The design of some physical instrument requires that there be a constant difference in length of 10 cm between an iron rod and a copper cylinder laid side by side at all temperature find their lengths
`(alpha_(Fe)=11 xx 10^(6).^(@)C^(-1),alpha_(Cu)=17 xx 10^(-6) .^(@)C^(-1))`

Explanation

Since copper expands more than iron the length of the iron rod must be great than that of the copper rod. Let their length be `l_1` and `l_2`. The `l_1-l_2=10cm`. Since the difference is always same at all temperatures, their increase in length must be the same whatever the rise in temperature.
`:. Deltal=l_1alpha_(Fe)DeltaT=l_2alpha_(Cu)DeltaT`
or `(l_1)/(l_2)=(alpha_(Cu))/(alpha_(Fe))=(17)/(11)`
Also `l_1-l_2=10cm`
Soving for `l_1` and `l_2`
`l_1=28.3cm` `l_2=18.3cm`