Four particles, each of mass 1 kg, are placed at the corners of a square of side 1m in the X- Y plane. If the point of intersection of the diagonals of the square, is taken as the origin, the co-ordinates of the centre of mass are:

Question

Four particles, each of mass 1 kg, are placed at the corners of a square of side 1m in the X- Y plane. If the point of intersection of the diagonals of the square, is taken as the origin, the co-ordinates of the centre of mass are: (A) (1, 1) (B) (-1, 1) (C) (1,-1) (D) (0, 0)

Tardigrade Admin · Accepted Answer

Given: m1=m2=m3=m4=1 kg AB=BC=CD=DA=1m Hence, the co-ordinates of A, B, C, D are given in the figure, from the relation for xcm is xcm=(m1x1+m2x2+m3x3+m4x4/m1+m2+m3+m4) =(1× 0.5+1× 0.5+1(-0.5)+1× (-0.5)/1+1+1+1)=0 ycm=(m1y1+m2y2+m3y3+m4y4/m1+m2+m3+m4) =(1× 0.5+1× (-0.5)+1× (-0.5)+1× (0.5)/1+1+1+1) Co-ordinates of centre of mass will be (0,0).

Q. Four particles, each of mass 1 kg, are placed at the corners of a square of side 1m in the X- Y plane. If the point of intersection of the diagonals of the square, is taken as the origin, the co-ordinates of the centre of mass are:

(1, 1)

(-1, 1)

(1,-1)

(0, 0)