Question

Four particles are located at points (1,3), (2,2), (3,3), (4,3).

Answer 1

1) Same mass:
a) calculate M-x = my₁+my₂+my₃+m4₄ = m(3+2+3+3) = 11m
b) calculate M-y = mx₁+mx₂+mx₃+mx₄ = m(1+2+3+4) = 10m
The center of mass (or center of gravity: POINT(X,Y) is given by:
X = 10m/∑(m) = 10m/4m, so X= 5/2
Y = 11m/∑(m) = 11m/4m ,so Y =11/4

2) Different masses: m₁ = 3; m₂ = 2 ; m₃ = 5 ; m₄ = 7
a) calculate M-x = m₁y₁+m₂y₂+m₃y₃+m₄y₄
    M-x= 3.(3)+2(2)+5(3)+7(3) = 50
b) calculate M-y =m₁x₁+m₂x₂+m₃x₃+m₄x₄
    M-y=3(1)+2(2)+5(3)+7(4) = 50
The center of mass (or center of gravity: POINT(X,Y) is given by
X= 50/17
Y= 50/17

Hope that I understood the given of the problem & I didn't make mistakes in calculation