A rod, of length L at room tempera ture and uniform area of cross section A, is made of a metal having coefficient of linear expansion `alpha//""^(@)C`. It is observed that an external compressive force F, is applied on each its ends, prevents any change in the length of the rod, when its temperature rises by `DeltaTK.` Young's modulus, Y, for this metal is :

Options

A. `(F)/(2AalphaDeltaT)`
B. `(F)/(Aalpha(DeltaT-273))`
C. `(F)/(AalphaDeltaT)`
D. `(2F)/(AalphaDeltaT)`

Answer

C

Explanation

For No change in length, `DeltaL+(-Deltal)=0`
`DeltaL` = increase in length due to change in temperature.
`-Deltal=` decrease in length due to compressive stress.
`rArrLalphaDeltaT=(FL)/(YA)rArrY=(F)/(AalphaDeltaT)`