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Question:

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 ΔT. 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 :

AYαΔT

l²YαΔT

AYαΔT

lAYαΔT

Solution:

ΔL = αΔT
Stress = Strain × Y
F/A = YαΔT
F = AYαΔT