If two rods of lengths L and 2 L , having coefficients of linear expansion α and 2 α respectively are connected end-to-end, then find the average coefficient of linear expansion of the composite rod.

Step-by-step solution

∆ δ L = α ∆ T L ∆ δ 2 L = 2 α ∆ T 2 L The rods are connected end to end means in series, therefore, net change in length after the composition of rods, ⇒ ∆ δ n e t = ∆ δ L + ∆ δ 2 L = α ∆ T L + 4 α ∆ T L = 5 α ∆ T L ⇒ ∆ δ n e t = α e f f ∆ T 3 L = ∆ δ L + ∆ δ 2 L ⇒ α e f f ∆ T 3 L = 5 α ∆ T L ⇒ α e f f = 5 α