When 'n' number of particles each of mass 'm' are at distances x_(1)=1, x_(2)=2, x_(3)=3, ……x_(n)=n units from origin on the x-axis then find the distance of their centre of mass from origin.

When 'n' number of particles each of mass 'm' are at distances x_(1)=1

1.	When 'n' number of particles each of mass 'm' are at distances x_(1)=1, x_(2)=2, x_(3)=3, ……x_(n)=n units from origin on the x-axis then find the distance of their centre of mass from origin.
Answer» SOLUTION :`x_(cm)=(m(1)+m(2)+m(3)+……+m(n))/(m+m+m+….+m(n"terms"))` `=(m(1+2+3+….+n))/(NM)=(m((n(n+1))/(2)))/(nm)` `x_(c)=(n+1)/(2)`