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 .................. $m/s$.

$A$ mass $M$ moving with velocity $V$ along the $x$-axis collides and sticks to another mass $2M$ which is moving along the $y$-axis with velocity $3V$. The velocity of the combination after the collision is:

Find the correct option based on the two statements given below.
Statement-$1$ : Two particles moving in the same direction do not lose all their energy in a perfectly inelastic collision.
Statement-$2$ : The law of conservation of linear momentum is obeyed for all types of collisions.

$A$ 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 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 $ms^{-1}$.

$A$ particle of mass $m$ moving with velocity $v$ collides with a stationary particle of mass $2m$. After collision,they stick together and continue to move together with velocity ........