In the arrangement shown in the fig, the block of mass $m=2\,kg$ lies on the wedge on mass $M=8\,kg$. Find the initial acceleration of the wedge if the surfaces are smooth and pulley and strings are massless.

In the arrangement shown in figure $a _{1}, a _{2}, a _{3}$ and $a _{4}$ are the accelerations of masses $m _{1}, m _{2}, m _{3}$ and $m _{4}$ respectively. Which of the following relation is true for this arrangement?

In the arrangement shown in figure the ends $P$ and $Q$ of an unstretchable string move downwards with uniform speed $ U$. Pulleys $A$ and $B$ are fixed. Mass $M$ moves upwards with a speed

If block $A$ is moving with an acceleration of $5\,m/s^2$, the acceleration of $B$ w.r.t. ground is

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 pulleys shown in the diagram are smooth and massless and $a_1$ and $a_2$ are acceleration of blocks of mass $4 \,kg$ and $8 \,kg$ respectively, then