2 A small bead of mass \(m\) is threaded on a thin smooth wire which forms a circle of radius \(a\). The wire is fixed in a vertical plane. A light inextensible string is attached to the bead and passes through a small smooth ring fixed at the centre of the circle. The other end of the string is attached to a particle of mass \(4 m\) which hangs freely under gravity. The bead is projected from the lowest point of the wire with speed \(\sqrt { } ( k g a )\). Show that, when the angle between the two parts of the string is \(\theta\), the normal force exerted on the bead by the wire is \(m g ( 3 \cos \theta + k - 6 )\), towards the centre. Given that the bead reaches the highest point of the wire, find an inequality which must be satisfied by \(k\).