Two particles A and B, initially at rest, move twoards eah other under a mutual force of attraction. At the instant when the speed of A is `upsilon` and the speed of B is 2 `upsilon`, the speed of centre of mass iis n v. What is the value of n?

Explanation

Force `F_(A)` on the particle A is given by, `" "F_(A)=m_(A)a_(A)=(m_(A)v)/t`
Similarly, `F_(B)=m_(B)a_(B)=(m_(B) times 2v)/t`
Now, `(m_(A)v)/t=(m_(B) times 2v)/t" "therefore "so, "m_(A)=2m_(B)`
Hence, the speed of the centre of mass of the system
`v_(CM)=(m_(A)v_(A)+m_(B)v_(B))/(m_(A)+m_(B)) rArr (2m_(B)v-m_(B) times 2v)/(2m_(B)+m_(B)) rArr 0`
`therefore` The speed of centre of mass of system is zero. Thus value of n = 0.