Two rods, one of aluminium and the other made of steel, having initial length ${\text{l}}_1 \mathrm{and} {\mathrm{l}}_2 \mathrm{are} \mathrm{connected} \mathrm{together} \mathrm{to} \mathrm{form} \mathrm{a} \mathrm{single} \mathrm{rod} \mathrm{of} \mathrm{length} {\mathrm{l}}_1+{\mathrm{l}}_2$. The coefficients of linear expansion for aluminium and steel are ${\mathrm{\alpha }}_{\mathrm{a}} \mathrm{and} {\mathrm{\alpha }}_{\mathrm{s}}$ respectively. If the length of each rod increases by the same amount when their temperature are raised by ${\mathrm{t}}^0\mathrm{C}, \mathrm{then} \mathrm{find} \mathrm{the} \mathrm{ratio} \frac{{\mathrm{l}}_1}{({\mathrm{l}}_1+{\mathrm{l}}_2)}$

• A

  $\frac{{\mathrm{\alpha }}_{\mathrm{s}}}{{\mathrm{\alpha }}_{\mathrm{a}}}$

• B

  $\frac{{\mathrm{\alpha }}_{\mathrm{a}}}{{\mathrm{\alpha }}_{\mathrm{s}}}$

• C

  $\frac{{\mathrm{\alpha }}_{\mathrm{s}}}{({\mathrm{\alpha }}_{\mathrm{a}}+{\mathrm{\alpha }}_{\mathrm{s}})}$

• D

  $\frac{{\mathrm{\alpha }}_{\mathrm{a}}}{({\mathrm{\alpha }}_{\mathrm{a}}+{\mathrm{\alpha }}_{\mathrm{s}})}$