Two rods, one of aluminium and the other made of steel, having initial length  ${\mathrm{l}}_1\text{ and }{\mathrm{l}}_2$  respectively are  connected together to  form a single rod of length ${\mathrm{l}}_1+{\mathrm{l}}_2$ . The coefficient  of linear  expansion for aluminium and steel are  ${\mathrm{\alpha }}_{\mathrm{a}}$ and  ${\mathrm{\alpha }}_{\mathrm{s}}$ respectively. If the length of each rod  increases by the same amount when their  temperature t⁰C are raised by  , then  find the ratio  $\frac{{\mathrm{l}}_1}{\left({\mathrm{l}}_1{+}_2\right)}$

• A

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

• B

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

• C

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

• D

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