$A$ bullet of mass $10\, g$ is fired from a gun of mass $1\, kg$. If the recoil velocity of the gun is $5\, m/s$,the muzzle velocity of the bullet is ........ $m/s$.

The figure shows a man of mass $m$ standing at the end $A$ of a trolley of mass $M$ placed at rest on a smooth horizontal surface. The man starts moving towards the end $B$ with a velocity $u_{rel}$ with respect to the trolley. The length of the trolley is $L$. When the man starts moving,then the velocity of the trolley $v_2$ with respect to ground will be

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

$A$ particle of mass $5m$ at rest suddenly breaks on its own into three fragments. Two fragments of mass $m$ each move along mutually perpendicular directions with speed $v$ each. The energy released during the process is

$A$ cannon ball is fired with a velocity $200 \, m/s$ at an angle of $60^{\circ}$ with the horizontal. At the highest point of its flight,it explodes into $3$ equal fragments. One fragment goes vertically upwards with a velocity $100 \, m/s$,and the second one falls vertically downwards with a velocity $100 \, m/s$. The third fragment will be moving with a velocity:

Under the influence of mutual internal forces,which of the following is true for a system?