Two blocks of masses $m$ and $2m$ are connected by a massless string which passes over a fixed frictionless pulley. If the system of blocks is released from rest,the speed of the centre of mass of the system of two blocks after a time of $5.4 \ s$ is (Acceleration due to gravity $= 10 \ ms^{-2}$) (in $ms^{-1}$)

In the given figure,if the speed given to block $A$ is $10\,m/s$ and block $B$ is initially at rest,then the speed of the centre of mass after $10\,s$ will be ....... $m/s$.

Two particles of equal mass have velocities $\overrightarrow{v}_1=4 \hat{i} \text{ ms}^{-1}$ and $\overrightarrow{v}_2=4 \hat{j} \text{ ms}^{-1}$. The first particle has an acceleration $\overrightarrow{a}_1=(5 \hat{i}+5 \hat{j}) \text{ ms}^{-2}$ while the acceleration of the other particle is zero. The centre of mass of the two particles moves in a path of

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,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 $g = 10 \, m/s^2$)

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 the centre of mass of the system will be