$A$ 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 $;mgl$)?

$A$ sphere is suspended by a thread of length $l$. What minimum horizontal velocity has to be imparted to the ball for it to reach the height of the suspension point?

$A$ simple pendulum has a length of $75 \, cm$. It describes a vertical semi-circle. What will be the velocity of the bob when it passes through the mean position?

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

The maximum value attained by the tension in the string of a swinging pendulum is four times the minimum value it attains. There is no slack in the string. The angular amplitude of the pendulum is (in $^{\circ}$)

$A$ ball of mass $2 \,g$ released from the top of an inclined plane describes a circular motion of radius $20 \,cm$ in the vertical plane upon reaching the bottom. The minimum height of the inclined plane is (in $\,cm$)