\(AB\) and \(CD\) are two perpendicular diameters of a uniform circular metal disc of radius \(\quantity{12}{in.}\) and centre \(O\). Two circular holes of radii \(\quantity{4}{in.}\) and \(\quantity{2}{in.}\) are cut out of the disc, their centres being \(\quantity{6}{in.}\) from \(O\) along \(OA\) and \(\quantity{10}{in.}\) from \(O\) along \(OC\) respectively. Find

  1. the distances of the centre of gravity, \(G\), of the remaining portion of the disc from the diameters \(CD\) and \(AB\);

It would be very helpful to sketch this!

It might also be useful to have coordinate axes so that we can refer to points easily. Where would you draw these?

How can we calculate the centre of gravity (also called the centre of mass) of a collection of objects?