Two rods having lengths `l_(1)` and `l_(2)`, made of material with linear expansion coefficients `alpha_(1)` and `alpha_(2)` were soldered together. The equivalent coefficeints linear expansion for the composite rod is

Options

A. `(l_(1)alpha_(2)+l_(2)alpha_(1))/(l_(1)+l_(2))`
B. `(l_(1)alpha_(1)+l_(2)alpha_(2))/(alpha_(1)+alpha_(2))`
C. `(l_(1)alpha_(1)+l_(2)alpha_(2))/(l_(1)+l_(2))`
D. `(l_(2)alpha_(1)+l_(1)alpha_(2))/(alpha_(1)+alpha_(2))`

Answer

C

Explanation

`l_(1) (1+alpha_(1) DeltaT) +l_(2)(1+alpha_(2)DeltaT) = l_(1)`
`l_(1) = l_(1) +l_(2) +(l_(1)alpha_(1) +l_(2)alpha_(2)) DeltaT`
`l_(1) = (l_(1)+l_(2)) (1+(l_(1)alpha_(1)+l_(2)alpha_(2))/(l_(1)+l_(2))DeltaT)`