6
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{65c47bd2-eace-4fec-b1e6-a0c904c4ec3f-3_538_478_758_836}
\captionsetup{labelformat=empty}
\caption{Fig. 1}
\end{figure}
A container is constructed from a hollow cylindrical shell and a hollow cone which are joined along their circumferences. The cylindrical shell has radius 0.2 m , and the cone has semi-vertical angle \(30 ^ { \circ }\). Two identical small spheres \(P\) and \(Q\) move independently in horizontal circles on the smooth inner surface of the container (see Fig. 1). Each sphere has mass 0.3 kg .
- \(P\) moves in a circle of radius 0.12 m and is in contact with only the conical part of the container. Calculate the angular speed of \(P\).
- \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{65c47bd2-eace-4fec-b1e6-a0c904c4ec3f-3_278_209_1845_1009}
\captionsetup{labelformat=empty}
\caption{Fig. 2}
\end{figure}
\(Q\) moves with speed \(2.1 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) and is in contact with both the cylindrical and conical surfaces of the container (see Fig. 2). Calculate the magnitude of the force which the cylindrical shell exerts on the sphere. - Calculate the difference between the mechanical energy of \(P\) and of \(Q\).
\section*{[Question 7 is printed overleaf.]}