Four particle of masses m1 = 2m, m2 = 4 m, m3 = m and m4 are placed at four corners of a square. What should be the value of m4 so that the centres of mass of all the four particles are exactly at the centre of the square?

Let side of square is a.xcm = a2 = m1×0+m2×a+m3×a+m4×0m1+m2+m3+m4solve to get m4 = 3 mycm = a2 = m1×0+m2×0+m3×a+m4×am1+m2+m3+m4solve to get m4 = 5mThey are contradicting, so it is not possible to have centre of mass at the centre of square.