5 Three uniform small smooth spheres \(A , B\) and \(C\) have equal radii and masses \(3 m , 2 m\) and \(m\) respectively. The spheres are at rest in a straight line on a smooth horizontal surface, with \(B\) between \(A\) and \(C\). The coefficient of restitution between \(A\) and \(B\) is \(e\) and the coefficient of restitution between \(B\) and \(C\) is \(e ^ { \prime }\). Sphere \(A\) is projected directly towards \(B\) with speed \(u\). Show that, after the collision between \(B\) and \(C\), the speed of \(C\) is \(\frac { 2 } { 5 } u ( 1 + e ) \left( 1 + e ^ { \prime } \right)\) and find the corresponding speed of \(B\). After this collision between \(B\) and \(C\) it is found that each of the three spheres has the same momentum. Find the values of \(e\) and \(e ^ { \prime }\).