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\includegraphics[max width=\textwidth, alt={}, center]{8d128de7-f6ca-4187-ae8b-cbd8dfcdfc93-4_647_641_260_751} A uniform circular disc has centre \(O\) and radius 1.2 m . The centre of the disc is at the origin of \(x\)-and \(y\)-axes. Two circular holes with centres at \(A\) and \(B\) are made in the disc (see diagram). The point \(A\) is on the negative \(x\)-axis with \(O A = 0.5 \mathrm {~m}\). The point \(B\) is on the negative \(y\)-axis with \(O B = 0.7 \mathrm {~m}\). The hole with centre \(A\) has radius 0.3 m and the hole with centre \(B\) has radius 0.4 m . Find the distance of the centre of mass of the object from

1. the \(x\)-axis,
2. the \(y\)-axis. The object can rotate freely in a vertical plane about a horizontal axis through \(O\).
3. Calculate the angle which \(O A\) makes with the vertical when the object rests in equilibrium.