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

$A$ particle with kinetic energy $K = 3 \ J$ makes an elastic head-on collision with a stationary particle of twice its mass. Which of the following statements is correct?

$A$ body falling on the ground from a height of $10 \, m$,rebounds to a height of $2.5 \, m$. The ratio of the velocities of the body just before and after the collision will be:

$A$ 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:

$A$ heavy body moving with a velocity of $6\,ms^{-1}$ collides elastically with a light body (whose mass is half of the mass of the heavy body) at rest. The velocity of the light body will be (in $ms^{-1}$):

An alpha-particle of mass $m$ undergoes a $1$-dimensional elastic collision with a nucleus of unknown mass $M$ at rest. It is scattered directly backwards,losing $64\%$ of its initial kinetic energy. The mass of the nucleus is .......... $m$.