$A$ body of mass $2 \,kg$ collides head-on with another body of mass $4 \,kg$. If the relative velocities of the bodies before and after collision are $10 \,ms^{-1}$ and $4 \,ms^{-1}$ respectively, the loss of kinetic energy of the system due to the collision is (in $\,J$)

$A$ body falls on a surface with a coefficient of restitution of $0.6$ from a height of $1 \, m$. The body rebounds to a height of ........... $m$.

$A$ 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

$A$ ball is dropped from a height $h$ on a floor of coefficient of restitution $e$. The total distance covered by the ball just before the second hit is

During an inelastic collision between two objects,which of the following quantities always remains conserved?

$A$ cricket ball hits the ground with a speed of $5 \,m \,s^{-1}$ making an angle of $30^{\circ}$ with the horizontal. If the coefficient of restitution is $0.2$, the speed of the reflected ball in $m \,s^{-1}$ is