8.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{60b9db45-b48e-40a1-bd22-909e11877bc3-4_442_924_877_443}
\captionsetup{labelformat=empty}
\caption{Fig. 3}
\end{figure}
Figure 3 shows two particles \(A\) and \(B\), of mass \(5 M\) and \(3 M\) respectively, attached to the ends of a light inextensible string of length 4 m . The string passes over a smooth pulley which is fixed to the edge of a rough horizontal table 2 m high. Particle \(A\) lies on the table at a distance of 3 m from the pulley, whilst particle \(B\) hangs freely over the edge of the table 1 m above the ground. The coefficient of friction between \(A\) and the table is \(\frac { 3 } { 20 }\).
The system is released from rest with the string taut.
- Show that the initial acceleration of the system is \(\frac { 9 } { 32 } \mathrm {~g} \mathrm {~ms} ^ { - 2 }\).
- Find, in terms of \(g\), the speed of \(A\) immediately before \(B\) hits the ground.
When \(B\) hits the ground, it comes to rest and the string becomes slack.
- Calculate how far particle \(A\) is from the pulley when it comes to rest.
END