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Question

# Four bodies of masses 2 kg,3 kg,5 kg and 8 kg respectively are placed at the four corners of a square of side 2 m. Then, position of centre of mass of the system will be:

A
(119,139)
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B
(119,79)
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C
(139,119)
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D
(75,119)
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Solution

## The correct option is A (119,139) Let us place the masses at the corners of a square ABCD of side 2 m, assuming origin (0,0) at A Writing the x and y coordinates of the bodies as shown below in the table: mass (kg)x(m)y(m)A200B320C502D822 From the formula for x and y coordinates of CM: xCM=mAxA+mBxB+mCxC+mDxDmA+mB+mC+mD =(2×0)+(3×2)+(5×0)+(8×2)2+3+5+8=2218 ∴xCM=119 Simillarly; yCM=mAyA+mByB+mCyC+mDyDmA+mB+mC+mD =(0)+(0)+(5×2)+(8×2)2+3+5+8=139 ∴(xCM,yCM)=(119,139)

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