3.
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\caption{Figure 1}
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\end{figure}
A uniform solid \(S\) is formed by taking a uniform solid right circular cone, of base radius \(2 r\) and height \(2 h\), and removing the cone, with base radius \(r\) and height \(h\), which has the same vertex as the original cone, as shown in Figure 1.
- Show that the distance of the centre of mass of \(S\) from its larger plane face is \(\frac { 11 } { 28 } h\).
The solid \(S\) lies with its larger plane face on a rough table which is inclined at an angle \(\theta ^ { \circ }\) to the horizontal. The table is sufficiently rough to prevent \(S\) from slipping. Given that \(h = 2 r\),
- find the greatest value of \(\theta\) for which \(S\) does not topple.