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  4. Two rods, one of aluminium and the other made of steel ,having initial length l1 + l2. are connected together to form a single rod of length l1+l2. The coefficients of linear expansion for aluminium and steel are αa and αs respectively. if the lenghth of each rod increases by the same amount when their temperature are raised by t°C, then find the ratio (l1/l1+l2)

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

IIT JEEIIT JEE 2003Thermodynamics

Solution:

Given $ \Delta l_1 =\Delta l_2$ or $ l_1\alpha_a t =l_2 \alpha_s l$
$\therefore \frac{l_1}{l_2}=\frac{\alpha_s}{\alpha_a}$ or $ \frac{l_1}{l_1 +l_2} =\frac{\alpha_s}{\alpha_a +\alpha_s}$