If a gas is filled in a stationary sphere,its molecules are in random motion due to thermal energy. Will the center of mass of these molecules be in motion?

Two identical bodies $A$ and $B$ of equal masses have initial velocities $v_1 = 4\hat{i} \text{ m/s}$ and $v_2 = 4\hat{j} \text{ m/s}$ respectively. The body $A$ has acceleration $a_1 = 6\hat{i} + 6\hat{j} \text{ m/s}^2$ while the acceleration of the other body $B$ is zero. The centre of mass of the two bodies moves in . . . . . . path.

$A$ 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

$A$ system consists of two particles of masses $m_1$ and $m_2$. If the particle of mass $m_1$ is moved towards the centre of mass through a distance $d$,then the distance the second particle should be moved,so as to keep the centre of mass at the same position is

Two men of masses $55 \ kg$ and $65 \ kg$ are standing at the opposite ends of a boat. The length of the boat is $3.0 \ m$ and its mass is $100 \ kg$. The $55 \ kg$ man walks up to the $65 \ kg$ man and sits beside him. If the boat is in still water,the center of mass of the system will shift by ..... $m$.

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?