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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−1. 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
FA α Δ T
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B
2FA α Δ T
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C
F2A α Δ T
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D
FA α (Δ T273)
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Solution

## The correct option is A FA α Δ TYoung's modulus, Y=stressstrain Y=(FA)(Δll) Using, coefficient of linear expansion, α=ΔllΔT⇒Δll=αΔT ∴Y=FAαΔT Hence, option (A) is correct.

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