$A$ 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:

$A$ 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 ........ $m$

$M$ mass of a man stands at one end of a plank of length $L$ which lies at rest on a frictionless surface. The man walks to the other end of the plank. If the mass of the plank is $\frac{M}{3}$,then the distance that the man moves relative to the ground is:

Two particles of masses $2 \ kg$ and $1 \ kg$ are moving along the same line with speeds of $2 \ m/s$ and $5 \ m/s$ respectively. If both particles are moving in the same direction,the speed of the centre of mass is $v_1$. If both particles are moving in opposite directions,the speed of the centre of mass is $v_2$. Find $v_1$ and $v_2$.

$A$ system of two particles has masses $m_1$ and $m_2$. If the particle of mass $m_1$ is pushed towards the centre of mass of the particles through a distance $d$,by what distance should the particle of mass $m_2$ be moved to keep the centre of mass of the particles at the original position?

Two identical particles are moving with velocities $2v$ and $v$ respectively. Find the velocity of the center of mass.