$A$ body is moving with a velocity $v$ and breaks up into two equal parts. One of the parts retraces its path with velocity $v$. Then the velocity of the other part is:

$A$ $300 \ kg$ trolley carrying a $25 \ kg$ sandbag is moving on a frictionless track with a uniform speed of $27 \ km/hr$. After some time,sand starts leaking out of the bag at a rate of $0.05 \ kg/s$ and falls onto the floor of the trolley. Find the speed of the trolley in $km/hr$ when the sandbag is completely empty.

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 $L$. The velocity of the man with respect to ground $v_1$ 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

$A$ body of mass $14 \ kg$ initially at rest explodes and breaks into three fragments of masses in the ratio $2:2:3$. The two pieces of equal masses fly off perpendicular to each other with a speed of $18 \ m/s$ each. The velocity of the heavier fragment is . . . . . . $m/s$.

$A$ machine gun of mass $10\,kg$ fires $20\,g$ bullets at the rate of $180$ bullets per minute with a speed of $100\,m s^{-1}$ each. The recoil velocity of the gun is $.............\,m/s$.