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Question:

A rod, of length L at room temperature and uniform area of cross section A, is made of a metal having a coefficient of linear expansion α oC. 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 ΔTK. Young's modulus, Y, for this metal is :

2FAαΔT

F/2AαΔT

FAα(ΔT⁻¹)

FAαΔT

Solution:

The correct option is FAαΔT
Young's modulus Y = Stress/Strain = F/A(ΔL/L) = FA(αΔT)