Question

Three particles $A,B$ and $C$ of equal mass, move with equal speed $v$ along the medians of an equilateral triangle as shown in figure. They collide at centroid $G$ of the triangle. If after collision, $A$ comes at rest, $B$ retraces its path with speed $v$, then the speed of $C$ after collision is

• A. $0$
• B. $v/2$
• C. $2v$
• D. $v$

Answer 1

The correct option is D $v$

The velocities of three particles are directed as shown in figure
It is clear that the three velocity vectors are inclined at an angle of ${12}^o$. We know that the resultant of three equal vectors inclined at angle of ${120}^o$ is zero. So, the resultant initial momentum of the system is zero. It means that the resultant final momentum of the system must be zero. As particle $A$ comes at rest after collision, the momentum of particle $C$ must be equal and opposite to the momentum of particle $B$, for the final momentum to be zero. Thus, the velocity of $C$ should be equal to $v$ and directed opposite to that of $B$.