Question

Three particles of equal mass m are situated at the vertices of an equilateral triangle. Where does its centre of mass lie?

Answer 1

The center of mass of 3 masses situated at vertices of the equilateral triangle lies at it's circumcenter or incenter

Let a be the length of each side

Taking a perpendicular bisector of 1 of its side

Length of the perpendicular

L = √[a² - (a/2)²]

= √3a/2

Hence length of the circumcenter or incenter from the opposite vertex

= 2/3 x L

= 2/3 x √3a/2

= a/√3

Hence the center of mass of 3 masses situated at vertices of the equilateral triangle lies at it's circumcenter or incenter at a distance of a/√3 from each vertex.