$A$ 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 $g = 10 \text{ m/s}^2$)

Two identical blocks of ice move in opposite directions with equal speed and collide with each other. What will be the minimum speed required to make both the blocks melt completely,if the initial temperatures of the blocks were $-8^{\circ} C$ each (in $ms^{-1}$)? (Specific heat of ice is $2100 \ Jkg^{-1} K^{-1}$ and latent heat of fusion of ice is $3.36 \times 10^{5} \ Jkg^{-1}$)

$A$ bullet of mass $m$ moving with velocity $v$ strikes a block of mass $M$ at rest and gets embedded into it. The kinetic energy of the composite block will be

Two masses of $0.25\, kg$ each move towards each other with speeds of $3\, ms^{-1}$ and $1\, ms^{-1}$. They collide and stick together. Find the final velocity in $ms^{-1}$.

Statement $1$: In a perfectly inelastic collision,the total energy of two particles moving in the same direction is not completely lost.
Statement $2$: The principle of conservation of momentum is valid for all types of collisions.

$A$ body of mass $2 \, kg$ is moving with velocity $10 \, m/s$ towards the east. Another body of the same mass and same velocity moving towards the north collides with the former,coalesces,and moves towards the north-east. What is its final velocity?