Two bodies of mass $4 \mathrm{g}$ and $25 \mathrm{g}$ are moving with equal kinetic energies. The ratio of magnitude of their linear momentum is :

Two bodies having same linear momentum have ratio of kinetic energy as $16:9$. Find the ratio of masses of these bodies.

A policeman fires a bullet of mass $50 \mathrm{g}$ with a speed of $200 \mathrm{m} {\mathrm{s}}^{-1}$, in a wooden piece of thickness $2.0 \mathrm{cm}$. The bullet leaves the wooden piece with only $10\%$ of its initial kinctic energy. By how much percentage has the speed of the bullet been reduced?

A bullet of mass $10 g$ pierces through a plate $A$ of mass $500 \mathrm{g}$ and then gets embedded into a second plate $B$ of mass $1.49 \mathrm{kg}$ as shown in the figure. Initially the two plates $A$ and $B$ are at rest and move with same velocity after collision. The percentage loss in the initial kinetic energy of the bullet when it is between the plates $A$ and $B$ is_______. (Neglect any loss of material of the plates during the collision)

A body is dropped on ground from a height $h_1$ and after hitting the ground, it rebounds to a height $h_2$. If the ratio of velocities of the body just before and after hitting ground is $4$, then percentage loss in kinetic energy of the body is $\frac{x}{4}$. The value of $x$ is _____.

A bullet of mass $200 \mathrm{g}$ having initial kinetic energy $90 \mathrm{J}$ is shot inside a long swimming pool as shown in the figure. If it's kinetic energy reduces to $40 \mathrm{J}$ within $1 \mathrm{s}$, the minimum length of the pool, the bullet has to travel so that it completely comes to rest is