6.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{8338c3a4-cb37-4979-a424-e7cf4901207a-09_410_1025_255_520}
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\caption{Figure 1}
\end{figure}
A smooth solid hemisphere of radius 0.5 m is fixed with its plane face on a horizontal floor. The plane face has centre \(O\) and the highest point of the surface of the hemisphere is \(A\). A particle \(P\) has mass 0.2 kg . The particle is projected horizontally with speed \(u \mathrm {~m} \mathrm {~s} ^ { - 1 }\) from \(A\) and leaves the hemisphere at the point \(B\), where \(O B\) makes an angle \(\theta\) with \(O A\), as shown in Figure 1. The point \(B\) is at a vertical distance of 0.1 m below the level of \(A\). The speed of \(P\) at \(B\) is \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\)
- Show that \(v ^ { 2 } = u ^ { 2 } + 1.96\)
- Find the value of \(u\).
The particle first strikes the floor at the point \(C\).
- Find the length of \(O C\).