$A$ $100\, g$ iron ball having velocity $10\, m/s$ collides with a wall at an angle of $30^\circ$ with the wall and rebounds with the same angle. If the period of contact between the ball and the wall is $0.1\, s$,then the force experienced by the wall is ........... $N$.

$A$ stationary body explodes into two parts of masses $M_{1}$ and $M_{2}$. They move in opposite directions with velocities $v_{1}$ and $v_{2}$. The ratio of their kinetic energies is

$A$ body at rest breaks up into $3$ parts. If $2$ parts having equal masses $m$ fly off perpendicularly to each other,each with a velocity of $12 \, m/s$,then the velocity of the third part,which has $3$ times the mass of each part,is:

$A$ body of mass $0.25 \, kg$ is projected with a muzzle velocity of $100 \, m/s$ from a tank of mass $100 \, kg$. What is the recoil velocity of the tank in $m/s$?

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.

$A$ shell at rest at the origin explodes into three fragments of masses $1 \ kg$,$2 \ kg$,and $m \ kg$. The $1 \ kg$ and $2 \ kg$ pieces fly off with speeds of $5 \ m/s$ along the $x$-axis and $6 \ m/s$ along the $y$-axis,respectively. If the $m \ kg$ piece flies off with a speed of $6.5 \ m/s$,the total mass of the shell must be ......... $kg$.