What is the minimum velocity at the lowest point of a vertical circle of radius $l$ such that the string just becomes slack at the highest point?

$A$ stone of mass $m$ $kg$ is tied to a string of length $L$ $m$ and moved in a vertical circle of radius $49$ $cm$ in a vertical plane. If it completes $30$ revolutions per minute,the tension in the string when it is at the lowermost point is nearly. [Take $\pi^2=10$ and acceleration due to gravity,$g=10$ $m/s^2$]

$A$ bucket filled with water is tied to a string of length $1.6 \, m$ and rotated in a vertical circle. What should be the minimum velocity at the highest point so that the water does not spill? $(g = 10 \, m/s^2)$

$A$ bucket containing water is revolved in a vertical circle of radius $r$. To prevent the water from falling down, the period of revolution required is ($g =$ gravitational acceleration)

$A$ stone is tied to a string of length $L$ and is whirled in a vertical circle with the other end of the string at the centre. At a certain instant of time, the stone is at its lowest position and has a speed $u$. The magnitude of the change in its velocity as it reaches a position where the string is horizontal is

$A$ weightless thread can bear a tension of up to $3.7 \, kg \, wt$. $A$ stone of mass $500 \, g$ is tied to it and revolved in a circular path of radius $4 \, m$ in a vertical plane. If $g = 10 \, m/s^2$,then the maximum angular velocity of the stone will be ........ $rad/s$.