Length of a simple pendulum is $1 \,m$. When its bob is at its lowest point its velocity is $7 \,ms^{-1}$. If the bob leaves its circular path at a height $h$ above the centre of the circle, then the value of $h$ is $(g=10 \,ms^{-2})$. (in $\,m$)

$A$ stone tied to a string of length $L$ 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

$A$ bucket tied at the end of a $1.6\, m$ long string is whirled in a vertical circle with constant speed. What should be the minimum speed so that the water from the bucket does not spill,when the bucket is at the highest position? (Take $g = 10\, m/s^2$)

$A$ stone of mass $2 \,kg$ tied to a light inextensible string of length $\frac{5}{3} \,m$ is whirling in a circular path in a vertical plane. If the ratio of the maximum tension to the minimum tension in the string is $4$, then the speed of the stone at the highest point of the circle is $\left(g=10 \,ms^{-2}\right)$.

$A$ body slides down a frictionless track which ends in a circular loop of diameter $D$. The minimum height $h$ of the body in terms of $D$ so that it may just complete the loop is:

You may have seen in a circus a motorcyclist driving in vertical loops inside a 'death well' (a hollow spherical chamber with holes,so the spectators can watch from outside). Explain clearly why the motorcyclist does not drop down when he is at the uppermost point,with no support from below. What is the minimum speed required at the uppermost position to perform a vertical loop if the radius of the chamber is $25 \; m$?