Q: Two rods, one of aluminium and the other made of steel, having initial length l1 and l2 are connected 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 length of each rod increases by the same amount when their temperature are raised by t°C, then find the ratio $\large \frac{l_1}{l_1 + l_2}$

(i) $\large \frac{\alpha_s}{\alpha_a}$

(ii) $\large \frac{\alpha_a}{\alpha_s}$

(iii) $\large \frac{\alpha_s}{\alpha_a + \alpha_s}$

(iv) $\large \frac{\alpha_a}{\alpha_a + \alpha_s}$

Ans: (iii)

Sol: $\large \Delta l_1 = \Delta l_2 $

$\large \alpha_a l_1 t = \alpha_s l_2 t $

$\large \frac{l_1}{l_2} = \frac{\alpha_s}{\alpha_a} $

$\large \frac{l_1}{l_1 + l_2} = \frac{\alpha_s}{\alpha_a + \alpha_s} $