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

The figure shows a man of mass $m$ standing at the end $A$ of a trolley of mass $M$ placed at rest on a smooth horizontal surface. The man starts moving towards the end $B$ with a velocity $u_{rel}$ with respect to the trolley. The length of the trolley is $L$. As the man walks on the trolley,the centre of mass of the system (man $+$ trolley)

$A$ $750 \ kg$ 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:

$A$ wooden plank of mass $90 \ kg$ and length $3.3 \ m$ is floating on still water. $A$ girl of mass $20 \ kg$ walks from one end to the other end of the plank. The distance through which the plank moves is (in $cm$)

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:

The figure shows a man of mass $m$ standing at the end $A$ of a trolley of mass $M$ placed at rest on a smooth horizontal surface. The man starts moving towards the end $B$ with a velocity $u_{rel}$ with respect to the trolley. The length of the trolley is $L$. The distance moved by the man with respect to ground is