(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.

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

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.
Answer» Solution :Let r be the POSITION VECTOR of the centre of MASS of a regular n-polygon. `(n-1)` equal point MASSES are placed at `(n-1)` vertices of the regular n-polygon, therefore, for its centre of mass. `r_(CM)=((n-1)mr+ma)/((n-1)m+m)` `therefore 0=((n-1)mr+ma)/((n-1)m+m)` (`because r_(CM)` is at origin) `therefore (n-1)mr+ma=0` `r=-(a)/((n-1))`