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

$A$ person of mass $80 \ kg$ is standing on a trolley of mass $320 \ kg$. The trolley is at rest on a frictionless horizontal rail. If the person walks on the trolley at a speed of $1 \ m/s$,what will be their displacement relative to the ground after $4 \ s$?

Two masses $A$ and $B$ of mass $M$ and $2M$ respectively are connected by a compressed ideal spring. The system is placed on a horizontal frictionless table and given a velocity $u \hat{k}$ in the $z$-direction as shown in the figure. The spring is then released. In the subsequent motion,the line from $B$ to $A$ always points along the $\hat{i}$ unit vector. At some instant of time,mass $B$ has an $x$-component of velocity as $V_x \hat{i}$. The velocity $\vec{V}_A$ of mass $A$ at that instant is:

$A$ stationary body explodes into two parts of masses $M_1$ and $M_2$. They move in opposite directions with velocities $V_1$ and $V_2$. The ratio of their kinetic energies is

$A$ bomb of mass $3m \text{ kg}$ explodes into two pieces of mass $m \text{ kg}$ and $2m \text{ kg}$. If the velocity of the $m \text{ kg}$ mass is $16 \text{ m/s}$,the total kinetic energy released in the explosion is ................. $m \text{ J}$.

$A$ projectile moving with velocity $v$ in space bursts into $2$ parts with masses in the ratio $1 : 3$. The smaller part becomes stationary. What is the velocity of the other part?