Three blocks $A, B$ and $C$ are suspended as shown in the figure. Mass of each blocks $A$ and $C$ is $m$. If system is in equilibrium and mass of $B$ is $M$, then :

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

The end $B$ of the rod $AB$ which makes angle $\theta$ with the floor is being pulled with, a constant velocity $v_0$ as shown. The length of the rod is $l.$ At the instant when $\theta = 37^o $ then

A uniform metal chain of mass $m$ and length ' $L$ ' passes over a massless and frictionless pulley. It is released from rest with a part of its length ' $l$ ' is hanging on one side and rest of its length ' $L -l$ ' is hanging on the other side of the pulley. At a certain point of time, when $l=\frac{L}{x}$, the acceleration of the chain is $\frac{g}{2}$. The value of $x$ is ........

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.