At certain temperature, rod A and rod B of different materials have lengths L_A and L_B respectively: Their coefficients of linear expansion are _A and _B respectively. It is observed that the difference between their length's remains constant at all temperatures. The ratio L _ A : L _ B is given by

Step-by-step solution

Length of rod A at temperature t = L _ A +l_ A _ A t Length of rod B at temperature t = L _ B +l_ B _ B t Length of rod A- length of rod B= ( L _ A - L _ B )+ (l_ A _ A -l_ B _ B ) t For difference in the length to be constant, coefficient of t must be zero. array ll & l_ A _ A -l_ B _ B =0 & l_ A _ A =l_ B _ B & l_ A l_ B = _ B _ A array