$A$ rod is constrained to move along a vertical wall and a horizontal floor. If the velocity of end $A$ is $V_A$ along the horizontal floor,find the velocity $V_B$ of end $B$ along the vertical wall in terms of $V_A$ and $\theta$.

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

Consider the situation shown in the figure. All the surfaces are smooth. The tension in the string connected to $2m$ is

In the adjoining figure,if the acceleration of the wedge $M$ with respect to the ground is $a$,then:

$A$ 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 $g = 10 \ m/s^2$)

The velocities of block $A$ and block $B$ are shown in the figure. The velocity of block $C$ is ......... $m/s$ (assume that the pulleys are ideal and the string is inextensible).