$A$ shell fired from a gun at an angle to the horizontal explodes in mid-air. Then the centre of mass of the shell fragments will move

$A$ system consists of two particles of masses $m_1$ and $m_2$ separated by a distance $r$. If the particles move towards each other with velocities $v_1$ and $v_2$ respectively,the velocity of the centre of mass of the system is:

$A$ body of mass $m_1 = 4 \text{ kg}$ moves at $5 \hat{i} \text{ m/s}$ and another body of mass $m_2 = 2 \text{ kg}$ moves at $10 \hat{i} \text{ m/s}$. The kinetic energy of the centre of mass is:

$A$ ladder $AP$ of length $5\, m$ is inclined to a vertical wall and is slipping over a horizontal surface with a velocity of $2\, m/s$. When the end $A$ is at a distance of $3\, m$ from the wall,what is the velocity of the center of mass $(C.M.)$ of the ladder at this moment (in $, m/s$)?

Two particles of masses $3 \ kg$ and $6 \ kg$ are approaching towards each other with accelerations $2 \ m/s^2$ and $4 \ m/s^2$ respectively,on a smooth horizontal surface. Then the acceleration of the centre of mass of the system is ..... $m/s^2$.

Two particles of equal mass have velocities $\overrightarrow{v}_1=4 \hat{i} \text{ ms}^{-1}$ and $\overrightarrow{v}_2=4 \hat{j} \text{ ms}^{-1}$. The first particle has an acceleration $\overrightarrow{a}_1=(5 \hat{i}+5 \hat{j}) \text{ ms}^{-2}$ while the acceleration of the other particle is zero. The centre of mass of the two particles moves in a path of