5.
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\caption{Figure 3}
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A uniform solid right circular cylinder has height \(h\) and radius \(r\). The centre of one plane face is \(O\) and the centre of the other plane face is \(Y\). A cylindrical hole is made by removing a solid cylinder of radius \(\frac { 1 } { 4 } r\) and height \(\frac { 1 } { 4 } h\) from the end with centre \(O\). The axis of the cylinder removed is parallel to \(O Y\) and meets the end with centre \(O\) at \(X\), where \(O X = \frac { 1 } { 4 } r\). One plane face of the cylinder removed coincides with the plane face through \(O\) of the original cylinder. The resulting solid \(S\) is shown in Figure 3.
- Show that the centre of mass of \(S\) is at a distance \(\frac { 85 h } { 168 }\) from the plane face
containing \(O\). containing \(O\).
The solid \(S\) is freely suspended from \(O\). In equilibrium the line \(O Y\) is inclined at an angle \(\arctan ( 17 )\) to the horizontal. - Find \(r\) in terms of \(h\).
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[Question 5 Continued]
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[Question 5 Continued]