A particle is suspended vertically from a point O by an inextensible mass less string of length L. A vertical line AB is at a distance of `L/8` from O as shown in figure. The particle is given a horizontal velocity u. At some point, its motion ceases to be circular and eventually the object passes through the line AB. At the instant of crossing AB, its velocity is horizontal. Find u.

Answer

`sqrt(gL(2+(3sqrt(3))/2))`