8.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{3280fdf1-d81a-4729-b065-e84dece6a220-13_648_1280_271_331}
\captionsetup{labelformat=empty}
\caption{Figure 3}
\end{figure}
Two particles \(P\) and \(Q\) have masses \(m\) and \(4 m\) respectively. The particles are attached to the ends of a light inextensible string. Particle \(P\) is held at rest on a rough horizontal table. The string lies along the table and passes over a small smooth light pulley which is fixed at the edge of the table. Particle \(Q\) hangs at rest vertically below the pulley, at a height \(h\) above a horizontal plane, as shown in Figure 3. The coefficient of friction between \(P\) and the table is 0.5 . Particle \(P\) is released from rest with the string taut and slides along the table.
- Find, in terms of \(m g\), the tension in the string while both particles are moving.
The particle \(P\) does not reach the pulley before \(Q\) hits the plane.
- Show that the speed of \(Q\) immediately before it hits the plane is \(\sqrt { 1.4 g h }\)
When \(Q\) hits the plane, \(Q\) does not rebound and \(P\) continues to slide along the table. Given that \(P\) comes to rest before it reaches the pulley,
- show that the total length of the string must be greater than 2.4 h