$A$ ball moving with velocity $2 \,m/s$ collides head-on with another stationary ball of double the mass. If the coefficient of restitution is $0.5$, then their velocities (in $m/s$) after collision will be:

$A$ body falling from a height of $10\,m$ rebounds from a hard floor. If it loses $20\%$ of its energy in the impact,then the coefficient of restitution is:

$A$ ball is projected vertically downward with an initial velocity from a height of $20 \ m$ onto a horizontal floor. During the impact,it loses $50\%$ of its energy and rebounds to the same height. The initial velocity of its projection is ............ $m/s$.

$A$ uniform rod of mass $M$ and length $L$ is placed on a smooth horizontal surface. $A$ particle of mass $m$ strikes the rod at one end with a velocity $v$ perpendicular to the rod. If the particle comes to rest after the collision,the velocity of the center of mass of the rod after the collision is:

$A$ spherical ball $A$ of mass $4 \ kg$,moving along a straight line,strikes another spherical ball $B$ of mass $1 \ kg$ at rest. After the collision,$A$ and $B$ move with velocities $v_1 \ ms^{-1}$ and $v_2 \ ms^{-1}$ respectively,making angles of $30^{\circ}$ and $60^{\circ}$ with respect to the original direction of motion of $A$. The ratio $\frac{v_1}{v_2}$ will be

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: