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

Two masses are connected by a string which passes over a pulley accelerating upwards at a rate $A$ as shown in the figure. If $a_1$ and $a_2$ be the acceleration of bodies $1$ and $2$, respectively, then (all the measured acceleration are with respect to ground)

In the figure shown below, blocks $A$ and $B$ move with velocities $v_1$ and $v_2$, respectively, along the horizontal direction. The ratio of $\frac{v_1}{v_2}$ is

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

In the figure shown, the pulley is moving with the velocity $u$. The velocity of the block attached with the string is

The velocity of end $A$ of a rigid rod, placed between two smooth vertical walls, is $u$ along the vertical direction. The velocity of end $B$ of the rod is (The rod always remains in contact with the vertical walls.)

Block $B$ is moving towards the right with a constant velocity $v_0.$ Velocity of the block $A$ with respect to block $B$ is (assume all the pulleys and strings are ideal).

In the figure shown below, block $B$ moves down with a velocity $10 \mathrm{m} {\mathrm{s}}^{-1}$. The velocity of $A$, in the position shown, is

The acceleration of block $B$, in the figure, will be (assume all the surfaces are frictionless; pulleys and strings are ideal)