A hole is drilled in a copper sheet. The diameter of the hole is 4.24cm at `27.0^(@)C`. What is the change in the diameter of the when the sheet is heated to `227^(@)C`? Coefficient of linear expansion of copper `=1.70xx10^-5""^(@) C^(-1)`?

Explanation

`d_(1)=4.24cm`
Area of the hole `=(pid_(1)^(2))/(4)=(3.14xx4.24xx4.24)/(4)=14.1124cm^(2)`
`theta_(1)=27^(@)C,theta_(2)=227^(@)C`.
`Deltatheta=200^(@)C=200K`
Coefficient of superficial expansion `beta=2alpha=3.4xx10^(-5)""^(@)C^(-1)`
i.e., `beta=(A_(2)-A_(1))/(A_(1)theta_(2)-A_(2)theta_(1))`
`3.4xx10^(-5)xx14.1124xx227-3.4xx10^(-5)xx27A_(2)=A_(2)-14.1124`
`:.A_(2)=(14.2213)/(1.000918)=14.20827cm^(2)`
and diameter of the hole `=d_(2)=sqrt((4A_(2))/(pi))=sqrt((4xx14.20827)/(3.14))`
`d_(2)=4.253cm.`