When 'n' number of particles of masses m,2m,3m,…..nm are at distances x_(1)=1,x_(2)=2,x_(3)=3,…..x_(n)=n units respectively from origin on the x-axis, then find the distance of centre of mass of the system from origin.

When 'n' number of particles of masses m,2m,3m,…..nm are at distance

1.	When 'n' number of particles of masses m,2m,3m,…..nm are at distances x_(1)=1,x_(2)=2,x_(3)=3,…..x_(n)=n units respectively from origin on the x-axis, then find the distance of centre of mass of the system from origin.
Answer» <html><body><p></p><a href="https://interviewquestions.tuteehub.com/tag/solution-25781" style="font-weight:bold;" target="_blank" title="Click to know more about SOLUTION">SOLUTION</a> :`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>)=(m(1)+2m(2)+<a href="https://interviewquestions.tuteehub.com/tag/3m-310999" style="font-weight:bold;" target="_blank" title="Click to know more about 3M">3M</a>(3)+……+(<a href="https://interviewquestions.tuteehub.com/tag/nm-579234" style="font-weight:bold;" target="_blank" title="Click to know more about NM">NM</a>)<a href="https://interviewquestions.tuteehub.com/tag/n-568463" style="font-weight:bold;" target="_blank" title="Click to know more about N">N</a>)/(m+2m+3m+….+nm)` <br/> `x_(cm)=(m(1^(2)+2^(2)+3^(2)+…..+n^(2)))/(m(1+2+3+….+n))` <br/> `X_(cm)=(((n(n+1)(2n+1))/(6)))/(((n(n+1))/(2)))=(2n+1)/(3)`</body></html>