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A uniform wire is bent to form an object which has a semicircular arc with diameter \(A B\) of length 1.2 m , with a smaller semicircular arc with diameter \(B C\) of length 0.6 m . The end \(C\) of the smaller arc is at the centre of the larger arc (see diagram). The two semicircular arcs of the wire are in the same plane.
- Show that the distance of the centre of mass of the object from the line \(A C B\) is 0.191 m , correct to 3 significant figures.
The object is freely suspended at \(A\) and hangs in equilibrium.
- Find the angle between \(A C B\) and the vertical.