4 Small smooth spheres \(A\) and \(B\), of equal radii and of masses 4 kg and 2 kg respectively, lie on a smooth horizontal plane. Initially \(B\) is at rest and \(A\) is moving towards \(B\) with speed \(10 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). After the spheres collide \(A\) continues to move in the same direction but with half the speed of \(B\).

1. Find the speed of \(B\) after the collision.
   A third small smooth sphere \(C\), of mass 1 kg and with the same radius as \(A\) and \(B\), is at rest on the plane. \(B\) now collides directly with \(C\). After this collision \(B\) continues to move in the same direction but with one third the speed of \(C\).
2. Show that there is another collision between \(A\) and \(B\).
3. \(\quad A\) and \(B\) coalesce during this collision. Find the total loss of kinetic energy in the system due to the three collisions.