6. Three uniform spheres \(A , B\) and \(C\) of equal radius have masses \(3 m , 2 m\) and \(2 m\) respectively. Initially, the spheres are at rest on a smooth horizontal table with their centres in a straight line and with \(B\) between \(A\) and \(C\). Sphere \(A\) is projected directly towards \(B\) with speed \(u\). Given that the coefficient of restitution between \(A\) and \(B\) is \(\frac { 2 } { 3 }\),

1. show that the speeds of \(A\) and \(B\) after the collision are \(\frac { 1 } { 3 } u\) and \(u\) respectively.
   (6 marks)
   The coefficient of restitution between \(B\) and \(C\) is \(e\). Given that \(A\) and \(B\) collide again,
2. show that \(e > \frac { 1 } { 3 }\).
   (8 marks)