Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • NCERT
  • (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 center of the polygon. Find the position vector of center of mass.

(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 center of the polygon. Find the position vector of center of mass.

Answers (1)

The centre of mass of a regular polygon with n sides lies on its geometric centre. If mass m is placed at all the n vertices, then the C.O.M is again at the geometric centre. Let   \overrightarrow{r} be the position vector of the COM and  \overrightarrow{a} of the vacant vertex. Then

r_{cm}=\frac{(n-1)mr+ma}{(n-1)m+m}=0 (when mass is placed at nth vertex also)

(n-1)mr+ma=0

r=-\frac{ma}{(n-1)m}

\overrightarrow{r}=-\frac{\overrightarrow{a}}{(n-1)}

The negative sign depicts that the C.O.M lies on the opposite side of the nth vertex.

Posted by

infoexpert23

View full answer

Similar Questions

Latest Question