\begin{tikzpicture}[>=Stealth, scale=2.5]
  % Coordinates
  \coordinate (O) at (0,0);
  \coordinate (A) at (-0.5,0);
  \coordinate (B) at (0,-0.7);
  
  % Main disc (filled light gray)
  \fill[gray!20] (O) circle (1.2);
  \draw[thick] (O) circle (1.2);
  
  % Hole at A (white to represent hole)
  \fill[white] (A) circle (0.3);
  \draw[thick] (A) circle (0.3);
  
  % Hole at B (white to represent hole)
  \fill[white] (B) circle (0.4);
  \draw[thick] (B) circle (0.4);
  
  % Axes
  \draw[->] (-1.5,0) -- (1.5,0) node[right] {$x$};
  \draw[->] (0,-1.5) -- (0,1.5) node[above] {$y$};
  
  % Radius dashed line from O to upper right edge
  \draw[dashed] (O) -- (45:1.2);
  \node[above right] at (0.42,0.42) {$1.2\,\mathrm{m}$};
  
  % Label O
  \node[above right, xshift=1pt, yshift=1pt] at (O) {$O$};
  
  % Label A
  \node[above left, xshift=-1pt] at (A) {$A$};
  
  % Label B
  \node[right, xshift=3pt] at (B) {$B$};
  
  % Small dot at O
  \fill (O) circle (0.02);
\end{tikzpicture}

A uniform circular disc has centre $O$ and radius $1.2\text{ m}$. The centre of the disc is at the origin of $x$- and $y$-axes. Two circular holes with centres at $A$ and $B$ are made in the disc (see diagram). The point $A$ is on the negative $x$-axis with $OA = 0.5\text{ m}$. The point $B$ is on the negative $y$-axis with $OB = 0.7\text{ m}$. The hole with centre $A$ has radius $0.3\text{ m}$ and the hole with centre $B$ has radius $0.4\text{ m}$. Find the distance of the centre of mass of the object from

\begin{enumerate}[label=(\roman*)]
\item the $x$-axis, [4]
\item the $y$-axis. [3]
\end{enumerate}

The object can rotate freely in a vertical plane about a horizontal axis through $O$.

\begin{enumerate}[label=(\roman*)]
\setcounter{enumi}{2}
\item Calculate the angle which $OA$ makes with the vertical when the object rests in equilibrium. [2]
\end{enumerate}

\hfill \mbox{\textit{CAIE M2 2015 Q6 [9]}}