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 distan

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(4)+3m(9)+.........+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)`