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

$A$ neutron having a mass of $1.67 \times 10^{-27} \ kg$ and moving at $10^8 \ m/s$ collides with a deuteron at rest and sticks to it. If the mass of the deuteron is $3.34 \times 10^{-27} \ kg$,then the speed of the combination is:

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

$A$ bag of mass $M$ is suspended by a string. $A$ bullet of mass $m$ moving with velocity $v$ enters the bag and gets embedded in it. Then,for the system:

Discuss the completely inelastic collision in one dimension.

$A$ block of mass $4 m$ travelling at a velocity $v_1$ in the $x$-direction on a frictionless horizontal plane makes a head-on collision with another block of mass $2 m$ travelling in the opposite direction with a velocity $v_2$. After the collision,both blocks travel as a single block along the $x$-direction with a final velocity $5 v_2$. The ratio of velocities $\frac{v_1}{v_2}$ is