Two rods of length `l_(1)` and `l_(2)` are made of material whose coefficient of linear expansion are `alpha_(1)` and `alpha_(2)` , respectively. The difference between their lengths will be independent of temperatiure if `l_(1)//l_(2)` is to

Options

A. `(l_(1))/(l_(2))=(alpha_(1))/(alpha_(2))`
B. `(l_(1))/(l_(2))=(alpha_(2))/(alpha_(1))`
C. `l_(2)^(2)alpha_(1)=l_(1)^(2)alpha`
D. `(alpha_(1)^(2))/(l_(1))=(alpha_(2)^(2))/(l_(2))`

Answer

B

Explanation

`Delta l_(1)=Delta l_(2)` or `l_(1)alpha_(1) Delta theta=l_(2)alpha_(2)Delta theta` or `(l_(1))/(l_(2))=(alpha_(2))/(alpha_(1))`