2 Three uniform small smooth spheres \(A , B\) and \(C\), of equal radii and of masses \(4 m , \lambda m\) and \(m\) respectively, are at rest in a straight line on a smooth horizontal plane, with \(B\) between \(A\) and \(C\). Sphere \(A\) is projected directly towards \(B\) with speed \(u\). The coefficient of restitution between \(A\) and \(B\), and between \(B\) and \(C\), is \(\frac { 1 } { 2 }\). Show that the speed of \(B\) after it is struck by \(A\) is \(\frac { 6 u } { \lambda + 4 }\). Given that the speed of \(C\) after it is struck by \(B\) is \(u\), find the value of \(\lambda\).