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)`