$A$ 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

$A$ 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 ............ $m/s$.

$A$ body dropped from a height $1\,m$ on a floor rises to a height $25\,cm$ after the first rebound. The coefficient of restitution is

$A$ ball falls freely from rest from a height of $6.25 \ m$ onto a hard horizontal surface. If the ball reaches a height of $81 \ cm$ after the second bounce from the surface,the coefficient of restitution is

$A$ bullet of mass $4.2 \times 10^{-2} \text{ kg}$, moving at a speed of $300 \text{ m/s}$, gets stuck into a block with a mass $9$ times that of the bullet. If the block is free to move without any kind of friction, the heat generated in the process will be (in $\text{ cal}$)

$A$ body falls freely from a height $h$ on a fixed horizontal plane and rebounds. If $e$ is the coefficient of restitution,the total distance travelled before it comes to rest is