2 Three uniform small smooth spheres, \(A , B\) and \(C\), have equal radii. Their masses are \(4 m , 2 m\) and \(m\) respectively. They lie in a straight line on a smooth horizontal surface with \(B\) between \(A\) and \(C\). Initially \(A\) is moving towards \(B\) with speed \(u , B\) is at rest and \(C\) is moving in the same direction as \(A\) with speed \(\frac { 1 } { 2 } u\). The coefficient of restitution between any two of the spheres is \(e\). The first collision is between \(A\) and \(B\). In this collision sphere \(A\) loses three-quarters of its kinetic energy. Show that \(e = \frac { 1 } { 2 }\). Find the speed of \(B\) after its collision with \(C\) and deduce that there are no further collisions between the spheres.