In the arrangement shown in figure the ends $P$ and $Q$ of an unstretchable string move downwards with uniform speed $ U$. Pulleys $A$ and $B$ are fixed. Mass $M$ moves upwards with a speed

The end $B$ of the rod $AB$ which makes angle $\theta$ with the floor is being pulled with, a constant velocity $v_0$ as shown. The length of the rod is $l.$ At the instant when $\theta = 37^o $ then

In the figure shown the velocity of lift is $2\,m / s$ while string is winding on the motor shaft with velocity $2\,m / s$ and block $A$ is moving downwards with a velocity of $2\,m / s$, then find out the velocity of block $B -$

Figure shows a boy on a horizontal platform $A$ on a smooth horizontal surface, holding a rope attached to a box $B$ . Boy pulls the rope with a constant force of $50\ N$ . (boy does not slip over the platform). The combined mass of platform $A$ and boy is $250\ kg$ and that of box $B$ is $500\ kg$ . The velocity of $A$ relative to the box $B$ , $5\ s$ after the boy on $A$ begins to pull the rope, will be ............ $m/s$

All surfaces shown in figure are assumed to be frictionless and the pulleys and the string are light. The acceleration of the block of mass $2 \mathrm{~kg}$ is :

Two blocks of same mass $(4\ kg)$ are placed according to diagram. Initial velocities of bodies are $4\ m/s$ and $2\ m/s$ and the string is taut. Find the impulse on $4\ kg$ when the string again becomes taut  .......... $N-s$