If a lighter body (mass $M_1$ and velocity $V_1$) and a heavier body (mass $M_2$ and velocity $V_2$) have the same kinetic energy,then

Explain why total linear momentum is conserved in an elastic collision,and define inelastic collision and perfectly inelastic collision.

Two particles $P$ and $Q$ each of mass $3m$ lie at rest on the $X$-axis at points $(-a, 0)$ and $(+a, 0)$,respectively. $A$ third particle $R$ of mass $2m$ initially at the origin moves towards the particle $Q$ with velocity $v$. If all the collisions of the system of $3$ particles are elastic and head-on,the total number of collisions in the system is

$A$ block of mass $1 \ kg$ is moved by a distance of $1 \ m$ on a horizontal surface by applying a force of $8 \ N$. Then it is lifted to a height of $2 \ m$. The total work done is ... $J$. (Take $g = 10 \ m/s^2$)

Three particles $A, B$,and $C$ of equal mass move with speed $V$ as shown to strike at the centroid of an equilateral triangle. After the collision,$A$ comes to rest and $B$ retraces its path with speed $V$. The speed of $C$ after the collision is:

$A$ free body of mass $8 \ kg$ is moving at $2 \ m \cdot s^{-1}$ along a straight line. It splits into two equal parts due to an internal explosion releasing $16 \ J$ of energy,and neither part deviates from the original line of motion. What happens to the two parts?