2. A closed container \(C\) consists of a thin uniform hollow hemispherical bowl of radius \(a\), together with a lid. The lid is a thin uniform circular disc, also of radius \(a\). The centre \(O\) of the disc coincides with the centre of the hemispherical bowl. The bowl and its lid are made of the same material.

1. Show that the centre of mass of \(C\) is at a distance \(\frac { 1 } { 3 } a\) from \(O\). The container \(C\) has mass \(M\). A particle of mass \(\frac { 1 } { 2 } M\) is attached to the container at a point \(P\) on the circumference of the lid. The container is then placed with a point of its curved surface in contact with a horizontal plane. The container rests in equilibrium with \(P , O\) and the point of contact in the same vertical plane.
2. Find, to the nearest degree, the angle made by the line \(P O\) with the horizontal.