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  4. Two identical particles move towards each other with velocity 2v and v respectively. The velocity of centre of mass is

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Q. Two identical particles move towards each other with velocity $2v$ and $v$ respectively. The velocity of centre of mass is

System of Particles and Rotational Motion

Solution:

$ v_{c}=\frac{m_{1} v_{1}+m_{2} v_{2}}{m_{1}+m_{2}}$
or $ v_{c}=\frac{m(2 v)+m(-v)}{m+m}=\frac{v}{2}$