A block is dragged on smooth plane with the help of a rope which moves with velocity $v$. The horizontal velocity of the block is

Two masses are connected by a string which passes over a pulley accelerating upward at a rate $A$ as shown. If $a_1$ and $a_2$ be the acceleration of bodies $1$ and $2$, respectively, then:

In the arrangement shown in figure. the ends $P$ and $Q$ of an unstretchable string move downwards with uniform speed $U$. Pulleys $A$ and $B$ are fixed. Mass $M$ moves upwards with a speed.

A system is shown in the figure. A man standing on the block is pulling the rope. Velocity of the point of string in contact with the hand of the man is $2 \mathrm{m} {\mathrm{s}}^{-1}$ downwards. The velocity of the block will be: [Assume that the block does not rotate]

A rod $AB$ is shown in figure. End $A$ of the rod is fixed on the ground. Block is moving with velocity $\sqrt{3} \mathrm{m} {\mathrm{s}}^{-1}$ towards right. The velocity of end $B$ of rod when rod makes an angle of $60°$ with the ground is:

System is shown in figure and wedge is moving towards left with speed $2 \mathrm{m} {\mathrm{s}}^{-1}$. Then velocity of the block $B$ will be:

In the figure shown the velocity of lift is $2 \mathrm{m} {\mathrm{s}}^{-1}$ while string is winding on the motor shaft with velocity $2 \mathrm{m} {\mathrm{s}}^{-1}$ and block $A$ is moving downwards with a velocity of $2 \mathrm{m} {\mathrm{s}}^{-1}$, then find out the velocity of block $B$.

Two beads $A$ and $B$ move along a fixed semicircular wire frame as shown in figure. The beads are connected by an inelastic string which always remains tight. At an instant the speed of $A$ is $u$, $\angle BAC=45°$ and $\angle BOC=75°$, where $O$ is the centre of the semicircular arc. The speed of bead $B$ at that instant is: