The coefficient of linear expansion of an inhomogeneous rod changes linearly from α 1 to α 2 from one end to the other end of the rod. the effective coefficient of linear expansion of rod is

Step-by-step solution

The value of α at a distance x from the left end is α x = α 1 + α 2 - α 1 L x Δ L Δ T = ∫ 0 L α x dx ∆ L ∆ T = α 1 L + α 2 - α 1 L L 2 2 ∆ L ∆ T = α 1 + α 2 2 L α eff = α 1 + α 2 2