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 $?$

$A$ body of mass $m$ slides down along a frictionless inclined plane from height $h$ and just completes motion in a vertical circle of radius $R = 2 \ m$ after reaching the bottom. What is the value of $h$? [Use $g = 10 \ m/s^2$]

$A$ 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?

$A$ stone of mass $m$ $kg$ is tied to a string of length $L$ $m$ and moved in a vertical circle of radius $49$ $cm$ in a vertical plane. If it completes $30$ revolutions per minute,the tension in the string when it is at the lowermost point is nearly. [Take $\pi^2=10$ and acceleration due to gravity,$g=10$ $m/s^2$]

In order to just complete the vertical circular motion,the ratio of kinetic energy of a particle at the highest point to that at the lowest point is

$A$ particle of mass $m$ is tied to a string of length $l$ and whirled in a vertical circle. The difference in tension and kinetic energy at the highest and lowest positions of the circular path will be: