Question

Three particles are situated 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. The centre of mass is

• A. $\left(\frac{5}{6}m,\frac{1}{\sqrt{3}}m\right)$
• B. $\left(\frac{5}{9}m,\frac{1}{2\sqrt{3}}m\right)$
• C. $\left(\frac{5}{18}m,\frac{1}{3\sqrt{3}}m\right)$
• D. $\left(\frac{5}{9}m,\frac{1}{\sqrt{3}}m\right)$

Answer 1

Answer: (C)

The coordinates of $100g,150g$ and $200g$ are
$(0m,0m),\left(\frac{1}{2}m,0m\right)$ and $\left(\frac{1}{4}m,\frac{\sqrt{3}}{4}m\right)$ respectively
$X_{cm}=\frac{m_1{x}_1+m_2{x}_2+m_3{y}_3}{m_1+m_2+m_3}$
$=\frac{100(0)+150(0.5)+200(0.25)}{100+150+200}=\frac{125}{450}=\frac{5}{18}m$
Similarly,
$Y_{cm}=\frac{100(0)+150(0)+200(0.25\sqrt{3})}{450}=\frac{50\sqrt{3}}{450}$
$=\frac{1}{3\sqrt{3}}m$