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).

###### There are **2** marks available for part (i) and **5** marks for part (ii).

###### In total, this question is worth **9.72%** of all available marks in the paper.

###### This is part of the set OCR A Level Problems.

\((\text{i})\) 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.**

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