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

A particle of mass $m$ travelling along $x-$ axis with speed $v_0$ shoots out $1/3^{rd}$ of its mass with a speed $2v_0$ along $y-$ axis. The velocity of remaining piece is

A particle of mass $m$ moving horizontally with $v_0$ strikes $a$ smooth wedge of mass $M$, as shown in figure. After collision, the ball starts moving up the inclined face of the wedge and rises to $a$ height $h$. When the particle has risen to $a$ height $h$ on the wedge, then choose the correct alternative $(s)$

$A$ projectile of mass $"m"$ is projected from ground with a speed of $50 \,m/s$ at an angle of $53^o$ with the horizontal. It breaks up into two equal parts at the highest point of the trajectory. One particle coming to rest immediately after the explosion. The ratio of the radii of curvatures of the moving particle just before and just after the explosion are:

A bob of mass $\mathrm{M}$ is suspended by a massless string of length $\mathrm{L}$. The horizontal velocity $\mathrm{V}$ at position $\mathrm{A}$ is just sufficient to make it reach the point $B$. The angle $\theta$ at which the speed of the bob is half of that at $A$, satisfies Figure:

A neutron moving with a speed $'v'$ makes a head on collision with a stationary hydrogen atom in ground state . The minimum kinetic energy of the neutron for which inelastic collision will take place is....$eV$