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4 point masses are placed at corners of a square of side 2m as shown.find centre of mass of system w.r.t. the square.
Let O is the centre of the square.A,B,C,D are the corners of the square.A = 1kgB= 2kgC = 3 kgD = 4 kgA HAVE COORDINATES = (1,1)B has cordinates = (−1,1)C = (−1,−1)D = (1,−1)as we are moving in anti−clockwise directionX coordinated of the centre fo mass:Xcm = m1x1+m2x2+m3x3+m4x4m1+m2+m3+m4Xcm = 1−2−3+41+2+3+4 = 0Y coordinate of the centre of mass:Ycm = m1y1+m2y2+m3y3+m4y4m1+m2+m3+m4Ycm = 1+2−3−41+2+3+4 = −0.4cordinates of centre of mass with respect to origin = (0, −0.4)
As they have asked to find the centre of mass of the system with respect to the centre of the square, let us consider the geometrical centre of the square as the origin(0,0)Let A=1kg ,B=2 kg, C=3 kg and D=4kgAnd the coordinates of A,B,C and D be(1,1),(1,-1),(-1,-1) and (-1,1) respectivelySo Xcom = [(1*1)+(1*2)+(3*-1)+(4*-1)]÷[1+2+3+4]Xcom = (1+2-3-4)÷ 10 = -0.4Ycom =[(1*1)+(-1*2)+(-1*3)+(4*1)]÷[1+2+3+4]Ycom = (1-2-3+4)÷ 10= 0Therefore the coordinates of COM is (-0.4,0)
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