Given:
- Mass of each particle, m = 1 kg
- Side length of the square, a = 1 m
The coordinates of the four corners of the square are: A(0, 0), B(1, 0), C(0, 1), D(1, 1)
The x-coordinate of the center of mass (Xcm) is given by: Xcm = (m1x1 + m2x2 + m3x3 + m4x4) / (m1 + m2 + m3 + m4)
Similarly, the y-coordinate of the center of mass (Ycm) is given by: Ycm = (m1y1 + m2y2 + m3y3 + m4y4) / (m1 + m2 + m3 + m4)
Here, since all particles have the same mass, m1 = m2 = m3 = m4 = 1 kg.
Let's plug in the values: Xcm = (0 + 1 + 0 + 1) / 4 = 0.5 Ycm = (0 + 0 + 1 + 1) / 4 = 0.5
So, the center of mass of the system is located at the coordinates (0.5, 0.5), which corresponds to the intersection point of the diagonals of the square.
