What should be the lengths of steel and copper rod so that the length of steel rod is 10 cm longer than the copper rod at all the temperatures. Coefficients of linear expansion for copper and steel are alpha_(Cu)=1.7xx10^(-5) " "^(0)C^(-1) and alpha_("steel") = 1.1xx10^(-5) ""^(@)C^(-1)

What should be the lengths of steel and copper rod so that the length

1.	What should be the lengths of steel and copper rod so that the length of steel rod is 10 cm longer than the copper rod at all the temperatures. Coefficients of linear expansion for copper and steel are alpha_(Cu)=1.7xx10^(-5) " "^(0)C^(-1) and alpha_("steel") = 1.1xx10^(-5) ""^(@)C^(-1)
Answer» Solution :t is given that the difference in length of the two rods is always 10 cm. Thus the EXPANSION in boththe rodsmust be same for all temperaturedifferences. Thus we can say that at all TEMPERATURE differences, we have `DeltaL_(Cu) =DeltaL_("steel") (or) alpha_(Cu) l_(1) DELTAT=Delta_(st) l_(2)DeltaT` [If `l_(1) and l_(2)` are the initial lengths of Cu and steel rods] (or) `alpha_(Cu)l_(1)=alpha_(st)l_(2)(or) 1.7l_(1)=1.1l_(2)""...(a)` It is given that`l_(2)-l_(1)=10cm "" ....(b)` From EQUATION (a) and (b) we have`((1.7)/(1.1)-1)l_(1)=10cm (or) l_(1)=(10xx11)/(0.6)=18.3cm` Now from equation(b) `l_(2)=28.3cm`