question_answer 53)

                  \[(n-1)\] equal point masses each of mass m are placed at die 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:

                  Let \[x\] be the distance of the C.M.                 Now \[(n-1)mx+ma=0\]                 \[\therefore \] \[x=\,-\frac{a}{(n-1)}\]