$A$ bullet hits and gets embedded in a solid block resting on a horizontal frictionless table. What is conserved?

$A$ body of mass $0.50 \ kg$ is moving on a smooth surface with a speed of $2.00 \ m/s$. It collides with another body of mass $1.00 \ kg$ at rest,and they move together as a single body. The energy loss during the collision is ....... $J$.

$A$ block of mass $10 \text{ g}$ is suspended from the ceiling by a string. $A$ bullet of mass $10 \text{ g}$ moving with a velocity of $1 \text{ m/s}$ strikes the block and gets embedded in it. To what height will the block rise (in $\text{ cm}$)? (Take $g = 10 \text{ m/s}^2$)

$A$ 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

$A$ particle of mass $m$ moves with velocity $v$ towards the East. It collides with another particle of the same mass and same speed moving towards the North and sticks to it. What will be the velocity of the combined particles?

$A$ bullet of mass $m$ travelling at speed $v$ strikes a block of mass $M$ at rest and gets embedded in it. Finally,both will have a combined kinetic energy of: