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» <html><body><p></p>Solution :`X_(<a href="https://interviewquestions.tuteehub.com/tag/cm-919986" style="font-weight:bold;" target="_blank" title="Click to know more about CM">CM</a>)=(ma+m(ar)+m(ar^(2))+………..+m(ar^(n)))/(m+m+m+……….+m("n terms"))`<br/>`X_(cm)=(m(a+ar+ar^(2)+………..+ar^(n)))/(mn)`<br/>If `<a href="https://interviewquestions.tuteehub.com/tag/r-611811" style="font-weight:bold;" target="_blank" title="Click to know more about R">R</a> <a href="https://interviewquestions.tuteehub.com/tag/gt-1013864" style="font-weight:bold;" target="_blank" title="Click to know more about GT">GT</a> 1` then `X_(cm)=(1)/(n)[(a(r^(n)-1))/(r-1)]=(a(r^(n)-1))/(n(r-1))`<br/>If `r lt 1` then `X_(cm)=(1)/(n)[(a(1-r^(n)))/(1-r)]=(a(1-r^(n)))/(n(1-r))`</body></html>