Two rods, one of aluminum and the other made of steel, having initial length ${l_1}$ 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 are raised by ${t^o}C$, then find the ratio $\frac{{{l_1}}}{{({l_1} + {l_2})}}$
Two rods, one of aluminum and the other made of steel, having initial length ${l_1}$ 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 are raised by ${t^o}C$, then find the ratio $\frac{{{l_1}}}{{({l_1} + {l_2})}}$
- [IIT 2003]
- 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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