6 Three particles, A, B and C are in a straight line on a smooth horizontal surface.
The particles have masses \(5 \mathrm {~kg} , 3 \mathrm {~kg}\) and 1 kg respectively. Particles B and C are at rest. Particle A is projected towards B with a speed of \(u \mathrm {~ms} ^ { - 1 }\) and collides with B . The coefficient of restitution between A and B is \(\frac { 1 } { 3 }\).
Particle B subsequently collides with C. The coefficient of restitution between B and C is \(\frac { 1 } { 3 }\).
- Determine whether any further collisions occur.
- Given that the loss of kinetic energy during the initial collision between A and B is 4.8 J , find the value of \(u\).
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{6b27d322-417e-4cea-85cc-65d3728173c8-5_607_501_294_301}
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\caption{Fig. 7}
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Fig. 7 shows a uniform rod AB of length \(4 a\) and mass \(m\).
The end A rests against a rough vertical wall. A light inextensible string is attached to the rod at B and to a point C on the wall vertically above A , where \(\mathrm { AC } = 4 a\). The plane ABC is perpendicular to the wall and the angle ABC is \(30 ^ { \circ }\).
The system is in limiting equilibrium.
Find the coefficient of friction between the wall and the rod.
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