When n number of particles each of mass m are at distances x_(1)=a, x_(2)=ar, x_(3)=ar^(2)…….x_(n)=ar^(n) units from origin on the x-axis, then the distance of their centre of mass from origin.

When n number of particles each of mass m are at distances x_(1)=a, x_

1.	When n number of particles each of mass m are at distances x_(1)=a, x_(2)=ar, x_(3)=ar^(2)…….x_(n)=ar^(n) units from origin on the x-axis, then the distance of their centre of mass from origin.
Answer» Solution :`X_(CM)=(ma+m(ar)+m(ar^(2))+………..+m(ar^(n)))/(m+m+m+……….+m("n terms"))` `X_(cm)=(m(a+ar+ar^(2)+………..+ar^(n)))/(mn)` If `R GT 1` then `X_(cm)=(1)/(n)[(a(r^(n)-1))/(r-1)]=(a(r^(n)-1))/(n(r-1))` If `r lt 1` then `X_(cm)=(1)/(n)[(a(1-r^(n)))/(1-r)]=(a(1-r^(n)))/(n(1-r))`