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  4. Three particles of masses 1 kg , 2 kg and 3 kg are situated at the corners of an equilateral triangle move at speed 6 ms -1, 3 ms -1 and 2 ms -1 respectively. Each particle maintains a direction towards the particle at the next corner symmetrically. Find velocity of CM of the system at this instant

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Q. Three particles of masses $1 \,kg , 2\, kg$ and $3\, kg$ are situated at the corners of an equilateral triangle move at speed $6 \,ms ^{-1}, 3\, ms ^{-1}$ and $2 \,ms ^{-1}$ respectively. Each particle maintains a direction towards the particle at the next corner symmetrically. Find velocity of CM of the system at this instantPhysics Question Image

System of Particles and Rotational Motion

Solution:

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$\vec{v}_{ cm }=\frac{m_{1} \vec{v}_{1}+m_{2} \vec{v}_{2}+m_{3} \vec{v}_{3}}{m_{1}+m_{2}+m_{3}} $
$\Rightarrow \vec{v}_{ cm }=\frac{\text { Total momentum }}{\text { Total mass }} $
Here total momentum of system is zero, because momentum of each particle is same in magnitude and they are symmetrically oriented as shown.
So $\vec{p}_{1}+\vec{p}_{2}+\vec{p}_{3}=0$
So, velocity of $CM$ of the system will be zero