The momentum of a system is conserved:

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:

$A$ 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 . . . . . . $m/s$.

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

$A$ stationary body explodes into three pieces. The momenta of two pieces are $2p\,\hat{i}$ and $p\,\hat{j}$ respectively,where $p$ is a positive constant. The third piece will have:

$A$ stationary particle breaks into two parts of masses $m_A$ and $m_B$ which move with velocities $v_A$ and $v_B$ respectively. The ratio of their kinetic energies $(K_B : K_A)$ is