Mathematics 9709 · AS & A Level · Representation of data

Representation of data — practice question

A uniform metal frame $OABC$ is constructed from a semicircular arc $ABC$ with radius $1.8\,\text{m}$ and a straight rod $AOC$, where $AO = OC = 1.8\,\text{m}$ (see diagram). A uniform semicircular lamina of radius $1.8\,\text{m}$ has weight $27.5\,\text{N}$. By attaching the frame $OABC$ around the boundary of the lamina, a non-uniform object is produced. The object is then freely hung from a fixed point at $A$ and is in equilibrium. The diameter $AOC$ of the object is at an angle of $22^\circ$ to the vertical.
(i)[3]

Calculate the distance from $O$ to the centre of mass of the frame.

(ii)[5]

Calculate the weight of the frame.

Worked solution & mark scheme

This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: Using correct geometry, for example $OG = 1.8\sin(\pi/2)/(\pi/2)$

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