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

If the pulleys shown in the diagram are smooth and massless,and $a_1$ and $a_2$ are the accelerations of the blocks of mass $4 \, kg$ and $8 \, kg$ respectively,then:

For the given diagram,when block $B$ is pulled with velocity $V$,the velocity of block $A$ will be:

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

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

$A$ frictionless cart $A$ of mass $100 \ kg$ carries two other frictionless carts $B$ and $C$ having masses $8 \ kg$ and $4 \ kg$ respectively,connected by a string passing over a pulley as shown in the figure. What horizontal force $F$ must be applied on the cart $A$ so that the smaller carts do not move relative to it (in $N$)? (Take $g = 10 \ m/s^2$)