When 'n' numbers 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 find the distance of their centre of mass from origin.

When 'n' numbers of particles each of mass 'm' are at distances x_(1)=

1.	When 'n' numbers 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 find 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))`