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_(T 1) = 5.231 m`
` L_(T2) = 5.243 m`
So,
` L_(T2) = L_(T1) [1 + alpha_(1) (T_(2) - T_(1)]`
` 5.243 m = 5.231 m [1 + 1.20 xx 10^(-5) K^(-1) (T_(2) - 27^(@) C)]`
or `T_(2) = 218^(@) C`.