A compressive force, F is applied at the two ends of a long thin steel rod. It is heated, simultaneously, such that its temeprature increass by `DeltaT`. The net change in its length is zero. Let l be the length of the rod, A its area of cross-section, Y its Young's modulus, and `alpha` its coefficient of linear expansion. Then, F is equal to

Options

A. `l^(2)Y alpha Delta T`
B. `lA Y alpha Delta T`
C. `A Y alpha Delta T`
D. `(AY)/(alpha DeltaT)`

Answer

C

Explanation

Due to thermal exp., change in length `(Delta l)=l alpha DeltaT ….(i)`
Young.s modulus `(Y)=("Normal stress")/("Longitudinal strain")`
`Y=(F//A)/(Delta l//l) rArr (Delta l)/(l)=(F)/(AY) " " Delta l = (Fl)/(AY)`
From `eq^(n) (i), (Fl)/(AY)=l alpha DeltaT" " F=AY alpha DeltaT`