Engineering
Physics
Thermal Expansion
Question

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 ΔT K. Young's modulus, Y, for this metal is:

FAα(ΔT−273)

2FAαΔT

F2AαΔT

FAαΔT

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Solution

ΔL = L∝ΔT

Strain=ΔLL=αΔT;Y=FA∝ΔT