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 ....... $m/s$.

$A$ small ball $B$ of mass $m$ is suspended with a light inelastic string of length $L$ from a block $A$ of the same mass $m$,which can move on a smooth horizontal surface as shown in the figure. The ball is displaced by an angle $\theta$ from the equilibrium position and then released. The displacement of the centre of mass of the $A+B$ system until the string becomes vertical is

$A$ man weighing $80\, kg$ is standing at the centre of a flat boat and he is $20\, m$ from the shore. He walks $8\, m$ on the boat towards the shore and then halts. The boat weighs $200\, kg$. How far is he from the shore at the end of this time?

The velocity of the centre of mass of the system as shown in the figure is

$A$ $2\ kg$ body and a $3\ kg$ body are moving along the $x-$ axis. At a particular instant,the $2\ kg$ body has a velocity of $3\ m/s$ and the $3\ kg$ body has a velocity of $2\ m/s$. The velocity of the centre of mass at that instant is

Two blocks of equal masses $M$ are tied with a light string passing over a massless pulley on a wedge with angles $60^{\circ}$ and $30^{\circ}$ (assuming frictionless surfaces). The acceleration of the centre of mass of the two blocks is $\left(g=10 \text{ ms}^{-2}\right)$.