Three bodies having masses $5 \, kg$,$4 \, kg$,and $2 \, kg$ are moving at speeds of $5 \, m/s$,$4 \, m/s$,and $2 \, m/s$ respectively along the $X$-axis. The magnitude of the velocity of the centre of mass is (in $m/s$):

Consider a system of two identical particles. One of the particles is at rest and the other has an acceleration $\vec{f}$. The centre of mass has an acceleration

$A$ ball of mass $M$ moving with a speed of $2 \ m \ s^{-1}$ hits another ball of mass $1 \ kg$ moving in the same direction with a speed of $1 \ m \ s^{-1}$. If the kinetic energy of the center of mass is $4/3 \ J$,then the magnitude of $M$ is: (in $kg$)

Two blocks of mass $m$ each,connected to each other by a massless string,are placed on two inclined planes as shown in the figure. After releasing from rest,find the magnitude of the acceleration of the centre of mass of both the blocks. (Given $g = 10 \, m/s^2$)

$A$ $750 \ kg$ boat is $10 \ m$ long and is floating without motion on still water. $A$ man of mass $80 \ kg$ is at one end. If he runs to the other end of the boat and stops,the displacement of the boat is:

Two blocks,each of mass $m$,are connected to each other by a massless string and placed on two inclined planes as shown in the figure. After releasing the system from rest,find the magnitude of the acceleration of the centre of mass of the two blocks. (Take $g = 10 \, m/s^2$)