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

$A$ stone tied to a string of length $L$ is whirled in a vertical circle with the other end of the string at the centre. At a certain instant of time, the stone is at its lowest position and has a speed $u$. The magnitude of the change in its velocity, as it reaches a position where the string is horizontal, is $\sqrt{x(u^{2}-gL)}$. The value of $x$ is .............

$A$ point mass '$m$' is moved in a vertical circle of radius '$r$' with the help of a string. The velocity of the mass is $\sqrt{7gr}$ at the lowest point. The tension in the string at the lowest point is .......... $mg$.

$A$ stone of mass $1 \ kg$ is tied to one end of a light string and is whirled in a vertical circle as shown in the figure. The tension in the string when the string becomes horizontal is ......... $N$.

$A$ particle attached to a string of length $r$ is moving in a vertical circular path. If the speed of the particle at the highest point is $\sqrt{7gr}$,then the ratio of the tension in the string at the highest point to the tension at the lowest point is ($g=$ acceleration due to gravity).

$A$ small bob tied at one end of a thin string of length $1\, m$ is describing a vertical circle so that the maximum and minimum tension in the string are in the ratio $5: 1$. The velocity of the bob at the highest position is ............. $m/s$ (Take $g=10\, m/s^2$).