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_(1)l_(2)^(2)=alpha_(2)l_(1)^(2)`
B. `alpha_(1)^(2)l_(2)=alpha_(2)^(2)l_(1)`
C. `alpha_(1)l_(1)=alpha_(2)l_(2)`
D. `alpha_(1)l_(2)=alpha_(2)l_(1)`

Answer

C

Explanation

According to question
Coefficient of linear expension of brass = `alpha_(1)`
Coeficient of linear expression of steel = `alpha_(2)`
Length of bress and steel rods are `l_(1) and l_(2)` respectively.
As given difference increase in length `(l_(1)- l_(2))` is same for all temperature.
So, `l_(2)-l_(1)=l_(2)-l_(1)`
`rArrl_(2)(1+alpha_(2)Deltat)-l_(1)(1+alpha_(1)Deltat)=l_(2)-l_(1)rArr l_(2)alpha_(2)=l_(1)alpha_(1)`