7.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{edcc4603-f006-4c4f-a4e5-063cab41da98-12_486_1257_230_347}
\captionsetup{labelformat=empty}
\caption{Figure 3}
\end{figure}
Two particles \(P\) and \(Q\), of mass 2 kg and 3 kg respectively, are connected by a light inextensible string. Initially \(P\) is held at rest on a fixed smooth plane inclined at \(30 ^ { \circ }\) to the horizontal. The string passes over a small smooth fixed pulley at the top of the plane. The particle \(Q\) hangs freely below the pulley and 0.6 m above the ground, as shown in Figure 3. The part of the string from \(P\) to the pulley is parallel to a line of greatest slope of the plane. The system is released from rest with the string taut.
For the motion before \(Q\) hits the ground,
- show that the acceleration of \(Q\) is \(\frac { 2 g } { 5 }\),
- find the tension in the string.
On hitting the ground \(Q\) is immediately brought to rest by the impact.
- Find the speed of \(P\) at the instant when \(Q\) hits the ground.
In its subsequent motion \(P\) does not reach the pulley.
- Find the total distance moved up the plane by \(P\) before it comes to instantaneous rest.
- Find the length of time between \(Q\) hitting the ground and \(P\) first coming to instantaneous rest.