$A$ boy of mass $20\, kg$ is standing on an $80\, kg$ cart that is free to move. There is negligible friction between the cart and the ground. Initially,the boy is standing $25\, m$ from a wall. If he walks $10\, m$ on the cart towards the wall,then the final distance of the boy from the wall will be ........ $m$

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 masses $m_1$ and $m_2$ $(m_1 > m_2)$ are connected by a massless,flexible,and inextensible string passed over a massless and frictionless pulley. The acceleration of the center of mass of the system is

Two blocks of masses $2 \text{ kg}$ and $1 \text{ kg}$ respectively, are tied to the ends of a string which passes over a light frictionless pulley as shown in the figure below. The masses are held at rest at the same horizontal level and then released. The distance traversed by the centre of mass in $2 \text{ s}$ is . . . . . . $\text{m}$. (Take $g = 10 \text{ m/s}^2$)

Two bodies of mass $4 \,kg$ and $5 \,kg$ are moving along east and north directions with velocities $5 \,m/s$ and $3 \,m/s$ respectively. The magnitude of the velocity of the centre of mass of the system is:

Two particles of masses $1\ kg$ and $3\ kg$ move towards each other under their mutual force of attraction. No other force acts on them. When the relative velocity of approach of the two particles is $2\ m/s,$ their centre of mass has a velocity of $0.5\ m/s$. When the relative velocity of approach becomes $3\ m/s,$ the velocity of the centre of mass is ........ $m/s$.