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Question

Three identical sphere each of radius R are placed touching each other on a horizontal table as shown in figure. The coordinates of centre of mass are:
1273343_acd578df0a58476da48a30b24b1a8c69.png

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Solution

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=m1r1+m2r2+m3r3m1+m2+m3

r=m(0,0)+m(2R,0)+m(R,3R)m+m+m

r=(0,0)+(2R,0)+(R,3R)3

r=(0,R3)

So above is the position of center of mass

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