The given figure shows two blocks each of mass $m$. The system is released from rest. If accelerations of blocks $A$ and $B$ at any instant (not initially) are $a_1$ and $a_2$, respectively, then
  

In order to raise a mass of $100 \mathrm{kg}$, a man of mass $60 \mathrm{kg}$ fastens a rope to it and passes the rope over a smooth pulley. He climbs the rope with acceleration $5g/4$ relative to the rope. The tension in the rope is (take $g=10 \mathrm{m} {\mathrm{s}}^{-2}$)

The system shown in the figure is released from rest. The spring gets elongated

(Neglect the friction and masses of pulley, string and spring.)
 

A man is raising himself as well as the crate on which he stands with an acceleration of $5 \mathrm{m} {\mathrm{s}}^{-2}$ by a massless rope-and-pulley arrangement. Mass of the man is $100 \mathrm{kg}$ and that of the crate is $50 \mathrm{kg}$. If $g=10 \mathrm{m} {\mathrm{s}}^{-2}$, then the tension in the rope is