Two rods, one of aluminium and the other made of steel, having initial lengths $l_1$ and ${\mathrm{l}}_2$ 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 ${\mathrm{\alpha }}_{\mathrm{a}} \mathrm{and} {\mathrm{\alpha }}_{\mathrm{s}}$respectively. If the length of each rod increases by the same amount when their temperature are raised by t° C, then find the 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

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

• D

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