Two roads 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 rods are $( \alpha_1 \: and \: \alpha_2)$ respectively, the effective coefficient of linear expansion of the composite rod is

Question

$\begin {array} {1 1} (1)\;\large\frac{L_1\alpha_1-L_2 \alpha_2}{L_1+L_2} & \quad (2)\;\large\frac{L_1\alpha_1+L_2 \alpha_2}{L_1+L_2} \\ (3)\;\sqrt{\alpha_1\: \alpha_2} & \quad (4)\;\large\frac{\alpha_1+\alpha_2}{2} \end {array}$