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(A) The system consists of two particles $A$ and $B$ moving under a mutual force of attraction. Since the mutual force of attraction is an internal fo

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(A) The system consists of two particles $A$ and $B$ moving under a mutual force of attraction. Since the mutual force of attraction is an internal force,there is no external force acting on the system $(F_{ext} = 0)$. According to the law of conservation of momentum,if the initial velocity of the system is zero,the velocity of the centre of mass remains zero at all times. Since both particles are initially at rest,the initial momentum of the system is $P_{initial} = m_A(0) + m_B(0) = 0$. Therefore,the velocity of the centre of mass $v_{cm} = \frac{P_{total}}{M_{total}} = 0$ at any instant.

Two particles $A$ and $B$ initially at rest move towards each other under a 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

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