Question

Three identical metal balls each of radius "R” are placed on a horizontal plane touching each other such that their centres form the vertices of an equilateral triangle. The distance of the centre of mass of the system from the centre of any one of the balls is

• A. R
• B.
• C.
• D. R/2

Answer 1

The correct option is C

$\therefore x_{cm}=\frac{m\left(0\right)+M\left(2R\right)+m\left(R\right)}{3m}=R$

$y_{cm}=\frac{m\left(0\right)+m\left(0\right)+m\left(\sqrt{3}R\right)}{3m}=\frac{R}{\sqrt{3}}$

$\therefore Distanceofcentreofmassfro{m}^{\prime }{O}^{\prime }=\sqrt{R^2+\frac{R^2}{3}}=\frac{R}{\sqrt{3}}$