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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 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

A
FAαΔT
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B
2FAαΔT
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C
F2AαΔT
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D
FAα(ΔT273)
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Solution

The correct option is A FAαΔT
We know that:

Y=stressstrain,Δll=αΔT

Expansion due to heat caused is balanced by compression cause by compressive force F.

Young’s modulus Y=stressstrain

=F/A(Δl/l)

=FA(αΔT)

Final Answer; (c)

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