Three spheres, with radius R and lie in the same plane, are given such that each of the spheres touches the other two. Determine the radius r of the fourth sphere that lies in the same plane and touches all three given spheres.
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Let center of mass of sphere A is (0,0)
So center of mass of sphere B is at (2R,0)
Center of mass of sphereC is at (R ,
3
)
Now for the center of mass of the system is given as
r=
m
1
+m
2
+m
3
m
1
r
1
+m
2
r
2
+m
3
r
3
r=
m+m+m
m(0,0)+m(2R,0)+m(R,
3
R)
r=
3
(0,0)+(2R,0)+(R,
3
R)
r=(0,
3
R
)
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