A body of mass $5 \,kg$  explodes at rest into three fragments with masses in the ratio $1 : 1 : 3$. The fragments with equal masses fly in mutually perpendicular directions with speeds of $21 \,m/s$. The velocity of the heaviest fragment will be

Two identical billiard balls strike a rigid wall with the same speed but at different angles, and get reflected without any change in speed, as shown in Figure. What is

$(i)$ the direction of the force on the wall due to each ball?

$(ii)$ the ratio of the magnitudes of impulses imparted to the balls by the wall ?

An object of mass $3\,m$ splits into three equal fragments. Two fragments have velocities $v\hat j$ and $v\hat i$. The velocity of the third fragment is

A bomb of mass $9 \,kg$ explodes into two pieces of masses $3 \,kg$ and $6 \,kg$. The velocity of mass $3 \,kg$ is $16 \,m / s$. The kinetic energy of mass $6 \,kg$ in joule is

A bullet $10\,g$ leaves the barrel of gun with a velocity of $600\,m / s$. If the barrel of gun is $50\,cm$ long and mass of gun is $3\,kg$, then value of impulse supplied to the gun will be $.....\,Ns$

An open water tight railway wagon of mass $5 \times 10^3 kg$ coasts at an initial velocity $1.2 m/s$ without friction on a railway track. Rain drops fall vertically downwards into the wagon. The velocity of the wagon after it has collected $10^3 kg$ of water will be .............. $\mathrm{m}/ \mathrm{s}$