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
√2(u2−2gL)
Now, since the two velocity vectors shown in Fig. 8.296 are mutually perpendicular, the magnitude of change of velocity will be given by
|Δ→v|=√u2+v2
Substituting the value of v2 from Eq. (i),
|Δ→v|=√u2+u2−2gL=√2(u2−gL)