Two persons are holding a rope of negligible weight tightly at its ends so that it is horizontal. A $15 \mathrm{kg}$ weight is attached to the rope at the midpoint which now no longer remains horizontal. The minimum tension required to completely straighten the rope 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 shown figure, acceleration of mass $M$ is

If points $1$ and $2$ both are acceleration with acceleration a downward, mass $M$ will move with

The ratio of magnitudes of acceleration of $A$ and $B$ is

In the arrangement shown in the 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 ratio of magnitudes of acceleration of $A$ and $B$ is 

In the figure shown, the pulley is moving with velocity $u$. The velocity of the block attached with string

The velocity of end $A$ of rigid rod placed between two smooth vertical walls moves with velocity $u$ along vertical direction. The velocity of end $B$ of that rod, rod always remains in contact with the vertical walls.