4 Two particles \(P\) and \(Q\), of masses 6 kg and 2 kg respectively, lie at rest 12.5 m apart on a rough horizontal plane. The coefficient of friction between each particle and the plane is 0.4 . Particle \(P\) is projected towards \(Q\) with speed \(20 \mathrm {~m} \mathrm {~s} ^ { - 1 }\).

1. Show that the speed of \(P\) immediately before the collision with \(Q\) is \(10 \sqrt { 3 } \mathrm {~m} \mathrm {~s} ^ { - 1 }\).
   In the collision \(P\) and \(Q\) coalesce to form particle \(R\).
2. Find the loss of kinetic energy due to the collision.
   The coefficient of friction between \(R\) and the plane is 0.4 .
3. Find the distance travelled by particle \(R\) before coming to rest.