Question

Four particle of mass $5,3,2,4kg$ are at the points $(1,6),(-1,5),(2,-3),(-1,-4)$. Find the coordinates of their center of mass.

Answer 1

Co-ordinates of centre of mass $(x,y)=\frac{\Sigma m_i{x}_i}{\Sigma m_i}$ $,\frac{\Sigma m_i{y}_i}{\Sigma m_i}$

So, x-coordinate $=\frac{5\left(1\right)+3(-1)+2\left(2\right)+4(-1)}{5+3+2+4}=\frac{1}{7}$

And, y-coordinate $=\frac{5\left(6\right)+3\left(5\right)+2(-3)+4(-4)}{5+3+2+4}=\frac{23}{14}$

Hence, the coordinates of their center of mass is $(\frac{1}{7},\frac{23}{14})$