8 The finite region enclosed by the line \(y = k x\), the \(x\)-axis and the line \(x = 5\) is rotated through \(360 ^ { \circ }\) around the \(x\) axis to form a solid cone.
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- Use integration to show that the position of the centre of mass of the cone is independent of \(k\)
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- (ii) State the distance between the base of the cone and its centre of mass.
8 - State one assumption that you have made about the cone.
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- The plane face of the cone is placed on a rough inclined plane.
The coefficient of friction between the cone and the plane is 0.8
The angle between the plane and the horizontal is gradually increased from \(0 ^ { \circ }\)
Find the range of values of \(k\) for which the cone slides before it topples.
[0pt]
[4 marks]