Two rods, one of aluminium and other made of steel, having initial lengths `l_(1) and l_(2)` are connected together to form a single 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))`.

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

`Deltal_(1) = Deltal_(2) implies l_(1) alpha_(a) DeltaT = l_(2)alpha_(S) DeltaT`
`implies (l_(1))/(l_(2)) = (alpha_(s))/(alpha_(a)) implies (l_(1))/(l_(1) + l_(2)) = (alpha_(s))/(alpha_(a) + alpha_(s))`