Two metal rods of lengths L1 and L2 and coefficients of linear expansion α1 and α2 respectively are welded together to make a composite rod of length (L1 + L2) at 0°C. Find the effective coefficient of linear expansion of the composite rod. [EAMCET 2015]

Given, the lengths of rods are L1 and L2and coefficients of linear expansions are α1 and α2.As, ∆L1 = α1L1∆t   and  ∆L2 = α2L2∆tand for combined rod,                              ∆L = α (L1+L2)∆tNow,                      ∆L = ∆L1+∆L2⇒       α (L1+L2) ∆t = α1L1∆t + α2 L2∆t⇒            α (L1+L2) = α1L1 + α2L2⇒                                 α = α1L1 + α2L2L1+L2