Question

the identical particles move towards each other with velocity 2v and V respectively the velocity of the centre of mass is

Answer 1

Assuming direction of first particle to be taken positive,
$v_{cm}=\dfrac{1}{\displaystyle\sum_{i}m_i}\displaystyle\sum_{i}m_iv_i\\ =\dfrac{2mv-mv}{2m}=\dfrac{v}{2}$