Two uniform metal rods one of aluminium of length l₁ and another made of steel of length l₂ and linear coefficients of expansion α_a and α_s respectively are connected to form a single rod of length l₁+l₂ . When the temperature of the combined rod is raised by t°C, the length of each rod increases by the same amount. Then $\frac{{\mathrm{l}}_1}{{\mathrm{l}}_1+{\mathrm{l}}_2}$ is

• A

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

• B

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

• C

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

• D

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