Q 11-10-013NEETJEE MainEAMCET 2012 (Engineering)Easy
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 coefficients 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
Answer: (B) $\dfrac{L_1\alpha_1 + L_2\alpha_2}{L_1 + L_2}$
Concept. The expansion of the composite rod is the sum of the expansions of its parts.
Step 1. Equate.
$$(L_1 + L_2)\alpha\Delta T = L_1\alpha_1\Delta T + L_2\alpha_2\Delta T$$
Step 2. Solve.
$$\alpha = \frac{L_1\alpha_1 + L_2\alpha_2}{L_1 + L_2}$$
Answer. $\dfrac{L_1\alpha_1 + L_2\alpha_2}{L_1 + L_2}$ (Option B).
Solution by Sreeraj P, M.Sc Physics