Two metal rods A and B have lengths ${\mathrm{L}}_1 \mathrm{and}{\mathrm{L}}_2$ and same radius. The coefficients of linear expansions of the materials of A and B are ${\alpha }_1$ and ${\alpha }_2$ respectively. If the two rods are joined to form a longer rod of length ${\mathrm{L}}_1+{\mathrm{L}}_2$, the equivalent coefficient of linear expansion of the composite rod will be 

• A

  $\frac{{\mathrm{L}}_1{\mathrm{\alpha }}_1+{\mathrm{L}}_2{\mathrm{\alpha }}_2}{{\mathrm{L}}_1+{\mathrm{L}}_2}$

• B

  $\frac{({\mathrm{L}}_1/{\mathrm{\alpha }}_1)+({\mathrm{L}}_2/{\mathrm{\alpha }}_2)}{{\mathrm{L}}_1+{\mathrm{L}}_2}$

• C

  $\frac{{\mathrm{L}}_1{\mathrm{\alpha }}_1+{\mathrm{L}}_2{\mathrm{\alpha }}_2}{(1/{\mathrm{L}}_1)+(1/{\mathrm{L}}_2)}$

• D

  $\frac{({\mathrm{\alpha }}_1/{\mathrm{L}}_1)+({\mathrm{\alpha }}_2/{\mathrm{L}}_2)}{{\mathrm{L}}_1+{\mathrm{L}}_2}$