$A$ frictionless track $ABCDE$ ends in a circular loop of radius $R$. $A$ body slides down the track from point $A$ which is at a height $h = 5\, cm$. The maximum value of $R$ for the body to successfully complete the loop is ........... $cm$.

$A$ stone of mass $1 \ kg$ is tied to a string $2 \ m$ long and is rotated at a constant speed of $40 \ ms^{-1}$ in a vertical circle. The ratio of the tension at the top and the bottom is [Take $g = 10 \ ms^{-2}$].

$A$ body of mass $m$ is tied to a string of length $l$ and rotated in a vertical circle. What is the difference in tension between the lowest point and the highest point (in $,mg$)?

$A$ 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

$A$ stone of mass $40$ g is tied to a light inextensible string of length $50$ cm and whirled in a vertical circle at the rate of $30$ revolutions per minute. The tension in the string when it is at the lowest point of the circle is (Take gravitational acceleration, $g = 10 \text{ m/s}^2$ and $\pi^2 = 10$) (in $N$)

$A$ can filled with water is revolved in a vertical circle of radius $r$ with constant speed such that the water just does not fall out. The time period of revolution is ($g=$ acceleration due to gravity).