Question

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 lenght of each rod increases by the same amount when their temperature are raised by t$^{\circ}C,$then find the ratio $\frac{l_1}{l_1+l_2}$

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

Answer 1

Answer: (C)

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

Answer 2

The correct option is(C): $\frac{\alpha_s }{(\alpha_a+\alpha_s)}$.

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