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 \(20 \mathrm {~m} \mathrm {~s} ^ { - 1 }\).
- 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 \(R\). - Find the loss of kinetic energy due to the collision.
The coefficient of friction between \(R\) and the plane is 0.4 . - Find the distance travelled by particle \(R\) before coming to rest.