$A$ clay ball of mass $m$ and speed $v$ strikes another metal ball of the same mass $m$,which is at rest. They stick together after the collision. The kinetic energy of the system after the collision is

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?

$A$ particle of mass $m$ moving eastward with a speed $v$ collides with another particle of the same mass moving northwards with the same speed $v$. The two particles coalesce on collision. The new particle of mass $2m$ will move with velocity:

$A$ $50\, g$ bullet moving with velocity $10\, m/s$ strikes a block of mass $950 \,g$ at rest and gets embedded in it. The loss in kinetic energy will be ............... $\%$

$A$ bag (mass $M$) hangs by a long thread and a bullet (mass $m$) comes horizontally with velocity $v$ and gets caught in the bag. Then for the combined (bag $+$ bullet) system

Two putty balls of equal mass $m$ moving with equal velocity $v = 45\sqrt{2} \, m/s$ in mutually perpendicular directions,stick together after collision. The velocity of their combined mass after collision is .................. $m/s$.