$A$ particle of mass $m$ moving in the $x$-direction with speed $2v$ is hit by another particle of mass $2m$ moving in the $y$-direction with speed $v$. If the collision is perfectly inelastic,the percentage loss in the energy during the collision is close to .............. $\%$

Two identical balls are suspended side by side by two long strings. One ball is pulled aside so that its center of gravity rises by a vertical distance $h$. It is then released and undergoes a perfectly inelastic collision with the other ball. What is the vertical distance to which the center of gravity of the combined system rises?

$A$ bullet of mass $m$ travelling with a speed $v$ hits a block of mass $M$ initially at rest and gets embedded in it. The combined system is free to move and there is no other force acting on the system. The heat generated in the process will be

$A$ body of mass $2 \ kg$ moving with a velocity of $6 \ m/s$ strikes inelastically another body of same mass at rest. The amount of heat evolved during collision is ............... $J$.

Two bodies $A$ and $B$ of same mass undergo a completely inelastic one-dimensional collision. The body $A$ moves with velocity $v_1$ while body $B$ is at rest before the collision. The velocity of the system after the collision is $v_2$. The ratio $v_1: v_2$ is

$A$ body of mass $1\,kg$ falls freely from a height of $100\,m$ onto a platform of mass $3\,kg$ which is mounted on a spring having spring constant $k = 1.25 \times 10^6\,N/m.$ The body sticks to the platform and the spring's maximum compression is found to be $x.$ Given that $g = 10\,m/s^2,$ the value of $x$ will be close to ................ $cm$.