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

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.

---

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 .