$A$ 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 $A$ and $B$ (both initially at rest) start moving towards each other under a mutual force of attraction. At the instant, when the speed of $A$ is $v$ and the speed of $B$ is $2v$, the speed of the centre of mass is

Two persons of masses $55\, kg$ and $65\, kg$ respectively,are at the opposite ends of a boat. The length of the boat is $3.0\, m$ and it weighs $100\, kg$. The $55\, kg$ man walks up to the $65\, kg$ man and sits with him. If the boat is in still water,the center of mass of the system shifts by ....... $m$.

Two bodies of masses $M$ and $4M$ initially at rest,start moving towards each other due to their mutual attraction. The velocity of their centre of mass when the first body attains a velocity $v_0$ is

If a bomb is thrown at a certain angle with the horizontal and after exploding on the way the different fragments move in different directions,then the centre of mass

Two particles which are initially at rest,move towards each other under the action of their internal attraction. If their speeds are $v$ and $2v$ at any instant,then the speed of centre of mass of the system will be