$A$ 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 ............ $m/s$.

$A$ body of mass $m$ moving with velocity $v$ makes a head-on collision with another body of mass $2m$ which is initially at rest. What is the ratio of the kinetic energy of the colliding body before and after the collision (in $: 1$)?

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

$A$ smooth sphere $A$ of mass $m$ collides elastically with an identical sphere $B$ at rest. The velocity of $A$ before collision is $8 \ m/s$ in a direction making $60^{\circ}$ with the line of centers at the time of impact.
$(i)$ The sphere $A$ comes to rest after collision.
$(ii)$ The sphere $B$ will move with a speed of $8 \ m/s$ after collision.
$(iii)$ The directions of motion of $A$ and $B$ after collision are at right angles.
$(iv)$ The speed of $B$ after collision is $4 \ m/s$.
The correct option is:

$A$ ball after falling from a height of $10\, m$ strikes the roof of a lift which is descending down with a velocity of $1\, m/s$. The recoil velocity of the ball will be .............. $m/s$.

Two identical balls $A$ and $B$ having velocities of $0.5 \, m s^{-1}$ and $-0.3 \, m s^{-1}$ respectively collide elastically in one dimension. The velocities of $B$ and $A$ after the collision respectively will be