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.

Explanation

`x_(cm) = (m(1) + 2m(2) + 3m(3)+….+(nm)n)/(m+2m+3m+…..+nm)`
`x_(cm) = (m(1^(2) + 2^(2) + 3^(2) +……+n^(2))/(m(1+2+3+…..+n))), X_(cm) = ((n(n+1)(2n+1))/6)/((n(n+1))/2) =(2n+1)/3`