CAIE M2 2019 March — Question 5

Exam BoardCAIE
ModuleM2 (Mechanics 2)
Year2019
SessionMarch
TopicMoments

5 A particle \(P\) of mass 0.3 kg is attached to one end of a light elastic string of natural length 0.6 m and modulus of elasticity 24 N . The other end of the string is attached to a fixed point \(O\). The particle \(P\) is released from rest at the point 0.4 m vertically below \(O\).
  1. Find the greatest speed of \(P\).
  2. Calculate the greatest distance of \(P\) below \(O\).
    \begin{figure}[h]
    \includegraphics[alt={},max width=\textwidth]{b8e52188-f9a6-46fc-90bf-97965c6dd324-10_608_611_258_767} \captionsetup{labelformat=empty} \caption{Fig. 1}
    \end{figure} Fig. 1 shows the cross-section of a solid cylinder through which a cylindrical hole has been drilled to make a uniform prism. The radius of the cylinder is \(5 r\) and the radius of the hole is \(r\). The centre of the hole is a distance \(2 r\) from the centre of the cylinder.