6.

\begin{figure}[h]
\begin{center}
  \includegraphics[alt={},max width=\textwidth]{ae189c40-0071-4a6b-91eb-8ffebe082a04-20_497_643_237_653}
\captionsetup{labelformat=empty}
\caption{Figure 5}
\end{center}
\end{figure}

Figure 5 shows a hollow sphere, with centre $O$ and internal radius $a$, which is fixed to a horizontal surface. A particle $P$ of mass $m$ is projected horizontally with speed $\sqrt { \frac { 7 a g } { 2 } }$ from the lowest point $A$ of the inner surface of the sphere. The particle moves in a vertical circle with centre $O$ on the smooth inner surface of the sphere. The particle passes through the point $B$, on the inner surface of the sphere, where $O B$ is horizontal.
\begin{enumerate}[label=(\alph*)]
\item Find, in terms of $m$ and $g$, the normal reaction exerted on $P$ by the surface of the sphere when $P$ is at $B$.

The particle leaves the inner surface of the sphere at the point $C$, where $O C$ makes an angle $\theta , \theta > 0$, with the upward vertical.
\item Show that, after leaving the surface of the sphere at $C$, the particle is next in contact with the surface at $A$.

\begin{center}
\begin{tabular}{|l|l|}
\hline

\hline
END &  \\
\hline
\end{tabular}
\end{center}
\end{enumerate}

\hfill \mbox{\textit{Edexcel M3 2019 Q6 [16]}}