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\includegraphics[max width=\textwidth, alt={}, center]{102e108b-2a36-4765-9990-78e2dd4276c0-3_216_1146_269_502} Three uniform spheres \(L , M\) and \(N\) have masses \(0.8 \mathrm {~kg} , 0.6 \mathrm {~kg}\) and 0.7 kg respectively. The spheres are moving in a straight line on a smooth horizontal table, with \(M\) between \(L\) and \(N\). The sphere \(L\) is moving towards \(M\) with speed \(4 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) and the spheres \(M\) and \(N\) are moving towards \(L\) with speeds \(2 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) and \(0.5 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) respectively (see diagram).

1. \(L\) collides with \(M\). As a result of this collision the direction of motion of \(M\) is reversed, and its speed remains \(2 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). Find the speed of \(L\) after the collision.
2. \(M\) then collides with \(N\).
   (a) Find the total momentum of \(M\) and \(N\) in the direction of \(M\) 's motion before this collision takes place, and deduce that the direction of motion of \(N\) is reversed as a result of this collision.
   (b) Given that \(M\) is at rest immediately after this collision, find the speed of \(N\) immediately after this collision.