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Question

Four uniform rods of mass m kg each form a rectangle as shown in figure. The rods have negligible area of cross-section. Find the position of center of mass of the rectangle made up of the four uniform rods.


A
(2,2) m
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B
(2,0) m
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C
(2,1) m
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D
(4,2) m
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Solution

The correct option is C (2,1) m

Given, mass of each rod =m kg
Co-ordinate of COM of rod I, (x1,y1)=(2,0) m
Co-ordinate of COM of rod II, (x2,y2)=(0,1) m
Co-ordinate of COM of rod III, (x3,y3)=(2,2) m
Co-ordinate of COM of rod IV, (x4,y4)=(4,1) m

Therefore, x co-ordinate of COM of rectangle
xCOM=m1x1+m2x2+m3x3+m4x4m1+m2+m3+m4
[m1=m2=m3=m4=m]
=m×2+m×0+m×2+m×4m+m+m+m
=8m4m=2 m
and y co-ordinate of COM of rectangle
yCOM=m1y1+m2y2+m3y3+m4y4m1+m2+m3+m4
=m×0+m×1+m×2+m×1m+m+m+m
=4m4m=1 m

The position of center of mass of the rectangle is (xCOM,yCOM)=(2,1) m

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