Two rods of lengths `L_(1)` and `L_(2)` are welded together to make a composite rod of length `(L_(1)+L_(2))`. If the coefficient of linear expansion of the materials of the rod are `alpha_(1)` and `alpha_(2)` respectively. The effective coefficient of linear expansion of the composite rod is

Options

A. `(L_(1)alpha_(1) - L_(2)alpha_(2))/(L_(1) + L_(2))`
B. `(L_(1)alpha_(1) + L_(2)alpha_(2))/(L_(1) + L_(2))`
C. `sqrt(alpha_(1)alpha_(2))`
D. `(alpha_(1) + alpha_(2))/(2)`

Answer

B

Explanation

`(DeltaL_(1))/(Deltat) = L_(1)alpha_(1) , (DeltaL_(2))/(Deltat) = L_(2)alpha_(2)`
`:. (DeltaL)/(Deltat) = (DeltaL_(1))/(Deltat) + (DeltaL_(2))/(Deltat) , (L_(1) + L_(2)) alpha = L_(1)alpha_(1) + L_(2)alpha_(2)`