$A$ ball of mass $m$ is thrown upward and another ball of same mass is thrown downward so as to move freely under gravity. The acceleration of the centre of mass is .........

If one observes from the reference frame in which the centre of mass appears to be at rest,what will be the velocity of the centre of mass?

Two particles $A$ and $B$ (both initially at rest) start moving towards each other under a mutual force of attraction. At the instant,when the speed of $A$ is $v$ and the speed of $B$ is $2v$,the speed of the centre of mass is

$A$ child is standing at one end of a long trolley moving with a speed $v$ on a smooth horizontal track. If the child starts running towards the other end of the trolley with a speed $u$,the centre of mass of the system (trolley + child) will move with a speed

Two particles $A$ and $B$,initially at rest,move towards each other under a mutual force of attraction. At the instant when the speed of $A$ is $v$ and the speed of $B$ is $2v$,the speed of the center of mass of the system is:

Two men $A$ and $B$ are standing on a plank. $B$ is at the middle of the plank and $A$ is at the left end of the plank. The bottom surface of the plank is smooth. The system is initially at rest and the masses are as shown in the figure. $A$ and $B$ start moving such that the position of $B$ remains fixed with respect to the ground and $A$ meets $B$. Then the point where $A$ meets $B$ is located at