3 The object shown shaded in Fig. 3.1 is cut from a flat sheet of thin rigid uniform material; LMJK, OAIJ, AEFH and CDEB are rectangles. The grid-lines in Fig. 3.1 are 1 cm apart. \begin{figure}[h] \end{figure}

1. Calculate the coordinates of the centre of mass of the object referred to the axes shown in Fig. 3.1. [5] The object is freely suspended from the point K and hangs in equilibrium.
2. Calculate the angle that KI makes with the vertical. The mass of the object is 0.3 kg .
   A particle of mass \(m \mathrm {~kg}\) is attached to the object at a point on the line OJ so that the new centre of mass is at the centre of the square OAIJ.
3. Calculate the value of \(m\) and the position of the particle referred to the axes shown in Fig. 3.1. The extra particle is now removed and the object shown in Fig. 3.1 is folded: LMJK is folded along JM so that it is perpendicular to OAIJ; ABCDEFH is folded along AH so that it is perpendicular to OAIJ and on the same side of OAIJ as LMJK. The folded object is placed on a horizontal table with the edges KL and FED in contact with the table. A plan view and a 3D representation are shown in Fig. 3.2. \begin{figure}[h]
   \includegraphics[alt={},max width=\textwidth]{42b6ee17-f0ae-4687-8392-281ba724a607-4_609_648_1836_246} \captionsetup{labelformat=empty} \caption{Fig. 3.2}
   \end{figure} \begin{figure}[h]
   \includegraphics[alt={},max width=\textwidth]{42b6ee17-f0ae-4687-8392-281ba724a607-4_332_695_2001_1144} \captionsetup{labelformat=empty} \caption{Fig. 3.2}
   \end{figure}
4. On the plan, indicate the region corresponding to positions of the centre of mass for which the folded object is stable. You are given that the \(x\)-coordinate of the centre of mass of the folded object is 1.7 . Determine whether the object is stable.