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Question

From the circular disk of radius 4R, two small discs of radius R each are cut off. If R=14 cm, then find the location of the center of mass of the new structure (in cm). (Take O to be the origin)


A
(14,14)
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B
(3,3)
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C
(56,3)
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D
(0,0)
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Solution

The correct option is B (3,3)

Area of each removed part A2=A3=πR2
Area of full circle A1=16πR2
Coordinates of centres of mass of removed parts are shown in the figure.
(x1,y1)=(0,0),(x2,y2)=(3R,0),(x3,y3)=(0,3R)

Then, x - coordinate of COM of remaining structure:
xCOM=A1x1A2x2A3x3A1A2A3
=16πR2(0)πR2×3RπR2×014πR2
=3πR314πR2
xCOM=3R14=3 cm

Similarly
y-coordinate of the new structure:
yCOM=A1y1+A2y2+A3y3A1+A2+A3
=16πR2(0)πR2×0πR2×3R14πR2
yCOM=3R14=3 cm

i.e (xCOM,yCOM)=(3,3).

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