Three particles $A, B$ and $C$ of masses $m, 2m$ and $3m$ are moving towards north, south and east respectively. If the velocities of the particles $A, B$ and $C$ are $6 \,ms^{-1}, 12 \,ms^{-1}$ and $8 \,ms^{-1}$ respectively, then the velocity of the centre of mass of the system of particles is (in $\,ms^{-1}$)

$A$ 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 $cm$)

Two blocks of masses $10 \; kg$ and $30 \; kg$ are placed on the same straight line with coordinates $(0,0) \; cm$ and $(x, 0) \; cm$ respectively. The block of $10 \; kg$ is moved on the same line through a distance of $6 \; cm$ towards the other block. The distance through which the block of $30 \; kg$ must be moved to keep the position of the centre of mass of the system unchanged is

Two particles of masses in the ratio $1:2$ are placed along a vertical line. The lighter particle is raised through a height of $9 \ cm$. To raise the centre of mass of the system by $2 \ cm$,the heavier particle should be

On a smooth horizontal plane,a uniform string of mass $M$ and length $L$ is lying in a state of rest. $A$ man of the same mass $M$ is standing next to one end of the string. Now,the man starts collecting the string. Finally,the man collects all the string and puts it in his pocket. What is the displacement of the man with respect to the Earth in the process of collection?

Two blocks of masses $5 \, kg$ and $2 \, kg$ are connected by a spring of negligible mass and placed on a frictionless horizontal surface. An impulse provides a velocity of $7 \, m/s$ to the heavier block in the direction of the lighter block. The velocity of the centre of mass is ............ $m/s$.