Representation of data — practice question

The cross-section $OABC$ passes through the centre of mass of a uniform prism whose weight is $20\,\text{N}$. This cross-section has the form of a sector of a circle with centre $O$, radius $OA = r\,\text{m}$ and angle $AOC = \frac{2}{3}\pi$ radians. The prism rests on a plane inclined at an angle $\theta$ radians to the horizontal, where $\theta < \tfrac{1}{3}\pi$. The line $OC$ is along a line of greatest slope, with $O$ higher than $C$. The prism is freely hinged to the plane at $O$. A force of magnitude $15\,\text{N}$ acts at $A$, directed towards the plane and at right angles to it (see diagram).