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

Answer

D