1 Particles \(P\) of mass \(m \mathrm {~kg}\) and \(Q\) of mass 0.2 kg are free to move on a smooth horizontal plane. \(P\) is projected at a speed of \(2 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) towards \(Q\) which is stationary. After the collision \(P\) and \(Q\) move in opposite directions with speeds of \(0.5 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) and \(1 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) respectively. Find \(m\).