A blacksmith fixes iron rings on the rim of the wooden wheel of a bullock cart .The diameter of the rim the iron rings are 6.264 m and 6.253 m respectively at `27^(@)C` . To what temperature should the ring be heated so as to fit the rim of the wheel ? (Given `alpha_(L)=1.20xx10^(-5)""^(@)C^(-1))`

Explanation

We are given `T_(1)=27^(@)C`
`L_(T_(1))=6.253`
`L_(T_(2))=6.264`
We are to calculate : Temperature of rim `T_(2)` .
Using relation , `L_(T_(2))=L_(T_(1))[1+alpha_(L)(T_(2)-T_(1))] " " ["Given" alpha_(L)=1.20xx10^(-5)]`
`6.264=6.253[1+1.20xx10^(-5)(T_(2)-27^(@)C)]`
`T_(2)=177^(@)C`.