If a particle completes a vertical circular motion,what is the ratio of its velocities at points $A$,$B$,and $C$?

In the case of vertical circular motion of a particle attached to a thread of length $r$, if the tension in the thread is zero at an angle of $30^{\circ}$ with the horizontal as shown in the figure, the velocity at the bottom point $(A)$ of the circular path is ($g =$ gravitational acceleration).

$A$ bullet of mass $m$ strikes a pendulum-bob of mass $M$ with velocity $u$. It passes through it and emerges out with a velocity $u/2$ from the bob. The length of the pendulum is $\ell$. What should be the minimum value of $u$,if the pendulum-bob will swing through a complete circle?

The minimum velocity $v$ required for a simple pendulum to complete one full rotation in a vertical plane is given. If the length of the string is reduced to one-fourth,what will be the new required velocity?

$A$ 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

For a particle moving in a vertical circle,the total energy at different positions along the path: