Question

Four particles, each of mass m, are placed at the corners of a square of side a in the x-y plane. If the origin of the coordinate system is taken at the point of intersection of the diagonals of the square, the coordinates of the centre of mass of the system are

• A. (a, a)
• B. (-a, a)
• C. (a, -a)
• D. (0, 0)

Answer 1

The correct option is D

(0, 0)

Given AB = BC = CD = AD = a. The (x, y) co-ordinates of the masses at A, B, C and D respectively are $(x_1=-\frac{a}{2},y_1=-\frac{a}{2}),(x_2=\frac{a}{2},y_2=-\frac{a}{2}),(x_3=\frac{a}{2},y_3=\frac{a}{2})$ and $(x_4=-\frac{a}{2},y_4=\frac{a}{2})$.
It is easy to see that all the masses are symmetrically situated with respect to O. Hence, the coordinates of the centre of mass are (0,0) and the correct choice is (d).