Coefficient of liner expansion of brass and steel rods are `alpha_(1)` and `alpha_(2)`. Length of brass and steel rods are `l_(1)` and `l_(2)` respectively. If `(l_(2)-l_(1))` is maintained same at all temperatures, which one of the following relations hold good ?

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)`