An initially stationary device lying on a frictionless floor explodes into two pieces and slides across the floor. If one piece is moving in the positive $x$ direction,then the other piece is moving in:

The motion of a rocket is based on the principle of conservation of

$A$ gun fires a bullet of mass $50 \ g$ with a velocity of $30 \ m \ s^{-1}$. Due to this,the gun recoils with a velocity of $1 \ m \ s^{-1}$. What is the mass of the gun in $kg$?

$A$ shell of mass $0.020 \; kg$ is fired by a gun of mass $100 \; kg$. If the muzzle speed of the shell is $80 \; m s^{-1}$,what is the recoil speed in $m/s$ of the gun?

$A$ shell of mass $5 M$, acted upon by no external force and initially at rest, bursts into three fragments of masses $M, 2 M$, and $2 M$ respectively. The first two fragments move in opposite directions with velocities of magnitudes $2 v$ and $v$ respectively. The third fragment will

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 time taken by the man to reach the other end is