Two particles of masses 1kg and 2kg are located at `x=0` and `x=3m`. Find the position of their centre of mass.

Explanation

Since , both the particles lie on x - axis , the CM will also lie on x- axis . Let the CM be located at x = x, then
`(m_(1)+m_(2)) x=m_(1)x_(1)+ m_(2)x_(2) " " rArr (1+2) x = 1 xx 1 + 2 xx 3 rArr x = 2.3 m `
Thus , the CM of the two masses and at located at x = 2.33 m from origin .
(i.e) between the two masses and at `1.33` m distance from the 1 kg mass .
Alternate Method : Let CM be at `r_(1)` distance from `m_(1)`
`d = x_(2) - x_(1) = 3 - 1 = 2m `
`r_(1)=((m_(2))/(m_(2)+m_(1))) = (2/(2+1)) xx 2 = 1.33 m `
Thus the CM lies at `1.33` m fron the 1 kg mass .