If the block $A$ & $B$ are moving towards each other with acceleration $a$ and $b$. Find the net acceleration of $C$.

Acceleration of system is :-

A rod of length $L$ leans against a smooth vertical wall while its other end is on a smooth floor. The end that leans against the wall moves uniformly vertically downward. Select the correct alternative

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 ............ $m/s$

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 ${s}$)

All surfaces shown in figure are assumed to be frictionless and the pulleys and the string are light. The acceleration of the block of mass $2 \mathrm{~kg}$ is :