6.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{8a687d17-ec7e-463f-84dd-605f5c230db1-20_789_858_121_536}
\captionsetup{labelformat=empty}
\caption{Figure 7}
\end{figure}
A particle of mass \(m\) is attached to one end of a light inextensible string of length \(2 a\). The other end of the string is attached to a fixed point \(O\). The particle is initially held at the point \(A\) with the string taut and \(O A\) making an angle of \(60 ^ { \circ }\) with the downward vertical.
The particle is then projected upwards with a speed of \(3 \sqrt { a g }\), perpendicular to \(O A\), in the vertical plane containing \(O A\), as shown in Figure 7.
In an initial model of the motion of the particle, it is assumed that the string does not break.
Using this model,
- show that the particle performs complete vertical circles.
In a refined model it is assumed that the string will break if the tension in it exceeds 7 mg . Using this refined model,
- show that the particle still performs complete vertical circles.
\includegraphics[max width=\textwidth, alt={}, center]{8a687d17-ec7e-463f-84dd-605f5c230db1-20_2249_50_314_1982}