Consider a system of two identical particles. One of the particles is at rest and the other has an acceleration $\vec{f}$. The centre of mass has an acceleration

Two blocks of masses $10\,kg$ and $4\,kg$ are connected by a spring of negligible mass and placed on a frictionless horizontal surface. An impulse gives a velocity of $14\,m/s$ to the heavier block in the direction of the lighter block. The velocity of the centre of mass is ........ $m/s$.

$A$ 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:

Two particles which are initially at rest,move towards each other under the action of their internal attraction. If their speeds are $v$ and $2v$ at any instant,then the speed of centre of mass of the system will be

If one observes from the reference frame in which the centre of mass appears to be at rest,what will be the velocity of the centre of mass?

$A$ ball of mass $1\, kg$ is thrown up with an initial speed of $4\, m/s$. $A$ second ball of mass $2\, kg$ is released from rest from some height as shown in the figure. Select the correct alternative.