Question

Find the centre of mass of three particles at the vertices of an equilateral triangle. The masses of the particles are $100g$, $150g$, and $200g$ respectively. Each side of the equilateral triangle is $0.5m$ long.

Answer 1

Let $COM$ is at $(x,y)$

$x=\frac{100\times 0+200\times 0.25+150\times 0.5}{100+200+150}\left[\frac{\sum x_1{m}_1}{\sum m}\right]$

$=\frac{5}{18}$

$y=\frac{\sum y_1{m}_1}{\sum m_1}=\frac{200\times 0+200\times 0.25\sqrt{3}+150\times 0}{100+200+150}$

$y=\frac{50\sqrt{3}}{450}=\frac{1}{3\sqrt{3}}COM=(\frac{5}{18},\frac{1}{3\sqrt{3}})$