7
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{8e1225a2-cb98-4b71-a4af-0150f093f852-4_444_771_258_687}
\captionsetup{labelformat=empty}
\caption{Fig. 1}
\end{figure}
A particle \(P\) of mass 0.2 kg is moving on the smooth inner surface of a fixed hollow hemisphere which has centre \(O\) and radius \(5 \mathrm {~m} . P\) moves with constant angular speed \(\omega\) in a horizontal circle at a vertical distance of 3 m below the level of \(O\) (see Fig.1).
- Calculate the magnitude of the force exerted by the hemisphere on \(P\).
- Calculate \(\omega\).
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{8e1225a2-cb98-4b71-a4af-0150f093f852-4_592_773_1231_687}
\captionsetup{labelformat=empty}
\caption{Fig. 2}
\end{figure}
A light inextensible string is now attached to \(P\). The string passes through a small smooth hole at the lowest point of the hemisphere and a particle of mass 0.1 kg hangs in equilibrium at the end of the string. \(P\) moves in the same horizontal circle as before (see Fig. 2). - Calculate the new angular speed of \(P\).