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

Three men $A, B$ and $C$ of masses $40\,kg, 50\,kg$ and $60\,kg$ are standing on a plank of mass $90\,kg$,which is kept on a smooth horizontal plane. If $A$ and $C$ exchange their positions,then mass $B$ will shift:

Two particles of equal mass have velocities $2\,\hat{i}\,ms^{-1}$ and $2\,\hat{j}\,ms^{-1}$. The first particle has an acceleration $(3\,\hat{i} + 3\,\hat{j})\,ms^{-2}$ while the acceleration of the second particle is zero. The centre of mass of the two particles moves in

$A$ 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

Two skaters $A$ and $B$ of weights in the ratio $5 : 7$ start facing each other $6\,m$ apart on a horizontal smooth surface. They pull on a rope stretched between them. How far has each moved when they meet?

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 $\left(g=10 \text{ ms}^{-2}\right)$.