OCR A Level: Mechanics 2 - Centre Of Mass [June 2006 Q3]

Classical Mechanics Level pending

A uniform solid hemisphere of weight $$12 \text{N}$$ and radius $$6 \text{cm}$$ is suspended by two vertical strings. One string is attached to the point $$O$$, the centre of the plane face, and the other string is attached to the point $$A$$ on the rim of the plane face. The hemisphere hangs in equilibrium and $$OA$$ makes an angle of $$60°$$ with the vertical (see diagram).

$$(\text{i})$$ Find the horizontal distance from the centre of mass of the hemisphere to the vertical through $$O$$.

$$(\text{ii})$$ Calculate the tensions in the strings (to three significant figures).

Input the product of the two tensions as your answer.

This is part of the set OCR A Level Problems.
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