$A$ body crosses the topmost point of a vertical circle with critical speed. Its centripetal acceleration,when the string is horizontal,will be

$A$ bucket containing water is revolved in a vertical circle of radius $r$. To prevent the water from falling down,the minimum frequency of revolution required is ($g =$ acceleration due to gravity).

$A$ particle originally at rest at the highest point of a smooth vertical circle is slightly displaced. It will leave the circle at a vertical distance $h$ below the highest point,such that

$A$ 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 $g = 10 \ m/s^2$]

$A$ mass is performing vertical circular motion (see figure). If the average velocity of the particle is increased,then at which point will the string break?

$A$ mass $m$ is attached to a thin wire and whirled in a vertical circle. The wire is most likely to break when