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A sign-board consists of a rectangular sheet of metal, of mass \(M\), which is 3 metres wide and 1 metre high, attached to two thin metal supports, each of mass \(m\) and length 2 metres. The board stands on horizontal ground.
- Calculate the height above the ground of the centre of mass of the sign-board, in terms of \(M\) and \(m\).
Given now that the centre of mass of the sign-board is \(2 \cdot 2\) metres above the ground, (b) find the ratio \(M : m\), in its simplest form.
\section*{MECHANICS 2 (A) TEST PAPER 9 Page 2}