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:

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"?

$A$ ladder $AP$ of length $5\, m$ is inclined to a vertical wall and is slipping over a horizontal surface with a velocity of $2\, m/s$. When the end $A$ is at a distance of $3\, m$ from the wall,what is the velocity of the center of mass $(C.M.)$ of the ladder at this moment (in $, m/s$)?

An object $A$ of mass $M$ is falling vertically downwards under the influence of gravity. It breaks into two parts: part $B$ of mass $\frac{1}{3}M$ and part $C$ of mass $\frac{2}{3}M$. The center of mass of the combined parts $B$ and $C$ will be displaced relative to object $A$ in which direction?

$A$ child sits stationary at one end of a long trolley moving uniformly with a speed $V$ on a smooth horizontal floor. If the child gets up and runs about on the trolley in any manner,what is the speed of the $CM$ of the (trolley + child) system?

Three particles $A, B$ and $C$ of masses $m, 2m$ and $3m$ are moving towards north, south and east respectively. If the velocities of the particles $A, B$ and $C$ are $6 \,ms^{-1}, 12 \,ms^{-1}$ and $8 \,ms^{-1}$ respectively, then the velocity of the centre of mass of the system of particles is (in $\,ms^{-1}$)