The velocity of the centre of mass of the system as shown in the figure is

Two particles of equal mass have velocities $\overrightarrow{v}_1=4 \hat{i} \text{ ms}^{-1}$ and $\overrightarrow{v}_2=4 \hat{j} \text{ ms}^{-1}$. The first particle has an acceleration $\overrightarrow{a}_1=(5 \hat{i}+5 \hat{j}) \text{ ms}^{-2}$ while the acceleration of the other particle is zero. The centre of mass of the two particles moves in a path of

Are you in agreement with the statement: "The velocity of all particles of a system is equal to the velocity of the centre of mass"?

Three men $A, B$ and $C$ of masses $40\,kg, 50\,kg$ and $60\,kg$ are standing on a plank of mass $90\,kg$,which is kept on a smooth horizontal plane. If $A$ and $C$ exchange their positions,then mass $B$ will shift:

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 centre of mass of the system will be

$A$ $500\,kg$ boat is $9\,m$ long and is floating without motion on still water. $A$ man of mass $100\,kg$ is at one end and if he runs to the other end of the boat and stops,the displacement of the boat is