`(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

Options

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

Answer

B

Explanation

Let the centre of mass be at a distance b from the centre.
Then, `((n-1)mb+ma)/(mn)=0," "b=-a/((n-1))`