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A compressive force, F is applied at the...

A compressive force, F is applied at the two ends of a long thin steel rod. It is heated, simultaneously, such that its temeprature increass by `DeltaT`. 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

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