Question

Three identical spheres each of radius R are placed touching each other on a horizontal table as shown in figure The coordinates of center of mass are

• A. $(R,R)$
• B. $(0,0)$
• C. $(\frac{R}{2},\frac{R}{2})$
• D. $(R,\frac{R}{\sqrt{3}})$

Answer 1

The correct option is D $(R,\frac{R}{\sqrt{3}})$

$\begin{array}{c}{x}_{com}=\frac{m\left(2R\right)+M\left(R\right)+M\left(0\right)}{3M}\\ =\frac{3MR}{3M}=R\\ y_{com}=\frac{M\left(\sqrt{3}R\right)+M\left(0\right)+M\left(0\right)}{3M}\\ =\frac{R}{\sqrt{3}}\\ Hence,\\ optionDiscorrectanswer.\end{array}$