`(n - 1)` equal point masses each of mass `m` are placed at the vertices of a angular 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. `b=-a/(n-1)`
B. `b=-(a^(2))/(n-1)`
C. `b=-a/((n-1)^(2))`
D. `b=-(3a)/(2n-1)`

Answer

A

Explanation

Let `b` 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
`t_(CM)=((n-1)mb+ma)/(n-1)m+n=0` ( `:.` centre of mass lies at centre)