Block $A$ of mass $\frac{m}{2}$ is connected to one end of light rope which passes over a pulley as shown in the figure. Man of mass $m$ climbs the other end of rope with a relative acceleration of $\frac{g}{6}$ with respect to rope find acceleration of block $A$ and tension in the rope.

 

In the figure, the ends $P$ and $Q$ of an unstrechable string move downwards with uniform speed $v$. Mass $M$ moves upward with speed

A block is dragged on a smooth plane with the help of a rope which moves with a velocity $v$ as shown in figure. The horizontal velocity of the block is:

A monkey is descending along the branch of a tree with constant acceleration. The breaking strength of the branch is $75\%$of the weight of the monkey. The minimum acceleration with which the monkey can slide down without breaking the branch is

A trolley of mass $5 \mathrm{kg}$ on a horizontal smooth surface is pulled by a load of mass $2 \mathrm{kg}$ by means of uniform rope $ABC$ of length $2 \mathrm{m}$ and mass $1 \mathrm{kg}$. As the load falls from $BC=0$ to $BC=2 \mathrm{m}$. its acceleration in $\mathrm{m} {\mathrm{s}}^{-2}$ changes