(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.

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)