A blacksmith fixes iron ring on the rim of the wooden wheel of a bullock cart. The diameter of the rim and the ring are `5.243 m` and `5.231 m` respectively at `27^(@)C`. To what temperature should the ring be heated so as to fit the rim of the wheel ? Coefficient of linear expansion of iron =` 1.20 xx 10^(-5) K^(-1)`

Explanation

Given, `T_(1)=27^(@)C`
`L_(T1)=5.231 m`
`L_(T2)=5.243 m`
So,
`L_(T2)=L_(T1)[1+a_(1)(T_(2)-T_(1)]`
`5.243m=5.231 m[1+1.20xx10^(-5)K^(-1)(T_(2)-27^(@)C)]" or " T_(2)=218^(@)C`.