(n -1) equal point masses each of mass m are placed at the vertices of a regular n-polygon

cbse
rotational-motion

#1

(n -1) equal point masses each of mass m are
placed at the vertices of a regular n-polygon. The vacant vertex has a position vector a with respect to the centre of the polygon. Find the position vector of centre of mass.


#2

Suppose, b be the position vector of centre of mass of regular n-polygon.
As (n — 1) equal point masses each of mass m are placed at (n — 1) vertices of regular polygon, therefore -
(n -1) mb + ma /{n-1+1)m
=> (n -1) mb + ma = 0
====> b = -a/(n-1)