First slide

Thermal expansion

Question

Two uniform metal rods of length L₁ and L₂ and their linear coefficients of expansion α₁ and α₂ respectively, are connected to form a single rod of length (L₁+L₂). When the temperature of the combined rod is raised by "t°C", the length of each rod increased by the same amount then $\large \left [ \frac {\alpha_2}{\alpha_1+\alpha_2} \right ]$ is

Easy

A

$\large \frac {L_1}{L_1+L_2}$
B

$\large \frac {L_1+L_2}{L_1}$
C

$\large \frac {L_2}{L_1+L_2}$
D

$\large \frac {L_1+L_2}{L_2}$

Solution

$\large L_1\alpha_1=L_2\alpha_2;\;\frac {L_1}{L_2}=\frac {\alpha_2}{\alpha_1}\Rightarrow \frac {L_2}{L_1}=\frac {\alpha_1}{\alpha_2}$
$\large \frac {L_2}{L_1}+1=\frac {\alpha_1}{\alpha_2}+1\Rightarrow \frac {L_2+L_1}{L_1}=\frac {\alpha_1+\alpha_2}{\alpha_2}$
$\large \frac {\alpha_2}{\alpha_1+\alpha_2}=\frac {L_1}{L_1+L_2}$

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