$A$ uniform rod of length $L$ and mass $M$ is placed on a smooth horizontal surface. $A$ particle of mass $m$ moving with velocity $v$ strikes the rod at one end perpendicularly and comes to rest. The velocity of the centre of mass of the rod after the collision is:

$A$ system of $N$ particles is free from any external forces. Which of the following must be true for the sum of the magnitudes of the momenta of the individual particles in the system?

$A$ uniform rod of mass $M$ and length $L$ is placed on a smooth horizontal surface. $A$ particle of mass $m$ moving with velocity $v$ strikes the rod at one end perpendicularly and comes to rest. The velocity of the centre of mass of the rod after the collision is:

Consider the following two statements:
$1.$ Linear momentum of a system of particles is zero.
$2.$ Kinetic energy of a system of particles is zero.
Then:

Consider the following two statements for a system of particles:
$A$: The linear momentum of the system is zero.
$B$: The kinetic energy of the system is zero.

Two men $A$ and $B$ are standing on a plank of length $120 \ cm$ and mass $40 \ kg$. $B$ (mass $60 \ kg$) is at the middle of the plank and $A$ (mass $40 \ kg$) is at the left end of the plank. The system is initially at rest on a smooth horizontal surface. $A$ and $B$ start moving such that the position of $B$ remains fixed with respect to the ground until $A$ meets $B$. The point where $A$ meets $B$ is located at: