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Question

Three identical spheres each of mass 1 kg are kept as shown in the figure. They are kept in such a way that they are touching each other with their respective centres on a straight line . If their centres are marked P, Q, R respectively, then the distance of the centre of mass of the system from P is:


A
PQ+QR+PR3
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B
PQ+PR3
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C
PQ+PR2
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D
PQ+QR2
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Solution

The correct option is B PQ+PR3

Since the centre of spheres are lying on a straight line, we can consider the coordinates of their centers on x-axis.
Assigning origin i.e x=0 at point P:
m1=1 kg, x1=0
m2=1 kg, x2=PQ
m3=1 kg, x3=PR

Applying the formula for x-coordinate of COM:
xCOM=m1x1+m2x2+m3x3m1+m2+m3

=(1×0)+(1×PQ)+(1×PR)1+1+1

xCOM=(PQ+PR3)
This is the distance of COM from point P.

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