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Calculate the compressional force required to prevent the metallic rod of length l cm and cross-sectional area A cm² when heated through t°C, from expanding along length wise. The Young's modulus of elasticity of the metal is E and mean coefficient of linear expansion is a per degree Celsius

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EAαt

$\frac{EAαt}{1 + αt}$

$\frac{EAαt}{1 - αt}$

Elαt

answer is B.

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Detailed Solution

Natural length of the rod at t°C = l + lαt

decrease in natural length due to stress = $∆$ l

$Δ_{1} - Δ = 0; E = \frac{- F (l + Δ)}{AΔ}; F = \frac{- EAat}{1 + at}$

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