In the figure shown the block $B$ moves down with a velocity $10 m/s$. The velocity of $A$ in the position shown is ......... $m/s$

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   .......... $m/s$

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?

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

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