In free space,a shell moving with velocity $60\,m/s$ along the positive $x$-axis passes through the origin and explodes into two pieces with a mass ratio of $1:2$. After the explosion,the velocity of the centre of mass is ....... $m/s$.

$A$ 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 persons of masses $55\, kg$ and $65\, kg$ respectively,are at the opposite ends of a boat. The length of the boat is $3.0\, m$ and it weighs $100\, kg$. The $55\, kg$ man walks up to the $65\, kg$ man and sits with him. If the boat is in still water,the center of mass of the system shifts by ....... $m$.

$A$ system consists of two particles of masses $m_1$ and $m_2$ separated by a distance $r$. If the particle of mass $m_1$ is moved towards the centre of mass by a distance $d$,then the particle of mass $m_2$ must be moved by a distance $d'$ so that the centre of mass remains at the same position. The value of $d'$ is:

In a system of two particles of masses $m_{1}$ and $m_{2}$,the first particle is moved by a distance $d$ towards the centre of mass. To keep the centre of mass unchanged,the second particle will have to be moved by a distance:

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 $L$. As the man walks on the trolley,the centre of mass of the system (man $+$ trolley)