Mathematics 9709 · AS & A Level · Representation of data

Representation of data — practice question

A uniform metal frame $OABC$ is formed from a semicircular arc $ABC$ with radius $1.8\text{ m}$ together with a straight rod $AOC$ where $AO = OC = 1.8\text{ m}$ (see diagram). A uniform semicircular lamina of radius $1.8\text{ m}$ weighs $27.5\text{ N}$. A non-uniform object is produced by fixing the frame $OABC$ around the edge of the lamina. The object is hung freely from a fixed point at $A$ and comes to equilibrium. The diameter $AOC$ of the object is inclined 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 frame's weight.

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