$A$ stone of mass $m$ is moving in a vertical circle of radius $20 \ cm$. What is the difference in kinetic energy between the lowest and highest points?

$A$ small bob tied at one end of a thin string of length $1\, m$ is describing a vertical circle so that the maximum and minimum tension in the string are in the ratio $5: 1$. The velocity of the bob at the highest position is ............. $m/s$ (Take $g=10\, m/s^2$).

The bob of a simple pendulum is of mass $10 \, g$. It is suspended with a thread of $1 \, m$. If we hold the bob so as to stretch the string horizontally and release it,what will be the tension at the lowest position? (Take $g = 10 \, m/s^2$)

$A$ 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? $(g = 10 \, m/s^2)$

$A$ car starts from rest at height $H$ and moves along a track to complete a vertical loop of radius $r$. If the car just completes the loop,find the ratio $H/h$,where $h$ is the height of the loop above the starting point of the loop track.

$A$ 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: