What is the acceleration of block $B$ for the given system?

The velocity of end $A$ of a rigid rod placed between two smooth perpendicular walls moves with velocity $u$ along the vertical direction. Find the velocity of end $B$ of the rod,given that the rod always remains in contact with the walls.

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

Two blocks of same mass $4 \ kg$ are placed as shown in the diagram. The initial velocities of the blocks are $4 \ m/s$ (horizontal) and $2 \ m/s$ (downward). The string is initially taut. Find the impulse on the $4 \ kg$ block when the string again becomes taut (in $N-s$).

At a given instant,block $A$ is moving with a velocity of $5\,m/s$ upwards. What is the velocity of block $B$ at that time?

In each of the three arrangements,the block of mass $m_1$ is being pulled left with constant velocity $v$. There is no friction anywhere. The strings are light and inextensible and pulleys are massless. The ratio of the speed of the block of mass $m_2$ in the three cases respectively is