2 The shaded region shown in Fig. 2.1 is cut from a sheet of thin rigid uniform metal; LBCK and EFHI are rectangles; EF is perpendicular to CK . The dimensions shown in the figure are in centimetres. The Oy and Oz axes are also shown.

\begin{figure}[h]
\begin{center}
  \includegraphics[alt={},max width=\textwidth]{a6297924-579e-4340-8fe6-2b43bd1a8698-3_716_1011_383_529}
\captionsetup{labelformat=empty}
\caption{Fig. 2.1}
\end{center}
\end{figure}

(i) Calculate the coordinates of the centre of mass of the metal shape referred to the axes shown in Fig. 2.1.

The metal shape is freely suspended from the point H and hangs in equilibrium.\\
(ii) Calculate the angle that HI makes with the vertical.

The metal shape is now folded along OJ , AD and EI to give the object shown in Fig. 2.2; LOJK, ABCD and IEFH are all perpendicular to OADJ; LOJK and ABCD are on one side of OADJ and IEFH is on the other side of it.

\begin{figure}[h]
\begin{center}
  \includegraphics[alt={},max width=\textwidth]{a6297924-579e-4340-8fe6-2b43bd1a8698-3_542_929_1713_575}
\captionsetup{labelformat=empty}
\caption{Fig. 2.2}
\end{center}
\end{figure}

(iii) Referred to the axes shown in Fig. 2.2, show that the $x$-coordinate of the centre of mass of the object is - 0.1 and find the other two coordinates of the centre of mass.

The object is placed on a rough inclined plane with LOAB in contact with the plane. OL is parallel to a line of greatest slope of the plane with L higher than O . The object does not slip but is on the point of tipping about the edge OA .\\
(iv) Calculate the angle of OL to the horizontal.

\hfill \mbox{\textit{OCR MEI M2 2012 Q2 [18]}}