If the coefficient of linear expansion of iron is `1.20xx10^-5K^(-1)` and diameters of the wooden and the iron rings are `1.472m` and `1.398m`, then calculate the temperature to which the iron ring has to be heated from `27^(@)`C, so that the iron ring fits over the wooden ring.

Explanation

Given : `prop=1.2xx10^(-5)K^(-1),2pir=1.378pi` and `2piR=1.472m,theta_2-theta_1=(theta-27)`
By using the relation,
`cancel(2pi)R=cancel(2pi)r[1+prop(theta_2-theta_1)]`
`theta_2=(R-r)/(rprop)+theta_1` Hence `theta_2=(1.736-0.699)/(0.699xx1.2xx10^(-5))+27`
i.e., `theta_2=(0.037xx10^5)/(8.368)+27" "theta_2=469.16^(@)C`