$A$ $1 \; kg$ stationary bomb explodes into three parts having mass ratio $1:1:3$. The parts with equal mass move in perpendicular directions with a velocity of $30 \; m/s$. What is the velocity of the third (heavier) part?

For a system to follow the law of conservation of linear momentum during a collision,the condition is:
$(1)$ Total external force acting on the system is zero.
$(2)$ Total external force acting on the system is finite and the time of collision is negligible.
$(3)$ Total internal force acting on the system is zero.

$A$ trolley of mass $200\; kg$ moves with a uniform speed of $36\; km/h$ on a frictionless track. $A$ child of mass $20\; kg$ runs on the trolley from one end to the other ($10\; m$ away) with a speed of $4\; m/s$ relative to the trolley in a direction opposite to its motion,and jumps out of the trolley. What is the final speed of the trolley? How much has the trolley moved from the time the child begins to run?

$A$ man of $50 \,kg$ is standing at one end of a boat of length $25 \,m$ and mass $200 \,kg$. If he starts running and when he reaches the other end, he has a velocity $2 \,ms^{-1}$ with respect to the boat. The final velocity of the boat is : (in $ms^{-1}$ )

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 only the person standing at $B$ jumps from the trolley towards the right while the person at $A$ keeps standing,then

The momentum of a system is conserved: