Bars of two different metals are bolted together , as shown in figure. The distance x does not change with temperature if :-

Options

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

Answer

B

Explanation

` x= l'_(A) -l'_(B) = l_(A) (1 + alpha_(A)DeltaT) - l_(B) (1+alpha_(B)DeltaT) = l_(A)-l_(B)`
` implies l_(A)alpha_(A) = l_(B)alpha_(B)`