Two balls at same temperature collide. What is conserved

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

A projectile is moving at $20\,m/sec$ at its highest point where it breaks into two equal parts due to an internal explosion. One part moves vertically up at $30\,m/sec$ . Then the other part will move at ............. $\mathrm{m}/ \mathrm{s}$

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 projectile is fired at a speed of $100\, m/sec$ at an angle of $37^o$ above the horizontal. At the highest point, the projectile breaks into two parts of mass ratio $1:3$ , the smaller coming to rest. Then the distance of heavier part from the launching point is ............... $\mathrm{m}$

A particle of mass $m$ with initial kinetics energy $K$ approaches the origin from $x =+\infty$. Assume that a conservative force acts on it and its potential energy $V ( x )$ is given by $V ( x )=\frac{ K }{\exp \left(3 x / x _0\right)+\exp \left(-3 x / x _0\right)}$ where, $x_0=1 m$. The speed of the particle at $x =0$ is