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Two different wires having lengths

Question:

Two different wires having lengths $\mathrm{L}_{1}$ and $\mathrm{L}_{2}$, and respective temperature coefficient of linear expansion $\alpha_{1}$ and $\alpha_{2}$, are joined end-to-end. Then the effective temperature coefficient of linear expansion is :

  1. $4 \frac{\alpha_{1} \alpha_{2}}{\alpha_{1}+\alpha_{2}} \frac{\mathrm{L}_{2} \mathrm{~L}_{1}}{\left(\mathrm{~L}_{2}+\mathrm{L}_{1}\right)^{2}}$

  2. $2 \sqrt{\alpha_{1} \alpha_{2}}$

  3. $\frac{\alpha_{1}+\alpha_{2}}{2}$

  4. $\frac{\alpha_{1} L_{1}+\alpha_{2} L_{2}}{L_{1}+L_{2}}$

Correct Option: , 4

Solution:

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