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Question

Three point masses M1=1.6 kg,M2=2.4 kg and M3=2 kg are placed at the corners of a thin massless rectangular sheet (1.2 m×1.0 m) as shown in the figure below. Centre of mass of the system will be located at a point (assuming M1 to be at the origin)


A
( 0.8,0.6 )m
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B
( 0.6,0.8 )m
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C
( 0.4,0.4 )m
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D
( 0.5,0.6 )m
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Solution

The correct option is C ( 0.4,0.4 )m
Given,
x1=0 my1=0 mm1=1.6 kgx2=0 my2=1 mm2=2.4 kgx3=1.2 my3=0 mm3=2.0 kg

xcm=m1x1+m2x2+m3x3m1+m2+m3
=1.60+2.40+2(1.2)1.6+2.4+2=0.4 m
ycm=m1y1+m2y2+m3y3m1+m2+m3
=1.60+2.41+2(0)1.6+2.4+2=0.4 m
(xcm,ycm)=( 0.4,0.4 )m

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