A bimetallic strip of thickness d and length `L` is clamped at one end at temperature `t_(1)`. Find the radius of curvature of the strip if it consists of two different metals of expansivity `alpha_(1)` and `alpha_(2) (alpha_(1) gt alpha_(2)`) when its temperature rises to `t_(2) "^(@)C`.

Answer

`(d)/((alpha_(1) - alpha_(2)) (t_(2) - t_(1)))`

Explanation

Here : `(R + (d)/(2))phi = L(1+alpha_(1)DeltaT)…..)i)`
`(R -(d)/(2))phi = L ( 1 + alpha_(2)DeltaT) …(ii)`
`implies R = (d[1 + ((alpha_(1) + alpha_(2))/(2))DeltaT])/((alpha_(1) - alpha_(2))DeltaT)`
Since `((alpha_(1) + alpha_(2))/(2)) DeltaT lt lt 1`
=` (d)/((alpha_(1) - alpha)DeltaT) = (d)/((alpha_(1) - alpha_(2))(t_(2) - t_(1)))`