The boxes of masses $2\, {kg}$ and $8\, {kg}$ are connected by a massless string passing over smooth pulleys. Calculate the time taken by box of mass $8\; {kg}$ to strike the ground starting from rest. (use $\left.{g}=10\, {m} / {s}^{2}\right)$ (in ${s}$)

If acceleration of $A$ is $2\,m / s ^2$ to left and acceleration of $B$ is $1\,m / s ^2$ to left, then acceleration of $C$ is -

The velocity of end ' $A$ ' of rigid rod placed between two smooth vertical walls moves with velocity ' $u$ ' along vertical direction. Find out the velocity of end ' $B$ ' of that rod, rod always remains in constant with the vertical walls.

At a given instant, $A$ is moving with velocity of $5\,m / s$ upwards. What is velocity of $B$ at the time

Figure shows a boy on a horizontal platform $A$ on a smooth horizontal surface, holding a rope attached to a box $B$ . Boy pulls the rope with a constant force of $50\ N$ . (boy does not slip over the platform). The combined mass of platform $A$ and boy is $250\ kg$ and that of box $B$ is $500\ kg$ . The velocity of $A$ relative to the box $B$ , $5\ s$ after the boy on $A$ begins to pull the rope, will be ............ $m/s$

Two blocks of same mass $(4\ kg)$ are placed according to diagram. Initial velocities of bodies are $4\ m/s$ and $2\ m/s$ and the string is taut. Find the impulse on $4\ kg$ when the string again becomes taut  .......... $N-s$