$A$ 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

Two particles of equal mass have velocities $\overrightarrow{v}_1=4 \hat{i} \text{ ms}^{-1}$ and $\overrightarrow{v}_2=4 \hat{j} \text{ ms}^{-1}$. The first particle has an acceleration $\overrightarrow{a}_1=(5 \hat{i}+5 \hat{j}) \text{ ms}^{-2}$ while the acceleration of the other particle is zero. The centre of mass of the two particles moves in a path of

The velocity of the centre of mass of the system as shown in the figure is

Two particles of mass $m$ each are fixed at the opposite ends of a massless rod of length $5 \ m$ which is oriented vertically on a smooth horizontal surface and released. Find the displacement of the lower mass on the ground when the rod makes an angle of $37^o$ with the vertical. (in $m$)

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 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