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 co-ordinate system is taken at the point of intersection of the diagonals of the square, the co - ordinates 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
$(x_1=-\frac{a}{2}{y}_1=-\frac{a}{2}),(x_2=\frac{a}{2},y_2=-\frac{a}{2})$
$(x_3=\frac{a}{2},y_3=\frac{a}{2}),(x_4=-\frac{a}{2},y_4=\frac{a}{2})$
It is easy to see that the co-ordinates of the centre of mass are (0, 0). Hence the correct choice is (d)