Three particles \(A , B\) and \(C\) lie at rest in a straight line on a smooth horizontal table with \(B\) between \(A\) and \(C\). The masses of \(A , B\) and \(C\) are \(3 m\), 4m, and 5m respectively. Particle \(A\) is projected with speed \(u\) towards particle \(B\) and collides directly with \(B\). The coefficient of restitution between \(A\) and \(B\) is \(\frac { 1 } { 3 }\).
Show that the impulse exerted by \(A\) on \(B\) in this collision has magnitude \(\frac { 16 } { 7 } m u\)
After the collision between \(A\) and \(B\) there is a direct collision between \(B\) and \(C\).
After this collision between \(B\) and \(C\), the kinetic energy of \(C\) is \(\frac { 72 } { 245 } m u ^ { 2 }\)
Find the coefficient of restitution between \(B\) and \(C\).