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# 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

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

(4) $\large\frac{\alpha_1+\alpha_2}{2}$
answered Nov 7, 2013 by 1 flag