Two rods, one of aluminium and the other made of steel, having initial length `l_1 and l_2` are connected together to from a single rod of length `l_1+l_2.` The coefficients of linear expansion for aluminium and steel are `alpha_a and alpha_s` and respectively. If the length of each rod increases by the same amount when their temperature are raised by `t^0C,` then find the ratio `l_1//(l_1+l_2)`

Options

A. `(alpha_(s))/(alpha_(a))`
B. `(alpha_(a))/(alpha_(s))`
C. `(alpha_(s))/((alpha_(a) + alpha_(s)))`
D. `(alpha_(a))/((alpha_(a) + alpha_(s)))`

Answer

C

Explanation

Given `Delta l_(1) = Delta l_(2) or l_(1) alpha_(a)t = l_(2)alpha_(s)t`
`:. (l_1)/(l_2) = (alpha_s)/(alpha_a) or (l_1)/(l_(1)+l_(2)) = (alpha_s)/(alpha_(a)+alpha_(s))`.