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

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.
`impliesL alpha Delta T=(FL)/(YA)impliesY=F/(A alpha DeltaT)`