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"?

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

Three blocks $A$,$B$ and $C$ are arranged as shown in the figure such that the distance between two successive blocks is $10 \ m$. Block $A$ has a mass of $10 \ kg$,block $B$ has a mass of $25 \ kg$,and block $C$ has a mass of $15 \ kg$. Block $A$ is displaced towards block $B$ by $2 \ m$ and block $C$ is displaced towards block $B$ by $3 \ m$. The distance through which the block $B$ should be moved so that the centre of mass of the system does not change is

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?

Two masses $m_1$ and $m_2$ start to move towards each other due to mutual gravitational force. If the distance covered by $m_1$ is $x$,then the distance covered by $m_2$ is:

$A$ 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 $m$)