A uniform wire is bent into the form of a rectangle of length L and width W The coordinates of - Physics - System Of Particles And Rotational Motion

Question

A uniform wire is bent into the form of a rectangle of length L and
width W The coordinates of its centre of mass from a corner are
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Somnath physics · Accepted Answer

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Let the lower left corner be the origin of the rectangular frame
OABC Coordinates of O, A, B,​ C are respectively, (0,0),
(L,0), (L,W), (0,W) Let the mass of the wire be =mTotal length of
the wire = 2(L+W)Mass of the piece of wire forming the longer side
of the frame= mL2(L+W)Mass of the piece of wire forming the shorter
side of the frame= mW2(L+W) CM of a uniform wire = middle point of
the wire So, CM of OA, AB, BC and CO are respectively A', B', C'
and O': the middle pointsof the sides So we can consider our system
to be consisted of two masses mL2(L+W) concentrated at A' and
C'mW2(L+W) concentrated at B' and O'Coordinates of A', B', C' and
O' are respectively (L2,0),(L,W2),(L2,W),(0,W2)x coordinate of CM
of the frame will be∑i=1nmixim
X=mL2(L+W)×L2+mW2(L+W)×L+mL2(L+W)×L2+mW2(L+W)×0m=L2(L+W)×L2+W2(L+W)×L+L2(L+W)×L2=L2(L+W)(L+W)=L2y
coordinate of CM of the frame will
be∑i=1nmiyimY=mL2(L+W)×0+mW2(L+W)×W2+mL2(L+W)×W+mW2(L+W)×W2m=W2(L+W)(W2+L+W2)=W2(L+W)(L+W)=W2Thus
coordinate of the CM (X,Y) is (L2,W2)

A uniform wire is bent into the form of a rectangle of length L and width W.The coordinates of its centre of mass from a corner are ----------