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Question

Two squares of size (a×a) each are removed from a bigger square of size (2a×2a) as shown in the figure. Removed parts are unshaded in the figure given below. Find the coordinates of the COM w.r.t the origin O.


A
(a2,a2)
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B
(a2,a2)
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C
(0,0)
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D
(a,a)
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Solution

The correct option is C (0,0)
Given: areas and COMs of the shapes, taing O as the origin.
AreaCOMparent square2a×2a=4a2(0,0)removed squaresa×a=a2(a/2,a/2)a×a=a2(a/2,a/2)

As we know,
xCOM=4a2×(0)+(a2)×(a/2)+(a2)×(a/2)4a2a2a2
(Take removed areas as negative)
xCOM=0

Similarly
yCOM=4a2×(0)+(a2)×(a/2)+(a2)×(a/2)4a2a2a2
yCOM=0

Hence, the COM will be at (0,0).

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