Two paricle A and B initially at rest, move towards each other under mutual force of attraction. At the instant when the speed of A is V and the speed of B is 2V, the speed of the centre of mass of the system is

Options

A. 2v
B. v
C. 1.5 v
D. zero

Answer

D

Explanation

Force `F_(A)` on particle A is given by
`F_(A)=m_(A)a_(A)=(m_(A)v)/(t)" "...(1)`
Similarly `F_(B)=m_(B)a_(B)=(m_(B)xx2v)/(t)" "...(2)`
Now `(m_(A)v)/(t)=(m_(B)xx2v)/(t)(because F_(A)=F_(B))`
So `m_(A)=2m_(B)`
For the centre of mass of the system
`v=(m_(A)v_(A)+m_(B)v_(B))/(m_(A)+m_(B))orv=(2m_(B)v-m_(B)xx2v)/(2m_(B)+m_(B))=0`
Negative sign is used because the particles are travelling in opposite directions.