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

Find the velocity of the hanging block if the velocities of the free ends of the rope are as indicated in the figure.

A slider block $A$ moves downward at a speed of $v_A = 2\ m/s$ , at an angle of $75^o$ with horizontal as shown in the figure. The velocity with respect to $A$ of the portion of belt $B$ between ideal pulleys $C$ and $D$ is $v_{CD/A} = 2\ m/s$ at an angle $\theta $ with the horizontal. The magnitude of velocity of portion $CD$ of the belt when $\theta  = 15^o$ is   .......... $m/s$

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

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