When n number of particles of masses m, 2m, 3m, …….. nm are at distances x_(1)=1, x_(2)=4, x_(3)=9, ………x_(n)=n^(2) units respectively from origin on the x-axis, then find the distance of their centre of mass from origin.

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

1.	When n number of particles of masses m, 2m, 3m, …….. nm are at distances x_(1)=1, x_(2)=4, x_(3)=9, ………x_(n)=n^(2) units respectively from origin on the x-axis, then find the distance of their centre of mass from origin.
Answer» Solution :`x_(CM)=(m(1)+2m(2)+3m(3)+……+(nm)n^(2))/(m+2m+3m+….+nm)` `=(m(1+2^(3)+3^(3)+…..+n^(3))/(m(1+2+3+….+n))` `=(((n(n+1))/(2))^(2))/((n(n+1))/(2))=(n(n+1))/(2)`