha \Delta T \)
(3) \( A Y \alpha \Delta T \)
(4) \( \frac{A Y}{\alpha \Delta T} \)


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