Two identical particles are moving with velocities $2v$ and $v$ respectively. Find the velocity of the center of mass.

Consider a two-particle system with particles having masses $m_1$ and $m_2$. If the first particle is pushed towards the centre of mass through a distance $d$,by what distance should the second particle be moved,so as to keep the centre of mass at the same position?

$A$ $750 \ kg$ boat is $10 \ m$ long and is floating without motion on still water. $A$ man of mass $80 \ kg$ is at one end. If he runs to the other end of the boat and stops,the displacement of the boat is:

$A$ particle of mass $m$ is thrown horizontally from the top of a tower and another particle of mass $2m$ is thrown vertically upward. The acceleration of the centre of mass is .............

Two particles of equal mass have velocities $2\,\hat{i}\,ms^{-1}$ and $2\,\hat{j}\,ms^{-1}$. The first particle has an acceleration $(3\,\hat{i} + 3\,\hat{j})\,ms^{-2}$ while the acceleration of the second particle is zero. The centre of mass of the two particles moves in

$A$ uniform rod of mass $M$ and length $L$ is placed on a smooth horizontal surface. $A$ horizontal force $F$ is applied at one end of the rod. The acceleration of the centre of mass of the rod is: