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A rod, of length L at room temperature and uniform area of cross section A, is made of a metal having coefficient of linear expansion α/°C. It is observed that an external compressive force F is applied on each of its ends, prevents any change in the length of the rod, when its temperature rises by ΔK. Young's modulus, Y, for this metal is:

1. F / A α ΔT
2. F / 2A α ΔT
3. 2F / A α ΔT
4. F / A α(ΔT - 273)

Correct answer: F / A α ΔT

Solution

Thermal strain prevented = alpha*dT. Compressive stress = F/A. Young's modulus Y = stress/strain = (F/A)/(alpha*dT) = F/(A*alpha*dT). Answer: F/(A alpha dT).

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