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

The velocities of block $A$ and block $B$ are shown in the figure. The velocity of block $C$ is ......... $m/s$ (assume that the pulleys are ideal and the string is inextensible).

Block $B$ moves to the right with a constant velocity $v_0$. The velocity of body $A$ relative to $B$ is:

$A$ frictionless cart $A$ of mass $100 \ kg$ carries two other frictionless carts $B$ and $C$ having masses $8 \ kg$ and $4 \ kg$ respectively,connected by a string passing over a pulley as shown in the figure. What horizontal force $F$ must be applied on the cart $A$ so that the smaller carts do not move relative to it (in $N$)? (Take $g = 10 \ m/s^2$)

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

In the pulley system shown in the figure, the mass of $A$ is half of that of $\text{rod } B$. The rod length is $500 \text{ cm}$. The mass of pulleys and the threads may be neglected. The mass $A$ is set at the same level as the lower end of the rod and then released. After releasing the mass $A$, it would reach the top end of the rod $B$ in time (Assume $g=10 \text{ m/s}^2$): (in $\text{ s}$)