Two rods, one of aluminium and other made of steel, having initial lenghts `l_(1) and l_(2)` are connected together to form a singel rod of length `(l_(1)+l_(2))`. The coefficient of linear expansions for aluminium and steel are `alpha_(a)` and `alpha_(s)` respectively. If length of each rod increases by same amount when their tempertures are raised by `t^(@)C`, then find the ratio `l_(1) (l_(1)+l_(2))`.

Explanation

Since the lengths of the two rods imcreses by same amount , hence `l_(1) alpha_(a) t = l_(2) alpha_(s) t`
or `(l_2)/(l_1) = (alpha_a)/(alpha_s) or (l_2)/(l_1) + 1 = (alpha_a)/(alpha_s) + 1`
or `(l_(2)+l_(1))/(l_1) = (alpha_(a)+alpha_(s))/(alpha_(s)) :. (l_1)/(l_(1)+l_(2)) = (alpha_(s))/(alpha_(a)+alpha_(s))`.