Question

Three particles are situated at the vertices of an equilateral triangle. The masses of the particles are $100\,g$, $150\,g$ and $200\,g$ respectively. Each side of the equilateral triangle is $0.5\, m$ 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 $100\, g , 150 \,g$ and $200 \,g$ are
$(0 m , 0 m ),\left(\frac{1}{2} m , 0 m \right)$ 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,
$Y_{ cm }=\frac{100(0)+150(0)+200(0.25 \sqrt{3})}{450}=\frac{50 \sqrt{3}}{450}$
$=\frac{1}{3 \sqrt{3}} \,m$