Two persons are holding a light rope tightly at its ends so that it is horizontal. A $15 \mathrm{kg}$ weight is attached to the rope at the mid point which now no longer remains horizontal. The minimum tension required to completely straighten the rope is 

In the system shown in the figure, the acceleration of the $1 \mathrm{kg}$ mass and the tension in the string connecting between $A$ and $B$ is:

A body of mass $8 \mathrm{kg}$ is hanging from another body of mass $12 \mathrm{kg}$. The combination is being pulled by a string with an acceleration of $2.2 \mathrm{m} {\mathrm{s}}^{–2}$. The tension $T_1$ and $T_2$ will be respectively: (use $g=9.8 \mathrm{m} {\mathrm{s}}^{-2}$)

A heavy block kept on a frictionless surface and being pulled by two ropes of equal mass $m$ as shown in figure. At $t=0$, the force on the left rope is withdrawn but the force on the right end continues to act. Let $F_1$ and $F_2$ be the magnitudes of the forces by the right rope and the left rope on the block, respectively.

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

Two masses are connected by a string which passes over a pulley accelerating upward at a rate $A$ as shown. If $a_1$ and $a_2$ be the acceleration of bodies $1$ and $2$, respectively, then:

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.

A system is shown in the figure. A man standing on the block is pulling the rope. Velocity of the point of string in contact with the hand of the man is $2 \mathrm{m} {\mathrm{s}}^{-1}$ downwards. The velocity of the block will be: [Assume that the block does not rotate]