Q 11-10-098JEE MainJEE Main 2020 (5 Sep, Shift 2)Easy
Two different wires having lengths $L_1$ and $L_2$ and respective temperature coefficients of linear expansion $\alpha_1$ and $\alpha_2$ are joined end-to-end. Then the effective temperature coefficient of linear expansion is:
Answer: (A) $\dfrac{\alpha_1L_1+\alpha_2L_2}{L_1+L_2}$
For a temperature rise $\Delta T$ the total extension is the sum of the two extensions:
$$(L_1+L_2)\alpha_{\text{eff}}\Delta T = L_1\alpha_1\Delta T + L_2\alpha_2\Delta T$$
$$\alpha_{\text{eff}} = \frac{\alpha_1L_1+\alpha_2L_2}{L_1+L_2}$$
Solution by Sreeraj P, M.Sc Physics