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Two particles initially at rest move towards each other under the action of their internal attraction. If their speeds are $v$ and $2v$ at any instant, then the speed of the centre of mass of the system is:

1. $2v$
2. zero
3. $1.5v$
4. $v$

Correct answer: zero

Solution

Since only internal forces act on the two-particle system, the total momentum remains constant. The particles start from rest, so the total momentum is zero and the centre of mass stays at rest; hence its speed is zero.

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