At certain temperature, rod A and rod B of different materials have lengths L_A and L_B respectively. Their co-efficients of linear expansion are _A and _B respectively. It is observed that the difference between their lengths remain constant at all temperatures. The ratio L_A / L_B is given by

Step-by-step solution

(L_B^ =L_B (1+ _B ) ) and (L_A^ =L_A (1+ _B ) ). So that (L_B^ -L_A^ =L_B-L_S+ (L_B _B-L_A _A ) ) So ( (L_B^ -L_A^ ) ) will be equal to ( (L_B-L_A ) ) at all temperature if, (L_B _B-L_A _A=0 ) ([ as 0] or L_B L_A = _ A _B ) i.e., the difference in the lengths of the two rods will be independent of temperature if the lengths are in the inverse ratio of their coefficients of linear expansion.