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 bodies of masses $M$ and $4M$ initially at rest,start moving towards each other due to their mutual attraction. The velocity of their centre of mass when the first body attains a velocity $v_0$ is

As shown in the figure,two blocks are connected with a light spring. When the spring is at its natural length,velocities are given to them as shown in the figure. Choose the wrong alternative.

The figure shows a man of mass $m$ standing at the end $A$ of a trolley of mass $M$ placed at rest on a smooth horizontal surface. The man starts moving towards the end $B$ with a velocity $u_{rel}$ with respect to the trolley. The length of the trolley is $L$. The distance moved by the man with respect to ground is

Two masses $m_1$ and $m_2$ are connected by a massless spring of spring constant $k$ and unstretched length $l$. The masses are placed on a frictionless straight channel,which we consider our $X$-axis. They are initially at rest at $x=0$ and $x=l$,respectively. At $t=0$,a velocity of $v_0$ is suddenly imparted to the first particle. At a later time $t$,the centre of mass of the two masses is at

Two particles of the same mass are moving towards each other with velocities $2v$ and $v$ respectively. The velocity of the centre of mass of the system is: