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.

An iron rod of length $1.5 \,m$ lying on a horizontal table is pulled up from one end along a vertical line so as to move it with a constant velocity $3 \,m/s$, while the other end of the rod slides along the floor. After how much time will the speed of the end sliding on the floor equal the speed of the end being pulled up?

In the figure shown,the velocities of different blocks are given. The velocity of $C$ is ......... $m/s$.

$A$ basket and its contents have mass $M$. $A$ monkey of mass $2M$ grabs the other end of the rope and very quickly (almost instantaneously) accelerates by pulling hard on the rope until he is moving with a constant speed of $v_{m/r} = 2 \, ft/s$ measured relative to the rope. The monkey then continues climbing at this constant rate relative to the rope for $3 \, s$. How fast is the basket rising at the end of the $3 \, s$? Neglect the mass of the pulley and the rope. (given : $g = 32 \, ft/s^2$)

In the arrangement shown in the figure,$a_{1}, a_{2}, a_{3}$ and $a_{4}$ are the accelerations of masses $m_{1}, m_{2}, m_{3}$ and $m_{4}$ respectively. Which of the following relations is true for this arrangement?