Question

if two particles of masses M1 and M2 move with velocities V1 and V2 towards each other on a smooth horizontal plane what is the velocity of their centre of mass?

Answer 1

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Here is Your Answer....!!!!!
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〽⭐Actually welcome to the concept of the Centre of Mass

Answer 2

Let two bodies of masses $m_1$ and $m_2$ lies any instant $x_1$ and $x_2$ respectively in smooth horizontal plane. so, position of centre of mass system of bodies at time t , $X=\frac{m_1x_1+m_2x_2}{m_1+m_2}$

as you know,
velocity is the rate of change of displacement or location of body. so, differentiate X with respect to time to get velocity of their centre of mass.

e.g., $\vec{v}=\frac{dX}{dt}=\frac{m_1\frac{dx_1}{dt}+m_2\frac{dx_2}{dt}}{m_1+m_2}$

$\vec{v}=\frac{m_1\vec{v_1}+m_2\vec{v_2}}{m_1+m_2}$