Two men of masses $55 \ kg$ and $65 \ kg$ are standing at the opposite ends of a boat. The length of the boat is $3.0 \ m$ and its mass is $100 \ kg$. The $55 \ kg$ man walks up to the $65 \ kg$ man and sits beside him. If the boat is in still water,the center of mass of the system will shift by ..... $m$.

Explain translational motion by the given illustration.

Two particles $X$ and $Y$,initially at rest,move towards each other under mutual attraction. If at any instant the velocity of particle $X$ is $V$ and the velocity of particle $Y$ is $2V$,then the velocity of their center of mass will be:

The figure shows a man of mass $m$ standing at the end $A$ of a trolley of mass $M$ placed at rest on a smooth horizontal surface. The man starts moving towards the end $B$ with a velocity $u_{rel}$ with respect to the trolley. The length of the trolley is $L$. When the man reaches the end $B$,the distance moved by the trolley with respect to ground is

Obtain Newton's second law for a system of particles and write its statement.

$A$ wooden plank of mass $90 \ kg$ and length $3.3 \ m$ is floating on still water. $A$ girl of mass $20 \ kg$ walks from one end to the other end of the plank. The distance through which the plank moves is (in $cm$)