According to the principle of conservation of linear momentum, if the external force acting on the system is zero, the linear momentum of the system will remain conserved. It means if the centre of mass of a system is initially at rest, it will remain at rest in the absence of external force, i.e. the displacement of centre of mass will be zero.

A plank of mass M is placed on a smooth horizontal surface. Two light identical springs each of stiffness k are rigidly connected to struts at the end of the plank as shown in the figure. When springs are in its natural length, their free ends are at a distance of  $3\mathcal{l}$ from y axis. A block of mass m is placed on the plank and pressed against right spring so that it is compressed by  $2\mathcal{l}$. To keep the block at rest it is connected to the strut by means of a light string. Initially the system is at rest. The right spring is in its natural length. Now the string is burnt.