Question

four particles of mass 1kg,2kg,3kg and 4kg are placed at the four vertices A,B,C and D of square of side 1m. find the position of center of mass of the particle

Answer 1

the position of the mass at the center can be the vertices A,B,C,D.

Answer 2

Let the masses be arranged at the corners of the square with 1kg at the origin.

X = (1 * 0 + 2 * 1 + 3 * 1 + 4 * 0) / (1 + 2 + 3 + 4)  = 5 / 10

This gives X = 1 for the x-coordinate of the C. M.

Likewise for Y:

Y = (1 * 0 + 2 * 0 + 3 * 1 + 4 * 1) / 10 = 7 / 10

Thus the center of mass is located at (X = .5 m, Y = .7 m)

Note: X = (m1 * x1 + m2 * x2 + m3 * x3 + m4 * x4) / (m1 + m2 + m3 + m4)

Calculate Y in a similar manner.

This result depends on the masses be numbered in counter-clockwise manner. The problem does not specify.