6.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{330c2068-fe0a-4c6d-b892-79ab173c6a11-09_519_537_210_708}
\captionsetup{labelformat=empty}
\caption{Figure 4}
\end{figure}
Two particles \(A\) and \(B\) have masses \(5 m\) and \(k m\) respectively, where \(k < 5\). The particles are connected by a light inextensible string which passes over a smooth light fixed pulley. The system is held at rest with the string taut, the hanging parts of the string vertical and with \(A\) and \(B\) at the same height above a horizontal plane, as shown in Figure 4. The system is released from rest. After release, \(A\) descends with acceleration \(\frac { 1 } { 4 } g\).
- Show that the tension in the string as \(A\) descends is \(\frac { 15 } { 4 } \mathrm { mg }\).
- Find the value of \(k\).
- State how you have used the information that the pulley is smooth.
After descending for 1.2 s , the particle \(A\) reaches the plane. It is immediately brought to rest by the impact with the plane. The initial distance between \(B\) and the pulley is such that, in the subsequent motion, \(B\) does not reach the pulley.
- Find the greatest height reached by \(B\) above the plane.