Calculate the compressional force required to prevent the metallic rod length `l cm` and cross-sectional area `A cm^(2)` 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 `alpha` per degree Celsiuss

Options

A. `EAalphat`
B. `(EAalphat)/(l + alphat)`
C. `(EAalphat)/(l - alphat)`
D. `Elalphat`

Answer

B

Explanation

Natural length of the rod at `t^(@)C = l + lalphat`
decrease in natural length due to stress `= Deltal`
`Deltal_(1) - Delta_(l) = 0 , E = (-F(l + Deltal))/(ADeltal) , F = (-Ealphat)/(1 + alphat)`