$A$ shell of mass $m$ moving with velocity $v$ suddenly breaks into $2$ pieces. The part having mass $m/3$ remains stationary. The velocity of the other part will be

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

$A$ bullet of mass $0.1\,kg$ is fired with a speed of $100\,m/s$. The mass of the gun is $50\,kg$. The recoil velocity of the gun is ........ $m/s$.

$A$ 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

$A$ 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

$A$ bomb of mass $10\, kg$ explodes into two pieces of masses $4\, kg$ and $6\, kg$. If the kinetic energy of the $4\, kg$ piece is $200\, J$,find the kinetic energy of the $6\, kg$ piece.