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

Two particles which are initially at rest,move towards each other under the action of their internal attraction. If their speeds are $v$ and $2v$ at any instant,then the speed of the centre of mass of the system will be

$M$ mass of a man stands at one end of a plank of length $L$ which lies at rest on a frictionless surface. The man walks to the other end of the plank. If the mass of the plank is $\frac{M}{3}$,then the distance that the man moves relative to the ground is:

On a smooth horizontal plane,a uniform string of mass $M$ and length $L$ is lying in a state of rest. $A$ man of the same mass $M$ is standing next to one end of the string. Now,the man starts collecting the string. Finally,the man collects all the string and puts it in his pocket. What is the displacement of the man with respect to the Earth in the process of collection?

$A$ ball of mass $100 \ g$ is dropped at time $t=0$. $A$ second ball of mass $200 \ g$ is dropped from the same point at $t=0.2 \ s$. The distance between the center of mass of the two balls and the release point at $t=0.4 \ s$ is: (Assume $g=10 \ m \ s^{-2}$) (in $m$)

The equation $M\vec{A} = \vec{F}_{ext}$ denotes what?