Two rods, one of aluminum and the other made of steel, having initial length `l_(1)` and `l_(2)` are connected togther 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 length of each rod increases by the same amount when their temperature 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))`