What should be the lengths of a brass and an aluminium rod at 0^(@). if the difference between their lengths is to be maintained equal to 5 cm at any temperature ? (For brass alpha=18xx10^(-6)""^(@)C^(-1) and for aluminium alpha=24xx10^(-6)" "^(@)C^(-1) )

What should be the lengths of a brass and an aluminium rod at 0^(@). i

1.	What should be the lengths of a brass and an aluminium rod at 0^(@). if the difference between their lengths is to be maintained equal to 5 cm at any temperature ? (For brass alpha=18xx10^(-6)""^(@)C^(-1) and for aluminium alpha=24xx10^(-6)" "^(@)C^(-1) )
Answer» Solution :Suppose `l_(1)` and `l_(2)` are the lengths of aluminium and brass rods at `0^(@)C` respectively. At any TEMPERATURE, DIFFERNCE of their lengths remains the same. Hence, increase in their lengths with increase in temperature MUST also be the same. `:.Deltal_(1)=Deltal_(2)` `:.alpha_(1)l_(1)DeltaT=alpha_(2)l_(2)DeltaT` `:.(l_(1))/(l_(2))=(alpha_(2))/(alpha_(2))=(24xx10^(-6))/(18xx10^(-6))=(4)/(2)`. . . (1) Now according to the given condition, `l_(1)-l_(2)=5` cm. .. . . (2) From equations (1) and (2). `(l_(1))/(l_(1)-5)=(4)/(3)` `:.3l_(1)=4l_(1)-20` `:.l_(1)=20` cm and `l_(2)=15` cm Thus, at `0^(@)C` lengths of brass and aluminium rods should be 20 cm and 15 cm respectively.