From the circular disk of radius 4R, two small discs of radius R each are cut off. If R=14cm, 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=A1x1−A2x2−A3x3A1−A2−A3 =16πR2(0)−πR2×3R−πR2×014πR2 =−3πR314πR2 ∴xCOM=−3R14=−3cm
Similarly y-coordinate of the new structure: yCOM=A1y1+A2y2+A3y3A1+A2+A3 =16πR2(0)−πR2×0−πR2×3R14πR2 ∴yCOM=−3R14=−3cm