What should be the length of steel and copper rods at `0^(@)C` that the length of steel rod is 5 cm longer than copper at all termperature? Given `alpha_(Cu) = 1.7 xx 10^(5) .^(@)C^(-1)` and `alpha_(steel) = 1.1 xx 10^(5) .^(@)C^(-1)`.

Explanation

It is given that the difference in length of the two rods is always 5 cm. Thus the expansion on both the rods mut be same for all temperature differences. Thus we can say that at all temperature differences, we have
`DeltaL_(Cu)=DeltaL_("steel")`
or `alpha_(Cu)l_(1)DeltaT=alpha_(st)l_(2)DeltaT`
[If `l_(1)` and `l_(2)` are the initial lengths of Cu and stgeel rods]
or `alpha_(Cu)l-(1)=alpha_(st)l_(2)`
or `1.7kl_(1)=1.1l_(2)`.1.29
It is given that `l_(2)-l_(1)=5 cm` 1.30
From equation (1.29) and (1.30) we have
`(1.7/1.1-1)l_(1)=5 cm`
or `l_(1)=(5xx1.1)/0.6=9.17cm`
Now from equation(1.30)
`l_(2)=14.17cm`