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

Two particles $A$ and $B$, move with constant velocities ${\vec v_1}$ and ${\vec v_2}$. At the initial moment their position vectors are ${\vec r_1}$ and ${\vec r_2}$ respectively. The condition for their collision is

Two identical ball bearings in contact with each other and resting on a frictionless table are hit head-on by another ball bearing of the same mass moving initially with a speed $V$. If the collision is elastic, which of the following figure is a possible result after collision ?

A ball is dropped vertically from a height of $h$ onto a hard surface. If the ball rebounds from the surface with a fraction $r$ of the speed with which it strikes the latter on each impact, what is the net distance travelled by the ball up to the 10th impact?

A particle of mass $m$ collides with a heavy mass (at rest) elastically and after collision returns with $4/9$ of it's initial kinetic energy. The mass of heavy object is ............... $\mathrm{m}$

$Assertion$ : If collision occurs between two elastic bodies their kinetic energy decreases during the time of collision.

$Reason$ : During collision intermolecular space decreases and hence elastic potential energy increases.