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 ........ $m/s$.

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

$A$ child sits stationary at one end of a long trolley moving uniformly with a speed $V$ on a smooth horizontal floor. If the child gets up and runs about on the trolley in any manner,what is the speed of the $CM$ of the (trolley + child) system?

Two masses $m_1$ and $m_2$ start to move towards each other due to mutual gravitational force. If the distance covered by $m_1$ is $x$,then the distance covered by $m_2$ is:

Two bodies of $6 \,kg$ and $4 \,kg$ masses have their velocities $5 \hat{i}-2 \hat{j}+10 \hat{k}$ and $10 \hat{i}-2 \hat{j}+5 \hat{k}$ respectively. Then the velocity of their centre of mass is

$A$ man inside a freely falling box throws a heavy ball towards a side wall. The ball keeps on bouncing between the opposite walls of the box. We neglect air resistance and friction. Which of the following figures depicts the motion of the centre of mass of the entire system (man,the ball and the box)?