Two rods,one of aluminum and another of steel,have initial lengths $l_1$ and $l_2$ respectively. They are joined together to form a single rod of length $(l_1 + l_2)$. If the coefficients of linear expansion for aluminum and steel are $\alpha_a$ and $\alpha_s$ respectively,and the increase in length for both rods is the same when the temperature of both is increased by $t \ ^\circ C$,then $\frac{l_1}{l_1 + l_2} = \dots$

  • A
    $\frac{\alpha_s}{\alpha_a}$
  • B
    $\frac{\alpha_a}{\alpha_s}$
  • C
    $\frac{\alpha_s}{(\alpha_a + \alpha_s)}$
  • D
    $\frac{\alpha_a}{(\alpha_a + \alpha_s)}$

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Two rods,one of aluminum and the other made of steel,having initial lengths $l_1$ and $l_2$ are connected together to form a single rod of length $l_1 + l_2$. The coefficients of linear expansion for aluminum and steel are $\alpha_a$ and $\alpha_s$ respectively. If the length of each rod increases by the same amount when their temperature is raised by $t ^\circ C$,then find the ratio $\frac{l_1}{l_1 + l_2}$.

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