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 d

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)`