$A$ ball of mass $10 \text{ g}$ is allowed to fall from a height of $10 \text{ m}$. After the collision with the ground, if $50\%$ of its energy is lost, then the height reached by the ball is: (in $\text{ m}$)

$A$ particle falls from a height $h$ on a static horizontal plane and rebounds. If $e$ is the coefficient of restitution,then the total distance traveled by the particle before coming to rest will be:

$A$ 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 $\,J$)

$A$ wooden block of mass $m$ moves with velocity $v$ and collides with another block of mass $4m$,which is at rest. After the collision,the block of mass $m$ comes to rest. The coefficient of restitution will be:

$A$ 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

$A$ large ball of mass $M$,moving with velocity $u$,strikes a small ball of mass $m$,which is at rest. After the collision,the small ball attains velocity $u$ and the large ball attains velocity $v$. What is the value of $v$?