4.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{962c2b40-3c45-4eed-a0af-a59068bda0e1-12_492_412_246_824}
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\caption{Figure 3}
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A uniform solid cylinder of base radius \(r\) and height \(\frac { 4 } { 3 } r\) has the same density as a uniform solid hemisphere of radius \(r\). The plane face of the hemisphere is joined to a plane face of the cylinder to form the composite solid \(S\) shown in Figure 3. The point \(O\) is the centre of the plane face of \(S\).
- Show that the distance from \(O\) to the centre of mass of \(S\) is \(\frac { 73 } { 72 } r\)
The solid \(S\) is placed with its plane face on a rough horizontal plane. The coefficient of friction between \(S\) and the plane is \(\mu\). A horizontal force \(P\) is applied to the highest point of \(S\). The magnitude of \(P\) is gradually increased.
- Find the range of values of \(\mu\) for which \(S\) will slide before it starts to tilt.