A metallic rod l cm long, A square cm in cross-section is heated through `t^(@)"C"`. If Young’s modulus of elasticity of the metal is E and the mean coefficient of linear expansion is `alpha` per degree celsius, then the compressional force required to prevent the rod from expanding along its length is

Options

A. `EA alphat`
B. `EA alphat//(1+alphat)`
C. `EA alpha t//(1-alpha t)`
D. `E l alpha t`

Answer

A

Explanation

`E=(F//A)/(Delta l//l)=("stress")/("strain")` where `Delta l=(l.-l)=l alphat " so " F=EA alpha t`