$A$ ball moving with a velocity $v$ collides head-on with a stationary second ball of the same mass. After the collision,the velocity of the first ball is reduced to $0.15 v$. The kinetic energy of the system is decreased nearly by (in $\%$)

$A$ sphere of mass $m$ moving with velocity $v$ collides head-on with another sphere of the same mass which is at rest. The ratio of the final velocity of the second sphere to the initial velocity of the first sphere is (where $e$ is the coefficient of restitution and the collision is inelastic).

$A$ 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 $\,J$)

$A$ bullet of mass $0.01\, kg$ travelling at a speed of $500\, m/s$ strikes and passes horizontally through a block of mass $2\, kg$ which is suspended by a string of length $5\, m$. The centre of gravity of the block is found to rise a vertical distance of $0.1\, m$. What is the speed of the bullet after it emerges from the block? (The time of passing of the bullet is negligible,$g = 9.8\, m/s^2$)

$A$ body moving along a straight line collides with another body of the same mass moving in the same direction with half of the velocity of the first body. If the coefficient of restitution between the two bodies is $0.5$,then the ratio of the velocities of the two bodies after collision is (treat the collision as one dimensional).

$A$ ball is dropped from a height of $5 \ m$ on a planet. It rebounds to a height of $1.8 \ m$. What is the fraction of velocity lost by the ball?