$A$ ball of $0.4 \, kg$ mass and a speed of $3 \, m/s$ has a head-on,completely elastic collision with a $0.6 \, kg$ mass initially at rest. Find the speeds of both balls after the collision:

Assertion $(A)$: In an elastic collision of two billiard balls,both kinetic energy and linear momentum remain conserved.
Reason $(R)$: During the collision of the balls,as the collision is elastic,there is no exchange of energy. Therefore,both energy and momentum are conserved.

When does the maximum energy transfer occur during an elastic collision?

Two balls $A$ and $B$,of masses $M$ and $2M$ respectively,collide with each other. If ball $A$ moves with a speed of $150 \ m \ s^{-1}$ and collides with ball $B$ moving with speed $v$ in the opposite direction,and after the collision ball $A$ comes to rest with the coefficient of restitution being $1$,then the speed of ball $B$ before it collides with ball $A$ is: (in $m \ s^{-1}$)

$A$ body of mass $5\, kg$ moving with a velocity $10\, m/s$ collides with another body of mass $20\, kg$ at rest and comes to rest. The velocity of the second body due to the collision is ............ $m/s$.

$A$ point mass $M$ moving with a certain velocity collides with a stationary point mass $M / 2$. The collision is elastic and in one-dimension. Let the ratio of the final velocities of $M$ and $M / 2$ be $x$. The value of $x$ is