Three particles of masses $100 ext{ g}$, $150 ext{ g}$, and $200 ext{ g}$ are placed at the verti

Question

Three particles of masses $100	ext{ g}$, $150	ext{ g}$, and $200	ext{ g}$ are placed at the vertices of an equilateral triangle of side $0.5	ext{ m}$. What are the $(x, y)$ coordinates of the centre of mass if the $100	ext{ g}$ mass is at the origin and the $150	ext{ g}$ mass is along the positive x-axis?

Professor PC Thomas Classes · Answer

The x-coordinate is $X = \frac{m_1x_1 + m_2x_2 + m_3x_3}{m_1 + m_2 + m_3} = \frac{100(0) + 150(0.5) + 200(0.25)}{450} = \frac{125}{450} = \frac{5}{18}	ext{ m}$. The y-coordinate is $Y = \frac{100(0) + 150(0) + 200(0.25\sqrt{3})}{450} = \frac{50\sqrt{3}}{450} = \frac{1}{3\sqrt{3}}	ext{ m}$.