2 Two small smooth spheres \(A\) and \(B\), of equal radii and of masses km kg and \(m \mathrm {~kg}\) respectively, where \(k > 1\), are free to move on a smooth horizontal plane. \(A\) is moving towards \(B\) with speed \(6 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) and \(B\) is moving towards \(A\) with speed \(2 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). After the collision \(A\) and \(B\) coalesce and move with speed \(4 \mathrm {~ms} ^ { - 1 }\).

1. Find \(k\).
2. Find, in terms of \(m\), the loss of kinetic energy due to the collision.