A regular polygon of n-sides with n vertices. On all but one vertex (n - 1) point masses each of mass m are placed. The vacant vertex has position vector `'veca'` w.r.t. the centre of polygen. What is the position vector of the centre of mass of polygon ?

Options

A. `(1)/(n-1)a`
B. `(1)/(n).a`
C. `(1-a)/(n)`
D. `(n-1)/(1-a)xxa`

Answer

A

Explanation

Let the centre of mass be at distance .d.. Then C-M can be found as follows :
`((n-1)m.d+ma)/(n.m)=0`
`therefore (n-1)d=-a`
or `d=-(1)/(n-1)a`
(neglecting - ve sign which indicates only the direction of position vector)