$A$ child is standing at one end of a long trolley moving with a speed $v$ on a smooth horizontal track. If the child starts running towards the other end of the trolley with a speed $u$,the centre of mass of the system (trolley + child) will move with a speed

Explain translational motion by the given illustration.

Four particles $A, B, C$ and $D$ with masses $m_A=m, m_B=2m, m_C=3m$ and $m_D=4m$ are at the corners of a square. They have accelerations of equal magnitude $a$ with directions as shown. The acceleration of the centre of mass of the particles is

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:

$A$ 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 ........ $m$

$A$ 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