Two identical balls $A$ and $B$ of equal mass $m$ are lying on a smooth surface as shown in the figure. If ball $A$ hits ball $B$ at rest with a velocity $16 \,ms^{-1}$,then the coefficient of restitution $e$ between $A$ and $B$ so that $B$ just reaches the highest point of the smooth inclined plane of height $5 \,m$ is $\left(g=10 \,ms^{-2}\right)$

An electron collides with a free molecule initially in its ground state. The collision leaves the molecule in an excited state that is metastable and does not decay to the ground state by radiation. Let $K$ be the sum of the initial kinetic energies of the electron and the molecule,and $p$ be the sum of their initial momenta. Let $K^{\prime}$ and $p^{\prime}$ represent the same physical quantities after the collision. Then,

$A$ particle falls from a height $h$ upon a fixed horizontal plane and rebounds. If $e$ is the coefficient of restitution,the total distance travelled before rebounding has stopped is

$A$ ball of mass $m$ is moving with a speed $V$ as shown in the figure. It undergoes an inelastic collision with a ball of mass $2m$ which was initially at rest. The velocity of the ball of mass $2m$ after the collision is given by

Two solid rubber balls $A$ and $B$ having masses $200 \, g$ and $400 \, g$ respectively are moving in opposite directions. The velocity of $A$ is $0.3 \, m/s$. After the collision,both balls come to rest. Determine the velocity of $B$ in $m/s$.

$A$ ball $P$ of mass $0.5 \ kg$ moving with a velocity of $10 \ ms^{-1}$ collides with another ball $Q$ of mass $1 \ kg$ at rest. If the coefficient of restitution is $0.4$,the ratio of the velocities of the balls $P$ and $Q$ after the collision is