Question

Two particles $A$ and $B$ initially at rest, move towards each other by mutual force of attraction. At the instant when the speed of $A$ is $v$ and the speed of $B$ is $2v$, identify the correct statement(s) regarding the speed of centre of mass ($v_{COM}$) of the system of particles :

• A. $v_{COM}=v$
• B. $v_{COM}=1.5v$
• C. $v_{COM}=0$
• D. Speed of centre mass of the system may change, if the vector sum of external forces acting on it is non-zero.

Answer 1

Answer: (C), (D)

Speed of centre mass of the system may change, if the vector sum of external forces acting on it is non-zero.

Velocity of $\text{COM}$ of a system will change only if a non-zero net external force is acting on it.

Some times ${\overrightarrow{v}}_{\text{COM}}$ may change due to change in direction only.
Therefore, speed of centre mass of the system may change, if the vector sum of external forces acting on it is non-zero.
Hence, option $\left(d\right)$ is correct.

Mutual attraction force is an internal force for system of $A$ and $B$ ). Since there is no external force acting on the system, $v_{COM}$ will not change.

Initially, $v_{COM}=0$ as both particles are at rest initially.
Therefore, speed of $COM$ at any given instant will also be zero. Hence option (c) is correct.