$A$ 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:

$A$ body tied to a string of length $L$ is revolved in a vertical circle with minimum velocity. When the body reaches the uppermost point,the string breaks and the body moves under the influence of the gravitational field of the Earth along a parabolic path. The horizontal range $AC$ of the body will be

$A$ stone of mass $m$ is tied to a string and is moved in a vertical circle of radius $r$ making $n$ revolutions per minute. The total tension in the string when the stone is at its lowest point is

$A$ bob of mass $m$ is suspended at a point $O$ by a light string of length $l$ and is set to perform vertical circular motion as shown in the figure. Initially,by applying a horizontal velocity $v_0$ at point $A$,the string becomes slack when the bob reaches point $D$. The ratio of the kinetic energy of the bob at points $B$ and $C$ is:

$A$ stone tied to a string is rotated in a vertical circle. The minimum speed with which the string has to be rotated at the lowest point is:

$A$ small body of mass $m$ slides down from the top of a hemisphere of radius $r$. The surfaces of the block and the hemisphere are frictionless. The height at which the body loses contact with the surface of the sphere is