Two thin rods of lengths $$l_1$$ and $$l_2$$ at a certain temperature are joined to each other end to end. The composite rod is then heated through a temperature $$\theta$$. The coefficients of linear expansion of the two rods are $$\alpha_1$$ and $$\alpha_2$$ respectively. Then, the effective coefficient of linear expansion of the composite rod is

A

$$\frac{\alpha_1 + \alpha_2}{2}$$

B

$$\sqrt{\alpha_1\alpha_2}$$

C

$$\frac{l_1\alpha_2 + l_2\alpha_1}{l_1 + l_2}$$

D

$$\frac{l_1\alpha_1 + l_2\alpha_2}{l_1 + l_2}$$