Edexcel M3 2017 January — Question 1

Exam BoardEdexcel
ModuleM3 (Mechanics 3)
Year2017
SessionJanuary
TopicCentre of Mass 2

1. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{85d8fc7d-8863-419e-8eef-8751a6fb6315-02_483_702_255_612} \captionsetup{labelformat=empty} \caption{Figure 1}
\end{figure} The shaded region \(R\) is bounded by the curve with equation \(y ^ { 2 } = 9 ( 4 - x )\), the positive \(x\)-axis and the positive \(y\)-axis, as shown in Figure 1. A uniform solid \(S\) is formed by rotating \(R\) through \(360 ^ { \circ }\) about the \(x\)-axis.
Use algebraic integration to find the \(x\) coordinate of the centre of mass of \(S\).