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)

Calculate the acceleration of mass $12 \mathrm{kg}$ and the tension in the string connecting to $12 \mathrm{kg}$ mass, shown in the figure (the strings are weightless and inextensible; the pulleys are weightless and frictionless).

Take acceleration due to gravity as $g$.