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 ${\alpha }_{cu} =17\times {10}^{-5 }per K and {\alpha }_{Al} =22\times {10}^{-5} per K$) . [NEET (National) 2019]

detailed solution

Correct option is C

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