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   .......... $m/s$

Two equal masses $A$ and $B$ are arranged as shown in the figure. Pulley and string are ideal and there is no friction. Block $A$ has a speed $u$ in the downward direction. The speed of the block $B$ is :-

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 ............ $m/s$

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

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