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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)

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B

(-a, a)

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C

(a, -a)

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D

(0, 0)

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Solution

## 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 (x1=−a2,y1=−a2),(x2=a2,y2=−a2),(x3=a2,y3=a2) and (x4=−a2,y4=a2). 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).

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