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 distanc

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» Solution :`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)`