3

\begin{figure}[h]
\begin{center}
  \includegraphics[alt={},max width=\textwidth]{8e1225a2-cb98-4b71-a4af-0150f093f852-2_528_688_845_731}
\captionsetup{labelformat=empty}
\caption{Fig. 1}
\end{center}
\end{figure}

A uniform conical shell has mass 0.2 kg , height 0.3 m and base diameter 0.8 m . A uniform hollow cylinder has mass 0.3 kg , length 0.7 m and diameter 0.8 m . The conical shell is attached to the cylinder, with the circumference of its base coinciding with one end of the cylinder (see Fig. 1).\\
(i) Show that the distance of the centre of mass of the combined object from the vertex of the conical shell is 0.47 m .

\begin{figure}[h]
\begin{center}
  \includegraphics[alt={},max width=\textwidth]{8e1225a2-cb98-4b71-a4af-0150f093f852-2_497_572_1836_788}
\captionsetup{labelformat=empty}
\caption{Fig. 2}
\end{center}
\end{figure}

The combined object is freely suspended from its vertex and is held with its axis horizontal. This is achieved by means of a wire attached to a point on the circumference of the base of the conical shell. The wire makes an angle of $80 ^ { \circ }$ with the slant edge of the conical shell (see Fig. 2).\\
(ii) Calculate the tension in the wire.

\hfill \mbox{\textit{OCR M2 2010 Q3 [8]}}