Question

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.​

Answer 1

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

)