A hole is drilled in a copper sheet. The diameter of the hole is `4.24 cm` at `27.0^(@)C`. What is the change in the diameter of the hole when the sheet is heated to `227^(0)C`? `alpha` for copper `= 1.70 xx 10^(-5)K^(-1)`

Explanation

In this problem superificial of copper sheet will be involved on heating.
Here, area of hole at `27^(@)C` , `S_(1)=(piD_(1)^(2))/(4) = (pi)/(4) xx(4.24)^(2)cm^(2)`
In `D^(2)cm` is the diameter of the hole at `227^(@)C` then area of the hole at `227^(@)C` , `S_(2)=(pID_(2)^(2))/(4) cm^(2)`
Coefficient of superfical expansion of copper is ,`beta = 2 alpha = 2 xx 1.70 xx 10^(-5)=3.4xx10^(-5) .^(@)C^(-1)`
Increase in area = `S_(2)-S_(1) = beta S_(1) Delta T` or `S_(2) = S_(1)+Beta S_(1)Delta T = S_(1)(1+beta DeltaT)`
`(piD_(2)(2))/(4) = (pi)/(4) (4.24)^(2) [1+3.4xx10^(-5)(228-27)]` or `D_(2)^(2)=(4.24)^(2) xx 1.0068`
`D_(2) = 2.2544cm`
Change in diameter = `D_(2)-D_(1) = 4.2544-4.24 = 0.0144cm`.