4. Figure 2
\includegraphics[max width=\textwidth, alt={}, center]{a46d3d34-2381-4e73-837f-a60663fb1419-4_532_907_229_691} Figure 2 shows the region \(R\) bounded by the curve with equation \(y ^ { 2 } = r x\), where \(r\) is a positive constant, the \(x\)-axis and the line \(x = r\). A uniform solid of revolution \(S\) is formed by rotating \(R\) through one complete revolution about the \(x\)-axis.

1. Show that the distance of the centre of mass of \(S\) from \(O\) is \(\frac { 2 } { 3 } r\).
   (6) The solid is placed with its plane face on a plane which is inclined at an angle \(\alpha\) to the horizontal. The plane is sufficiently rough to prevent \(S\) from sliding. Given that \(S\) does not topple,
2. find, to the nearest degree, the maximum value of \(\alpha\).
   (4)