$A$ uniform rod of mass $M$ and length $L$ is placed on a smooth horizontal surface. $A$ horizontal force $F$ is applied at one end of the rod perpendicular to its length. The acceleration of the centre of mass of the rod 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:

$A$ body $A$ of mass $M$ falls vertically downwards under gravity. It breaks into two parts: a body $B$ of mass $1/3 M$ and a body $C$ of mass $2/3 M$. The center of mass of bodies $B$ and $C$ taken together shifts from the direction of $A$ by:

$A$ particle of mass $m$ is thrown horizontally from the top of a tower and another particle of mass $2m$ is thrown vertically upward. The acceleration of the centre of mass is .............

Two particles of masses $2 \ kg$ and $3 \ kg$ are moving along the $X$-axis with velocities $3 \ m/s$ and $2 \ m/s$ respectively. The velocity of the center of mass of this system is ........ $m/s$.

$A$ boy of mass $20\, kg$ is standing on an $80\, kg$ cart that is free to move. There is negligible friction between the cart and the ground. Initially,the boy is standing $25\, m$ from a wall. If he walks $10\, m$ on the cart towards the wall,then the final distance of the boy from the wall will be ........ $m$