When two balls at the same temperature collide,which of the following quantities is conserved?

An object of mass $2m$ is projected with a speed of $100 \ m/s$ at an angle $\theta = \sin^{-1}(3/5)$ to the horizontal. At the highest point, the object breaks into two pieces of same mass $m$ and the first one comes to rest. The distance between the point of projection and the point of landing of the second piece (in metres) is $(g = 10 \ m/s^2)$.

$A$ shell is fired from a cannon with a velocity $V$ at an angle $\theta$ with the horizontal direction. At the highest point in its path,it explodes into two pieces of equal masses. One of the pieces comes to rest. The speed of the other piece immediately after the explosion is

Two persons of mass $m_1$ and $m_2$ are standing at the two ends $A$ and $B$ respectively,of a trolley of mass $M$ as shown. When both the persons jump simultaneously with $u_{rel}$ with respect to the trolley,then the velocity of the trolley is

Neglecting friction,if a person sitting at the back of a motorcycle moving on a straight path falls off while the motorcycle is in motion,will the velocity of the motorcycle increase or decrease? Why?

$A$ shell of mass $m$ moving with velocity $v$ suddenly breaks into $2$ pieces. The part having mass $m/4$ remains stationary. The velocity of the other shell will be