6.
\begin{figure}[h]
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\caption{Figure 4}
\includegraphics[alt={},max width=\textwidth]{e590030f-0c46-42ab-80b8-3627d3c36908-5_345_1255_1329_265}
\end{figure}
A particle of mass \(m\) rests on a rough plane inclined at an angle \(\alpha\) to the horizontal, where \(\tan \alpha = \frac { 3 } { 4 }\). The particle is attached to one end of a light inextensible string which lies in a line of greatest slope of the plane and passes over a small light smooth pulley \(P\) fixed at the top of the plane. The other end of the string is attached to a particle \(B\) of mass \(3 m\), and \(B\) hangs freely below \(P\), as shown in Fig. 4. The particles are released from rest with the string taut. The particle \(B\) moves down with acceleration of magnitude \(\frac { 1 } { 2 } g\). Find
- the tension in the string,
- the coefficient of friction between \(A\) and the plane.