Question

Three identical metal balls each of radius $r$ are placed touching each other on a horizontal surface such that an equilateral triangle is formed. When the centre of the three balls are joined, centre of mass of the system is located at

• A. horizontal surface.
• B. centre of one of the balls.
• C. line joining centre of any two balls.
• D. point of intersection of the medians of the triangle

Answer 1

The correct option is D point of intersection of the medians of the triangle


Balls are identical & of same radius, so, volume and density of the balls are the same.
$\because$ Mass = density $\times$ volume
Masses of the balls will be the same
i.e $m_1=m_2=m_3=m$

$x_{\text{cm}}=\frac{m{x}_1+m{x}_2+m{x}_3}{m+m+m}=\left(\frac{x_1+x_2+x_3}{3}\right)$
$y_{\text{cm}}=\frac{m{y}_1+m{y}_2+m{y}_3}{m+m+m}=\left(\frac{y_1+y_2+y_3}{3}\right)$

Hence $(x_{\text{cm}},y_{\text{cm}})$ is the centroid of the equilateral triangle.
i.e the point of intersection of the medians of the equilateral triangle.