2.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{e0668f31-4b72-4dfd-9cf7-470acef0bfdb-2_469_465_776_680}
\captionsetup{labelformat=empty}
\caption{Fig. 1}
\end{figure}
A particle \(P\) of mass 0.5 kg is at rest at the highest point \(A\) of a smooth sphere, centre \(O\), of radius 1.25 m which is fixed to a horizontal surface.
When \(P\) is slightly disturbed it slides along the surface of the sphere. Whilst \(P\) is in contact with the sphere it has speed \(v \mathrm {~ms} ^ { - 1 }\) when \(\angle A O P = \theta\) as shown in Figure 1.
- Show that \(v ^ { 2 } = 24.5 ( 1 - \cos \theta )\).
- Find the value of \(\cos \theta\) when \(P\) leaves the surface of the sphere.