$A$ 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 $\,J$)

$A$ ball hits the floor and rebounds after an inelastic collision. In this case:

$A$ body falls freely from a height of $100 \ m$ onto the ground and rebounds to a maximum height of $36 \ m$ after collision. The coefficient of restitution between the ground and the body is

$A$ ball of mass $1.2 \ kg$ moving with a velocity of $12 \ ms^{-1}$ makes a one-dimensional collision with another stationary ball of mass $1.2 \ kg$. If the coefficient of restitution is $\frac{1}{\sqrt{2}}$,then the ratio of the total kinetic energy of the balls after the collision to the initial kinetic energy is:

Hail stones are observed to strike the surface of a frozen lake at $30^{\circ}$ with the vertical and rebound at $60^{\circ}$ with the vertical. Assuming the contact to be smooth,the coefficient of restitution is

The sphere $A$ of mass $m$ moving with a constant velocity hits another sphere $B$ of mass $2m$ at rest. If the coefficient of restitution is $0.4$,the ratio of the velocities of the spheres $A$ and $B$ after collision is