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Question

Masses 8,2,4,2 kg are placed at the corners A,B,C,D respectively of a square ABCD of diagonal 80 cm. The distance of centre of mass from A will be

A
20 cm
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B
30 cm
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C
40 cm
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D
60 cm
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Solution

The correct option is B 30 cm
Let corner A of square ABCD is at the origin and the mass 8 kg is placed at this corner (given in problem) Diagonal of square d=a2=80cma=402cm
m1=8kg,m2=2kg,m3=4kg,m4=2kg
Let r1,r2,r3,r4 are the position vectors of respective masses
r1=0ˆi+0ˆj,r2=aˆi+0ˆj,r3=aˆi+aˆj,r4=0ˆi+aˆj
From the formula of centre of mass
r=m1r1+m2r2+m3r3+m4r4m1+m2+m3+m4=152i+152j
co-ordinates of centre of mass (152,152) and co-ordination of the corner = (0,0)
From the formula of distance between two points (x1,y1) and (x2,y2)
distance = (x2x1)2+(y2y1)2=(1520)2+(1520)2=900=30cm

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