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(n-1) equal point masses each of mass m ...

`(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.

Text Solution

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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))`
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