Two particles A and B, initially at rest, move towards each other under the 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
Question
Two particles A and B, initially at rest, move towards each other under the 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
Solution
The speed of the center of mass of a system of particles is given by the equation:
Vcm = (m1v1 + m2v2) / (m1 + m2)
where m1 and m2 are the masses of the particles and v1 and v2 are their respective velocities.
In this case, we know that the particles A and B were initially at rest, so the initial velocity of the center of mass was zero.
Since no external force is acting on the system, the velocity of the center of mass should remain constant (which is zero in this case) according to the law of conservation of momentum.
So, the speed of the center of mass of the system is zero.
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