2.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{bd1e2b07-4a87-49d6-addd-c9f67467ef2f-04_351_993_246_536}
\captionsetup{labelformat=empty}
\caption{Figure 2}
\end{figure}
A particle \(P\) of mass \(m\) is attached to one end of a light inextensible string of length \(2 l\). The other end of the string is attached to a fixed point \(A\) above a smooth horizontal floor. The particle moves in a horizontal circle on the floor with the string taut. The centre \(O\) of the circle is vertically below \(A\) with \(O A = l\), as shown in Figure 2 .
The particle moves with constant angular speed \(\omega\) and remains in contact with the floor.
Show that
$$\omega \leqslant \sqrt { \frac { g } { l } }$$