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:

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 sphere$C$ is at $(R$ , $\sqrt{3}$ )

Now for the center of mass of the system is given as

$r=\frac{m_1{r}_1+m_2{r}_2+m_3{r}_3}{m_1+m_2+m_3}$

$r=\frac{m(0,0)+m(2R,0)+m(R,\sqrt{3}R)}{m+m+m}$

$r=\frac{(0,0)+(2R,0)+(R,\sqrt{3}R)}{3}$

$r=(0,\frac{R}{\sqrt{3}})$

So above is the position of center of mass