Question

Locate the centre of mass of three particles of mass $m_1=1kg,m_2=2kg$ and $m_3=3kg$ at the corners of an equilateral triangle of each side of $1m$.

Answer 1

$X_{com}=\frac{m_1\times 0+m_2\times \frac{1}{2}+m_3\times 1}{m_1+m_2+m_3}$

$=\frac{2\times \frac{1}{2}+3\times 1}{6}=\frac{4}{6}=\frac{2}{3}$

$Y_{com}=\frac{m_1\times 0+m_2\times \frac{\sqrt{3}}{2}+m_3\times 0}{6}=\frac{\sqrt{3}}{6}=\frac{1}{2\sqrt{3}}$

C=$(\frac{2}{3},\frac{1}{2\sqrt{3}})$