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^(0)C , l_(1) = 5.231 m, l_(2) = 5.243 m`
`l_(2) = l_(1) [1 + alpha_(1)(t_(2) - t_(1)]`
`5.243 = 5.23 l [1 + 1.20 xx 10^(-5)(t_(2) - 27)]`
or `t_(2) = 218^(@)C`