$A$ 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:

$A$ stone of mass $1 \ kg$ tied to a light inextensible string of length $L = \frac{5}{3} \ m$ is rotating in a circular path of radius $L$ in a vertical plane. If the ratio of maximum tension in the string to the minimum tension in the string is $3$,the speed of the stone at the highest point of the circle is ($g =$ acceleration due to gravity).

$A$ $2 \, kg$ stone at the end of a string $1 \, m$ long is whirled in a vertical circle at a constant speed. The speed of the stone is $4 \, ms^{-1}$. The tension in the string will be $52 \, N$ when the stone is

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 $^{\circ}$)

$A$ bucket filled with water is tied to a string of length $4 \ m$ and rotated in a vertical circle. To ensure that the water does not spill,the time period of rotation should be ........ $s$.

$A$ $1\, kg$ stone at the end of a $1\, m$ long string is whirled in a vertical circle at a constant speed of $4\, m/s$. The tension in the string is $6\, N$ when the stone is at $(g = 10\, m/s^2)$.