$A$ body of mass $m$ moving with a velocity $v$ collides head-on with another body of mass $2m$ at rest. If the coefficient of restitution between the two bodies is $e$,then the ratio of the velocities of the two bodies after collision is:

$A$ body of mass $m$ moving with velocity $v$ makes a head-on elastic collision with another body of mass $2m$ which is initially at rest. The loss of kinetic energy of the colliding body (mass $m$) is:

$A$ ball hits the floor and rebounds. For this elastic collision case,which of the following is true?

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.

$A$ smooth sphere of mass $M$ moving with velocity $u$ directly collides elastically with another sphere of mass $m$ at rest. After collision,their final velocities are $V$ and $v$ respectively. The value of $v$ is

$A$ body $A$ of mass $m=0.1 \; kg$ has an initial velocity of $3 \hat{i} \; ms^{-1}$. It collides elastically with another body $B$ of the same mass which has an initial velocity of $5 \hat{j} \; ms^{-1}$. After the collision,$A$ moves with a velocity $\vec{v}_A = 4(\hat{i} + \hat{j}) \; ms^{-1}$. The energy of $B$ after the collision is written as $\frac{x}{10} \; J$. The value of $x$ is: