For a particle moving in a vertical circle,the total energy at different positions along the path (the motion is under gravity) is:

What is the minimum velocity with which a body of mass $m$ must enter a vertical loop of radius $R$ so that it can complete the loop $?$

$A$ particle is tied to a $20 \ cm$ long string. It performs circular motion in a vertical plane. What is the angular speed of the particle when the tension in the string at the top is zero? (Take $g = 9.8 \ m/s^2$)

$A$ body initially at rest and sliding along a frictionless track from a height $h$ (as shown in the figure) just completes a vertical circle of diameter $AB = D$. The height $h$ is equal to

$A$ bob of mass $m$ is tied to a string of length $l$. What is the minimum kinetic energy that must be provided to the bob at the lowest point so that it completes a full vertical circle (in $;mgl$)?

$A$ body of mass $2 \, kg$ is tied to a string of length $2 \, m$ and rotated in a vertical circle. What is the difference between the maximum and minimum kinetic energy in $J$?