If a rubber ball falls from a height $h$ and rebounds upto the height of $h / 2$. The percentage loss of total energy of the initial system as well as velocity ball before it strikes the ground, respectively, are :

Six identical balls are lined in a straight groove made on a horizontal frictionless surface as shown. Two similar balls each moving with a velocity $v$ collide elastically with the row of $6$ balls from left. What will happen

A moving block having mass $m,$ collides with another stationary block having mass $4\,m$ . The lighter block comes to rest after collision. When the initial velocity of the lighter block is $v,$ then the value of coefficient of restitution $( e)$ will be

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

Three different projectiles, each with the same mass, are fired with speed $v$ at a wall. In case $A,$ the projectile bounces straight back with speed $v.$ In case $B$, the projectile sticks to the wall. In case $C$, the projectile crashes through the wall and emerges with half its original speed. These three cases are shown here.

Place the impulse exerted by the wall on the projectile in each of these three cases in the correct order.

Two particles of masses ${m_1}$ and ${m_2}$ in projectile motion have velocities ${\vec v_1}$ and ${\vec v_2}$ respectively at time $t = 0$. They collide at time ${t_0}$. Their velocities become ${\vec v_1}'$ and ${\vec v_2}'$ at time $2{t_0}$ while still moving in air. The value of $|({m_1}\overrightarrow {{v_1}} '\, + {m_2}\overrightarrow {{v_2}} ') - ({m_1}\overrightarrow {{v_1}} \, + {m_2}\overrightarrow {{v_2}} )$| is