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,

$A$ body moving along a straight line collides with another body of the same mass moving in the same direction with half of the velocity of the first body. If the coefficient of restitution between the two bodies is $0.5$,then the ratio of the velocities of the two bodies after collision is (treat the collision as one dimensional).

An unknown nucleus of mass $m_1$ collides with a stationary ${}^4He$ nucleus of mass $m_2$. After the collision,the two nuclei travel in perpendicular directions relative to each other. If kinetic energy is lost in the collision,the unknown nucleus must be:

$A$ ball is thrown with a velocity of $6\, m/s$ vertically downwards from a height $H = 3.2\, m$ above a horizontal floor. If it rebounds back to the same height,then the coefficient of restitution $e$ is $[g = 10\, m/s^2]$.

In an inelastic collision,after collision the kinetic energy