Question

Define centre of mass of a system of particles. Find the centre of mass of three particles at the vertices of an equilateral triangle.
The masses of the particles one $100g,150g$, and $200g$. Each side of the equilateral

triangle is $0.5m$ long. [Take $100gm$ at origin].

Answer 1

Center of mass is the point where the whole mass of the system can be supposed to be $concentrated.$

X coordinate of the center of mass of a 3 mass system will be $X_{cm}=\frac{m_1{x}_1+m_2{x}_2+m_3{x}_3}{m_1+m_2+m_3}$

Y coordinate of the center of mass of a 3 mass system will be $Y_{cm}=\frac{m_1{y}_1+m_2{y}_2+m_3{y}_3}{m_1+m_2+m_3}$

Taking 100g at origin and 150 g at x axis will get $x_1=0,y_1=0$ with $m_1=100g$

and $x_2=0.5,y_2=0$ with $m_2=150g$

and $x_3=\frac{0.5}{2},y_3=0.5\frac{\sqrt{3}}{2}$ with $m_3=200g$

putting all these values we get $X_{cm}=\frac{5}{18}m$

and $Y_{cm}=\frac{1}{3\sqrt{3}}m$