In the figure shown the velocity of different blocks is shown. The velocity of $C$ is ......... $m/s$

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

A light string passing over a smooth light fixed pulley connects two blocks of masses $m_1$ and $m_2$. If the acceleration of the system is $g / 8$, then the ratio of masses 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 ${s}$)

The pulleys in the diagram are all smooth and light. The acceleration of $A$ is a upwards and the acceleration of $C$ is $f$ downwards. The acceleration of $B$ is

A block is dragged on a smooth plane with the help of a rope which moves with a velocity $v$ as shown in figure. The horizontal velocity of the block is