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 `d_1 = 5.231 m`
` d_2 = 5.243m`
` T_1 = 27^@C`
` T_2 = ? , alpha = 1.2 xx 10^(-5) ""^@C^(-1)`
` Delta d = d_2 - d_1 = alpha d_1 (T_2 - T_1)`
`rArr T_2 - T_1 = (d_2 - d_1)/(alpha d_1) = (5.243 - 5.231)/(1.2 xx 10^(-5) xx 5.231) = 191^@C`
`T_2 = 191 + T_1 = 191 + 27 = 218^@C`