Standard +0.3 This is a standard M3 centre of mass question requiring volume of revolution and the centroid formula. Students apply familiar integration techniques (∫πy² dx for volume, ∫πxy² dx for moment) with a straightforward function y=√x. The calculation is routine with clear boundaries, making it slightly easier than average for A-level but typical for M3 material.
A uniform solid is formed by rotating the region enclosed between the curve with equation \(y = \sqrt{x}\), the \(x\)-axis and the line \(x = 4\), through one complete revolution about the \(x\)-axis. Find the distance of the centre of mass of the solid from the origin \(O\).
[5]
A uniform solid is formed by rotating the region enclosed between the curve with equation $y = \sqrt{x}$, the $x$-axis and the line $x = 4$, through one complete revolution about the $x$-axis. Find the distance of the centre of mass of the solid from the origin $O$.
[5]
\hfill \mbox{\textit{Edexcel M3 2006 Q1 [5]}}