A stone tide 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,…

A stone tide 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 $\displaystyle u$. The magnitude of change in its velocity, as it reaches a position where the string is horizontal, is $\displaystyle \sqrt{x\left(u^2-g L\right)}$. The value of $\displaystyle x$ is-