A copper rod of length 88 cm and an aluminium rod of unknown length have their increase in length independent of increase in temperature. The length of aluminium rod is (Here αcu =17×10-5 per K and αAl =22×10-5 per K) . [NEET (National) 2019]

Due to change in temperature, the thermal strain produced in a rod of length L is given by                            ΔLL=αΔT⇒ΔL=LαΔTwhere, L = original length of rod and α = coefficient of linear expansion of solid rod.As, the change in length (∆l) of the two given rods of copper and aluminium are independent of temperature change, i.e. ∆T is same for both copper and aluminium.                                  LCuαCu = LAlαAl                          …(i)Here,                         αCu = 17 × 10-5 K-1                                  αAl = 22 × 10-5 K-1and                             LCu= 88 cmSubstituting the given values in Eq. (i), we get                                  LAl=αCuLCuαAl=17×10-5×8822×10-5≃68 cm