Question

The coefficient of linear expansion of an in homogeneous rod change linearly from `alpha_(1)` to `alpha_(2)` from one end to the other end of the rod. The effective coefficient of linear expansion of rod is
A. `alpha_(1) + alpha_(2)`
B. `(alpha_(1) + alpha_(2))/(2)`
C. `sqrt(alpha_(1)alpha_(2))`
D. `alpha_(1) - alpha_(2)`

Answer 1

Correct Answer - B
`alpha_(n)=alpha_(1)+((alpha_(2)-alpha_(1))/(L))x,DeltaL=overset(L)underset(0)intalpha_(n)dxDeltat`
`L=((alpha_(1)+alpha_(2))/(2))LDeltaT , alpha_(eff) = ((alpha_(1)+alpha_(2))/(2))`