OCR A Level: Mechanics 2 - Centre Of Mass [June 2006 Q5]

A uniform lamina $ABCDE$ consists of a square and an isosceles triangle. The square has sides of $18 \text{cm}$ and $BC = CD = 15 \text{cm}$ (see diagram).

$(\text{i})$ Taking $x$ - and $y$ -axes along $AE$ and $AB$ respectively, find the coordinates of the centre of mass of the lamina.

$(\text{ii})$ The lamina is freely suspended from $B$ . Calculate the acute angle that $BD$ makes with the vertical.

---

Input the angle in degrees, to three significant figures, as your answer.

---

There are 7 marks available for part (i) and 2 marks for part (ii).

In total, this question is worth 12.5% of all available marks in the paper.

---

This is part of the set OCR A Level Problems .